• Home   /  
  • Archive by category "1"

Mttr Analysis Essay

Reliability engineering is a sub-discipline of systems engineering that emphasizes dependability in the lifecycle management of a product. Dependability, or reliability, describes the ability of a system or component to function under stated conditions for a specified period of time.[1] Reliability is closely related to availability, which is typically described as the ability of a component or system to function at a specified moment or interval of time.

Reliability is theoretically defined as the probability of success as the frequency of failures; or in terms of availability, as a probability derived from reliability, testability and maintainability. Testability, maintainability and maintenance are often defined as a part of "reliability engineering" in Reliability Programs. Reliability plays a key role in the cost-effectiveness of systems.

Reliability engineering deals with the estimation, prevention and management of high levels of "lifetime" engineering uncertainty and risks of failure. Although stochastic parameters define and affect reliability, reliability is not (solely) achieved by mathematics and statistics.[2][3] You cannot really find a root cause (needed to effectively prevent failures) by only looking at statistics. "Nearly all teaching and literature on the subject emphasize these aspects, and ignore the reality that the ranges of uncertainty involved largely invalidate quantitative methods for prediction and measurement."[4] For example, it is easy to represent "probability of failure" as a symbol or value in an equation, but it is almost impossible to predict its true magnitude in practice, which is massively multivariate, so having the equation for reliability does not begin to equal having an accurate predictive measurement of reliability.

Reliability engineering relates closely to safety engineering and to system safety, in that they use common methods for their analysis and may require input from each other. Reliability engineering focuses on costs of failure caused by system downtime, cost of spares, repair equipment, personnel, and cost of warranty claims. Safety engineering normally focuses more on preserving life and nature than on cost, and therefore deals only with particularly dangerous system-failure modes. High reliability (safety factor) levels also result from good engineering and from attention to detail, and almost never from only reactive failure management (using reliability accounting and statistics).[5]

History[edit]

The word reliability can be traced back to 1816, and is first attested to the poet Samuel Taylor Coleridge.[6] Before World War II the term was linked mostly to repeatability; a test (in any type of science) was considered "reliable" if the same results would be obtained repeatedly. In the 1920s product improvement through the use of statistical process control was promoted by Dr. Walter A. Shewhart at Bell Labs,[7] around the time that Waloddi Weibull was working on statistical models for fatigue. The development of reliability engineering was here on a parallel path with quality. The modern use of the word reliability was defined by the U.S. military in the 1940s, characterizing a product that would operate when expected and for a specified period of time.

In World War II, many reliability issues were due to the inherent unreliability of electronic equipment available at the time, and to fatigue issues. In 1945, M.A. Miner published the seminal paper titled "Cumulative Damage in Fatigue" in an ASME journal. A main application for reliability engineering in the military was for the vacuum tube as used in radar systems and other electronics, for which reliability proved to be very problematic and costly. The IEEE formed the Reliability Society in 1948. In 1950, the United States Department of Defense formed group called the "Advisory Group on the Reliability of Electronic Equipment" (AGREE) to investigate reliability methods for military equipment.[8] This group recommended the following 3 main ways of working:

  1. Improve component reliability;
  2. Establish quality and reliability requirements for suppliers;
  3. Collect field data and find root causes of failures.

In the 1960s more emphasis was given to reliability testing on component and system level. The famous military standard 781 was created at that time.[citation needed] Around this period also the much-used (and also much-debated) military handbook 217 was published by RCA (Radio Corporation of America) and was used for the prediction of failure rates of components. The emphasis on component reliability and empirical research (e.g. Mil Std 217) alone slowly decreases. More pragmatic approaches, as used in the consumer industries, are being used. In the 1980s, televisions were increasingly made up of solid-state semiconductors. Automobiles rapidly increased their use of semiconductors with a variety of microcomputers under the hood and in the dash. Large air conditioning systems developed electronic controllers, as had microwave ovens and a variety of other appliances. Communications systems began to adopt electronics to replace older mechanical switching systems. Bellcore issued the first consumer prediction methodology for telecommunications, and SAE developed a similar document SAE870050 for automotive applications. The nature of predictions evolved during the decade, and it became apparent that die complexity wasn't the only factor that determined failure rates for Integrated Circuits (ICs). Kam Wong published a paper questioning the bathtub curve[9]—see also reliability-centered maintenance. During this decade, the failure rate of many components dropped by a factor of 10. Software became important to the reliability of systems. By the 1990s, the pace of IC development was picking up. Wider use of stand-alone microcomputers was common, and the PC market helped keep IC densities following Moore's law and doubling about every 18 months. Reliability engineering now was more changing towards understanding the physics of failure. Failure rates for components kept on dropping, but system-level issues became more prominent. Systems thinking became more and more important. For software, the CCM model (Capability Maturity Model) was developed, which gave a more qualitative approach to reliability. ISO 9000 added reliability measures as part of the design and development portion of Certification. The expansion of the World-Wide Web created new challenges of security and trust. The older problem of too little reliability information available had now been replaced by too much information of questionable value. Consumer reliability problems could now have data and be discussed online in real time. New technologies such as micro-electromechanical systems (MEMS), handheld GPS, and hand-held devices that combined cell phones and computers all represent challenges to maintain reliability. Product development time continued to shorten through this decade and what had been done in three years was being done in 18 months. This meant that reliability tools and tasks must be more closely tied to the development process itself. In many ways, reliability became part of everyday life and consumer expectations.

Overview[edit]

Objective[edit]

The objectives of reliability engineering, in decreasing order of priority, are:[10]

  1. To apply engineering knowledge and specialist techniques to prevent or to reduce the likelihood or frequency of failures.
  2. To identify and correct the causes of failures that do occur despite the efforts to prevent them.
  3. To determine ways of coping with failures that do occur, if their causes have not been corrected.
  4. To apply methods for estimating the likely reliability of new designs, and for analysing reliability data.

The reason for the priority emphasis is that it is by far the most effective way of working, in terms of minimizing costs and generating reliable products. The primary skills that are required, therefore, are the ability to understand and anticipate the possible causes of failures, and knowledge of how to prevent them. It is also necessary to have knowledge of the methods that can be used for analysing designs and data.

Scope and techniques[edit]

Reliability engineering for "complex systems" requires a different, more elaborate systems approach than for non-complex systems. Reliability engineering may in that case involve:

  • System availability and mission readiness analysis and related reliability and maintenance requirement allocation
  • Functional system failure analysis and derived requirements specification
  • Inherent (system) Design Reliability Analysis and derived requirements specification for both Hardware and Software design
  • System Diagnostics design
  • Fault tolerant systems (e.g. by redundancy)
  • Predictive and preventive maintenance (e.g. reliability-centered maintenance)
  • Human factors / Human interaction / Human errors
  • Manufacturing- and Assembly-induced failures (effect on the detected "0-hour Quality" and reliability)
  • Maintenance-induced failures
  • Transport-induced failures
  • Storage-induced failures
  • Use (load) studies, component stress analysis, and derived requirements specification
  • Software (systematic) failures
  • Failure / reliability testing (and derived requirements)
  • Field failure monitoring and corrective actions
  • Spare parts stocking (availability control)
  • Technical documentation, caution and warning analysis
  • Data and information acquisition/organisation (creation of a general reliability development Hazard Log and FRACAS system)
  • Chaos Engineering

Effective reliability engineering requires understanding of the basics of failure mechanisms for which experience, broad engineering skills and good knowledge from many different special fields of engineering,[11] for example:

Definitions[edit]

Reliability may be defined in the following ways:

  • The idea that an item is fit for a purpose with respect to time
  • The capacity of a designed, produced, or maintained item to perform as required over time
  • The capacity of a population of designed, produced or maintained items to perform as required over specified time
  • The resistance to failure of an item over time
  • The probability of an item to perform a required function under stated conditions for a specified period of time
  • The durability of an object.

Basics of a reliability assessment[edit]

Many engineering techniques are used in reliability risk assessments, such as reliability hazard analysis, failure mode and effects analysis (FMEA),[12]fault tree analysis (FTA), Reliability Centered Maintenance, (probabilistic) load and material stress and wear calculations, (probabilistic) fatigue and creep analysis, human error analysis, manufacturing defect analysis, reliability testing, etc. It is crucial that these analysis are done properly and with much attention to detail to be effective. Because of the large number of reliability techniques, their expense, and the varying degrees of reliability required for different situations, most projects develop a reliability program plan to specify the reliability tasks (statement of work (SoW) requirements) that will be performed for that specific system.

Consistent with the creation of a safety cases, for example ARP4761, the goal of reliability assessments is to provide a robust set of qualitative and quantitative evidence that use of a component or system will not be associated with unacceptable risk. The basic steps to take[13] are to:

  • First thoroughly identify relevant unreliability "hazards", e.g. potential conditions, events, human errors, failure modes, interactions, failure mechanisms and root causes, by specific analysis or tests
  • Assess the associated system risk, by specific analysis or testing
  • Propose mitigation, e.g. requirements, design changes, detection logic, maintenance, training, by which the risks may be lowered and controlled for at an acceptable level.
  • Determine the best mitigation and get agreement on final, acceptable risk levels, possibly based on cost/benefit analysis

Risk is here the combination of probability and severity of the failure incident (scenario) occurring.

In a de minimis definition, severity of failures include the cost of spare parts, man-hours, logistics, damage (secondary failures), and downtime of machines which may cause production loss. A more complete definition of failure also can mean injury, dismemberment, and death of people within the system (witness mine accidents, industrial accidents, space shuttle failures) and the same to innocent bystanders (witness the citizenry of cities like Bhopal, Love Canal, Chernobyl, or Sendai, and other victims of the 2011 Tōhoku earthquake and tsunami)—in this case, reliability engineering becomes system safety. What is acceptable is determined by the managing authority or customers or the affected communities. Residual risk is the risk that is left over after all reliability activities have finished, and includes the un-identified risk—and is therefore not completely quantifiable.

The complexity of the technical systems such as Improvements of Design and Materials, Planned Inspections, Fool-proof design, and Backup Redundancy decreases risk and increases the cost. The risk can be decreased to ALARA (as low as reasonably achievable) or ALAPA (as low as practically achievable) levels.

Reliability and availability program plan[edit]

Implementing a reliability program is not simply a software purchase; it's not just a checklist of items that must be completed that will ensure you have reliable products and processes. A reliability program is a complex learning and knowledge-based system unique to your products and processes. It is supported by leadership, built on the skills that you develop within your team, integrated into your business processes and executed by following proven standard work practices. [15]

A reliability program plan is used to document exactly what "best practices" (tasks, methods, tools, analysis, and tests) are required for a particular (sub)system, as well as clarify customer requirements for reliability assessment. For large-scale complex systems, the reliability program plan should be a separate document. Resource determination for manpower and budgets for testing and other tasks is critical for a successful program. In general, the amount of work required for an effective program for complex systems is large.

A reliability program plan is essential for achieving high levels of reliability, testability, maintainability, and the resulting system Availability, and is developed early during system development and refined over the system's life-cycle. It specifies not only what the reliability engineer does, but also the tasks performed by other stakeholders. A reliability program plan is approved by top program Management, which is responsible for allocation of sufficient resources for its implementation.

A reliability program plan may also be used to evaluate and improve availability of a system by the strategy of focusing on increasing testability & maintainability and not on reliability. Improving maintainability is generally easier than improving reliability. Maintainability estimates (repair rates) are also generally more accurate. However, because the uncertainties in the reliability estimates are in most cases very large, they are likely to dominate the availability calculation (prediction uncertainty problem), even when maintainability levels are very high. When reliability is not under control, more complicated issues may arise, like manpower (maintainers / customer service capability) shortages, spare part availability, logistic delays, lack of repair facilities, extensive retro-fit and complex configuration management costs, and others. The problem of unreliability may be increased also due to the "domino effect" of maintenance-induced failures after repairs. Focusing only on maintainability is therefore not enough. If failures are prevented, none of the other issues are of any importance, and therefore reliability is generally regarded as the most important part of availability. Reliability needs to be evaluated and improved related to both availability and the Total Cost of Ownership (TCO) due to cost of spare parts, maintenance man-hours, transport costs, storage cost, part obsolete risks, etc. But, as GM and Toyota have belatedly discovered, TCO also includes the downstream liability costs when reliability calculations have not sufficiently or accurately addressed customers' personal bodily risks. Often a trade-off is needed between the two. There might be a maximum ratio between availability and cost of ownership. Testability of a system should also be addressed in the plan, as this is the link between reliability and maintainability. The maintenance strategy can influence the reliability of a system (e.g., by preventive and/or predictive maintenance), although it can never bring it above the inherent reliability.

The reliability plan should clearly provide a strategy for availability control. Whether only availability or also cost of ownership is more important depends on the use of the system. For example, a system that is a critical link in a production system—e.g., a big oil platform—is normally allowed to have a very high cost of ownership if that cost translates to even a minor increase in availability, as the unavailability of the platform results in a massive loss of revenue which can easily exceed the high cost of ownership. A proper reliability plan should always address RAMT analysis in its total context. RAMT stands for Reliability, Availability, Maintainability/Maintenance, and Testability in context to the customer needs.

Reliability requirements[edit]

For any system, one of the first tasks of reliability engineering is to adequately specify the reliability and maintainability requirements allocated from the overall availability needs and, more importantly, derived from proper design failure analysis or preliminary prototype test results. Clear requirements (able to designed to) should constrain the designers from designing particular unreliable items / constructions / interfaces / systems. Setting only availability, reliability, testability, or maintainability targets (e.g., max. failure rates) is not appropriate. This is a broad misunderstanding about Reliability Requirements Engineering. Reliability requirements address the system itself, including test and assessment requirements, and associated tasks and documentation. Reliability requirements are included in the appropriate system or subsystem requirements specifications, test plans, and contract statements. Creation of proper lower-level requirements is critical.[16] Provision of only quantitative minimum targets (e.g., MTBF values or failure rates) is not sufficient for different reasons. One reason is that a full validation (related to correctness and verifiability in time) of a quantitative reliability allocation (requirement spec) on lower levels for complex systems can (often) not be made as a consequence of (1) the fact that the requirements are probabilistic, (2) the extremely high level of uncertainties involved for showing compliance with all these probabilistic requirements, and because (3) reliability is a function of time, and accurate estimates of a (probabilistic) reliability number per item are available only very late in the project, sometimes even after many years of in-service use. Compare this problem with the continuous (re-)balancing of, for example, lower-level-system mass requirements in the development of an aircraft, which is already often a big undertaking. Notice that in this case masses do only differ in terms of only some %, are not a function of time, the data is non-probabilistic and available already in CAD models. In case of reliability, the levels of unreliability (failure rates) may change with factors of decades (multiples of 10) as result of very minor deviations in design, process, or anything else.[17] The information is often not available without huge uncertainties within the development phase. This makes this allocation problem almost impossible to do in a useful, practical, valid manner that does not result in massive over- or under-specification. A pragmatic approach is therefore needed—for example: the use of general levels / classes of quantitative requirements depending only on severity of failure effects. Also, the validation of results is a far more subjective task than for any other type of requirement. (Quantitative) reliability parameters—in terms of MTBF—are by far the most uncertain design parameters in any design.

Furthermore, reliability design requirements should drive a (system or part) design to incorporate features that prevent failures from occurring, or limit consequences from failure in the first place. Not only would it aid in some predictions, this effort would keep from distracting the engineering effort into a kind of accounting work. A design requirement should be precise enough so that a designer can "design to" it and can also prove—through analysis or testing—that the requirement has been achieved, and, if possible, within some a stated confidence. Any type of reliability requirement should be detailed and could be derived from failure analysis (Finite-Element Stress and Fatigue analysis, Reliability Hazard Analysis, FTA, FMEA, Human Factor Analysis, Functional Hazard Analysis, etc.) or any type of reliability testing. Also, requirements are needed for verification tests (e.g., required overload stresses) and test time needed. To derive these requirements in an effective manner, a systems engineering-based risk assessment and mitigation logic should be used. Robust hazard log systems must be created that contain detailed information on why and how systems could or have failed. Requirements are to be derived and tracked in this way. These practical design requirements shall drive the design and not be used only for verification purposes. These requirements (often design constraints) are in this way derived from failure analysis or preliminary tests. Understanding of this difference compared to only purely quantitative (logistic) requirement specification (e.g., Failure Rate / MTBF target) is paramount in the development of successful (complex) systems.[18]

The maintainability requirements address the costs of repairs as well as repair time. Testability (not to be confused with test requirements) requirements provide the link between reliability and maintainability and should address detectability of failure modes (on a particular system level), isolation levels, and the creation of diagnostics (procedures). As indicated above, reliability engineers should also address requirements for various reliability tasks and documentation during system development, testing, production, and operation. These requirements are generally specified in the contract statement of work and depend on how much leeway the customer wishes to provide to the contractor. Reliability tasks include various analyses, planning, and failure reporting. Task selection depends on the criticality of the system as well as cost. A safety-critical system may require a formal failure reporting and review process throughout development, whereas a non-critical system may rely on final test reports. The most common reliability program tasks are documented in reliability program standards, such as MIL-STD-785 and IEEE 1332. Failure reporting analysis and corrective action systems are a common approach for product/process reliability monitoring.

Reliability culture / human errors / human factors[edit]

In practice, most failures can be traced back to some type of human error, for example in:

  • Management decisions (e.g. in budgeting, timing, and required tasks)
  • Systems Engineering: Use studies (load cases)
  • Systems Engineering: Requirement analysis / setting
  • Systems Engineering: Configuration control
  • Assumptions
  • Calculations / simulations / FEM analysis
  • Design
  • Design drawings
  • Testing (e.g. incorrect load settings or failure measurement)
  • Statistical analysis
  • Manufacturing
  • Quality control
  • Maintenance
  • Maintenance manuals
  • Training
  • Classifying and Ordering of information
  • Feedback of field information (e.g. incorrect or too vague)
  • etc.

However, humans are also very good at detecting such failures, correcting for them, and improvising when abnormal situations occur. Thererfore policies that completely rule out human actions in design and production processes to improve reliability may not be effective. Some tasks are better performed by humans and some are better performed by machines.[19]

Furthermore, human errors in management; the organization of data and information; or the misuse or abuse of items, may also contribute to unreliability. This is the core reason why high levels of reliability for complex systems can only be achieved by following a robust systems engineering process with proper planning and execution of the validation and verification tasks. This also includes careful organization of data and information sharing and creating a "reliability culture", in the same way that having a "safety culture" is paramount in the development of safety critical systems.

Reliability prediction and improvement[edit]

See also: Risk Assessment § Quantitative risk assessment

Reliability prediction combines:

  • creation of a proper reliability model (see further on this page)
  • estimation (and justification) of input parameters for this model (e.g. failure rates for a particular failure mode or event and the mean time to repair the system for a particular failure)
  • estimation of output reliability parameters at system or part level (i.e. system availability or frequency of a particular functional failure)

Some recognized reliability engineering specialists (e.g. Patrick O'Connor, R. Barnard) have argued that too much emphasis is often given to the prediction of reliability parameters, instead more effort should be devoted to the prevention of failure (reliability improvement).[4] Failures can and should be prevented in the first place for most cases. The emphasis on quantification and target setting (e.g. MTBF) might imply there is a limit to achievable reliability, however there is no inherent limit and development of higher reliability does not need to be more costly. In addition they argue that prediction of reliability from historic data can be very misleading, with comparisons only valid for identical designs, products, manufacturing processes, and maintenance with identical operating loads and usage environments. Even minor changes in any of these could have major effects on reliability. Furthermore, the most unreliable and important items (i.e. the most interesting candidates for a reliability investigation) are most likely to be modified and re-engineered since historical data was gathered, making the standard (re-active or pro-active) statistical methods and processes used in e.g. medical or insurance industries less effective. Another surprising — but logical — argument is that to be able to accurately predict reliability by testing, the exact mechanisms of failure must be known and therefore — in most cases — could be prevented! Following the incorrect route of trying to quantify and solve a complex reliability engineering problem in terms of MTBF or probability using an-incorrect – for example, the re-active – approach is referred to by Barnard as "Playing the Numbers Game" and is regarded as bad practice.[5]

For existing systems, it is arguable that any attempt by a responsible programs to correct the root cause of discovered failures may render the initial MTBF estimate invalid, as new assumptions (themselves subject to high error levels) of the effect of this correction must be made. Another practical issue is the general un-availability of detailed failure data, with those available often featuring inconsistent filtering of failure (feedback) data, and ignoring statistical errors (which are very high for rare events like reliability related failures). Very clear guidelines must be present to count and compare failures related to different type of root-causes (e.g. manufacturing-, maintenance-, transport-, system-induced or inherent design failures). Comparing different types of causes may lead to incorrect estimations and incorrect business decisions about the focus of improvement.

To perform a proper quantitative reliability prediction for systems may be difficult and very expensive if done by testing. At the individual part-level, reliability results can often be obtained with comparatively high confidence, as testing of many sample parts might be possible using the available testing budget. However, unfortunately these tests may lack validity at a system-level due to assumptions made at part-level testing. These authors emphasized the importance of initial part- or system-level testing until failure, and to learn from such failures to improve the system or part. The general conclusion is drawn that an accurate and absolute prediction — by either field-data comparison or testing — of reliability is in most cases not possible. An exception might be failures due to wear-out problems such as fatigue failures. In the introduction of MIL-STD-785 it is written that reliability prediction should be used with great caution, if not used solely for comparison in trade-off studies.

Design for reliability[edit]

Design for Reliability (DfR) is a process that encompasses tools and procedures to ensure that a product meets its reliability requirements, under its use environment, for the duration of its lifetime. DfR is implemented in the design stage of a product to proactively improve product reliability.[20] DfR is often used as part of an overall Design for Excellence (DfX) strategy.

Statistics Based Approach (i.e. MTBF)[edit]

Reliability design begins with the development of a (system) model. Reliability and availability models use block diagrams and Fault Tree Analysis to provide a graphical means of evaluating the relationships between different parts of the system. These models may incorporate predictions based on failure rates taken from historical data. While the (input data) predictions are often not accurate in an absolute sense, they are valuable to assess relative differences in design alternatives. Maintainability parameters, for example Mean time to repair (MTTR), can also be used as inputs for such models.

The most important fundamental initiating causes and failure mechanisms are to be identified and analyzed with engineering tools. A diverse set of practical guidance as to performance and reliability should be provided to designers so that they can generate low-stressed designs and products that protect, or are protected against, damage and excessive wear. Proper validation of input loads (requirements) may be needed, in addition to verification for reliability "performance" by testing.

One of the most important design techniques is redundancy. This means that if one part of the system fails, there is an alternate success path, such as a backup system. The reason why this is the ultimate design choice is related to the fact that high-confidence reliability evidence for new parts or systems is often not available, or is extremely expensive to obtain. By combining redundancy, together with a high level of failure monitoring, and the avoidance of common cause failures; even a system with relatively poor single-channel (part) reliability, can be made highly reliable at a system level (up to mission critical reliability). No testing of reliability has to be required for this. In conjunction with redundancy, the use of dissimilar designs or manufacturing processes (e.g. via different suppliers of similar parts) for single independent channels, can provide less sensitivity to quality issues (e.g. early childhood failures at a single supplier), allowing very-high levels of reliability to be achieved at all moments of the development cycle (from early life to long-term). Redundancy can also be applied in systems engineering by double checking requirements, data, designs, calculations, software, and tests to overcome systematic failures.

Another effective way to deal with reliability issues is to perform analysis that predicts degradation, enabling the prevention of unscheduled downtime events / failures. RCM (Reliability Centered Maintenance) programs can be used for this.

Physics-of-Failure Based Approach[edit]

For electronic assemblies, there has been an increasing shift towards a different approach called physics of failure. This technique relies on understanding the physical static and dynamic failure mechanisms. It accounts for variation in load, strength, and stress that lead to failure with a high level of detail, made possible with the use of modern finite element method (FEM) software programs that can handle complex geometries and mechanisms such as creep, stress relaxation, fatigue, and probabilistic design (Monte Carlo simulations/DOE). The material or component can be re-designed to reduce the probability of failure and to make it more robust against such variations. Another common design technique is component derating: i.e. selecting components whose specifications significantly exceed the expected stress levels, such as using heavier gauge electrical wire than might normally be specified for the expected electric current.

Common Tools and Techniques[edit]

Many of the tasks, techniques, and analyses used in Reliability Engineering are specific to particular industries and applications, but can commonly include:

Results from these methods are presented during reviews of part or system design, and logistics. Reliability is just one requirement among many for a complex part or system. Engineering trade-off studies are used to determine the optimum balance between reliability requirements and other constraints.

The importance of language[edit]

Reliability engineers, whether using quantitative or qualitative methods to describe a failure or hazard, rely on language to pinpoint the risks and enable issues to be solved. The language used must help create an orderly description of the function/item/system and its complex surrounding as it relates to the failure of these functions/items/systems. Systems engineering is very much about finding the correct words to describe the problem (and related risks), so that they can be readily solved via engineering solutions. Jack Ring said that a systems engineer's job is to "language the project." [Ring et al. 2000].[22] For part/system failures, reliability engineers should concentrate more on the "why and how", rather that predicting "when". Understanding "why" a failure has occurred (e.g. due to over-stressed components or manufacturing issues) is far more likely to lead to improvement in the designs and processes used [4] than quantifying "when" a failure is likely to occur (e.g. via determining MTBF). To do this, first the reliability hazards relating to the part/system need to be classified and ordered (based on some form of qualitative and quantitative logic if possible) to allow for more efficient assessment and eventual improvement. This is partly done in pure language and proposition logic, but also based on experience with similar items. This can for example be seen in descriptions of events in Fault Tree Analysis, FMEA analysis, and hazard (tracking) logs. In this sense language and proper grammar (part of qualitative analysis) plays an important role in reliability engineering, just like it does in safety engineering or in-general within systems engineering.

Correct use of language can also be key to identifying or reducing the risks of human error, which are often the root-cause of many failures. This can include proper instructions in maintenance manuals, operation manuals, emergency procedures, and others to prevent systematic human errors that may result in system failures. These should be written by trained or experienced technical authors using so-called simplified English or Simplified Technical English, where words and structure are specifically chosen and created so as to reduce ambiquity or risk of confusion (e.g. an "replace the old part" could ambiguously refer to a swapping a worn-out part with a non worn-out part, or replacing a part with one using a more recent and hopefully improved design).

Reliability modeling[edit]

Reliability modeling is the process of predicting or understanding the reliability of a component or system prior to its implementation. Two types of analysis that are often used to model a complete system's availability behavior (including effects from logistics issues like spare part provisioning, transport and manpower) are Fault Tree Analysis and reliability block diagrams. At a component level, the same types of analyses can be used together with others. The input for the models can come from many sources including: Testing; prior operational experience; field data; as well as data handbooks from similar or related industries. Regardless of source, all model input data must be used with great caution, as predictions are only valid in cases where the same product was used in the same context. As such, predictions are often only used to help compare alternatives.

For part level predictions, two separate fields of investigation are common:

  • The physics of failure approach uses an understanding of physical failure mechanisms involved, such as mechanical crack propagation or chemical corrosion degradation or failure;
  • The parts stress modeling approach is an empirical method for prediction based on counting the number and type of components of the system, and the stress they undergo during operation.

Software reliability is a more challenging area that must be considered when computer code provides a considerable component of a system's functionality.

Reliability theory[edit]

Main articles: Reliability theory, Failure rate, and Survival analysis

Reliability is defined as the probability that a device will perform its intended function during a specified period of time under stated conditions. Mathematically, this may be expressed as,

,

where is the failure probability density function and is the length of the period of time (which is assumed to start from time zero).

There are a few key elements of this definition:

  1. Reliability is predicated on "intended function:" Generally, this is taken to mean operation without failure. However, even if no individual part of the system fails, but the system as a whole does not do what was intended, then it is still charged against the system reliability. The system requirements specification is the criterion against which reliability is measured.
  2. Reliability applies to a specified period of time. In practical terms, this means that a system has a specified chance that it will operate without failure before time . Reliability engineering ensures that components and materials will meet the requirements during the specified time. Note that units other than time may sometimes be used (e.g. "a mission", "operation cycles").
  3. Reliability is restricted to operation under stated (or explicitly defined) conditions. This constraint is necessary because it is impossible to design a system for unlimited conditions. A Mars Rover will have different specified conditions than a family car. The operating environment must be addressed during design and testing. That same rover may be required to operate in varying conditions requiring additional scrutiny.

Quantitative system reliability parameters—theory[edit]

Quantitative Requirements are specified using reliability parameters. The most common reliability parameter is the mean time to failure (MTTF), which can also be specified as the failure rate (this is expressed as a frequency or conditional probability density function (PDF)) or the number of failures during a given period. These parameters may be useful for higher system levels and systems that are operated frequently (i.e. vehicles, machinery, and electronic equipment). Reliability increases as the MTTF increases. The MTTF is usually specified in hours, but can also be used with other units of measurement, such as miles or cycles. Using MTTF values on lower system levels can be very misleading, especially if they do not specify the associated Failures Modes and Mechanisms (The F in MTTF).[17]

In other cases, reliability is specified as the probability of mission success. For example, reliability of a scheduled aircraft flight can be specified as a dimensionless probability or a percentage, as often used in system safety engineering.

A special case of mission success is the single-shot device or system. These are devices or systems that remain relatively dormant and only operate once. Examples include automobile airbags, thermal batteries and missiles. Single-shot reliability is specified as a probability of one-time success, or is subsumed into a related parameter. Single-shot missile reliability may be specified as a requirement for the probability of a hit. For such systems, the probability of failure on demand (PFD) is the reliability measure — this is actually an "unavailability" number. The PFD is derived from failure rate (a frequency of occurrence) and mission time for non-repairable systems.

For repairable systems, it is obtained from failure rate, mean-time-to-repair (MTTR), and test interval. This measure may not be unique for a given system as this measure depends on the kind of demand. In addition to system level requirements, reliability requirements may be specified for critical subsystems. In most cases, reliability parameters are specified with appropriate statistical confidence intervals.

Reliability testing[edit]

The purpose of reliability testing is to discover potential problems with the design as early as possible and, ultimately, provide confidence that the system meets its reliability requirements.

Reliability testing may be performed at several levels and there are different types of testing. Complex systems may be tested at component, circuit board, unit, assembly, subsystem and system levels.[23] (The test level nomenclature varies among applications.) For example, performing environmental stress screening tests at lower levels, such as piece parts or small assemblies, catches problems before they cause failures at higher levels. Testing proceeds during each level of integration through full-up system testing, developmental testing, and operational testing, thereby reducing program risk. However, testing does not mitigate unreliability risk.

With each test both a statistical type 1 and type 2 error could be made and depends on sample size, test time, assumptions and the needed discrimination ratio. There is risk of incorrectly accepting a bad design (type 1 error) and the risk of incorrectly rejecting a good design (type 2 error).

It is not always feasible to test all system requirements. Some systems are prohibitively expensive to test; some failure modes may take years to observe; some complex interactions result in a huge number of possible test cases; and some tests require the use of limited test ranges or other resources. In such cases, different approaches to testing can be used, such as (highly) accelerated life testing, design of experiments, and simulations.

The desired level of statistical confidence also plays a role in reliability testing. Statistical confidence is increased by increasing either the test time or the number of items tested. Reliability test plans are designed to achieve the specified reliability at the specified confidence level with the minimum number of test units and test time. Different test plans result in different levels of risk to the producer and consumer. The desired reliability, statistical confidence, and risk levels for each side influence the ultimate test plan. The customer and developer should agree in advance on how reliability requirements will be tested.

A key aspect of reliability testing is to define "failure". Although this may seem obvious, there are many situations where it is not clear whether a failure is really the fault of the system. Variations in test conditions, operator differences, weather and unexpected situations create differences between the customer and the system developer. One strategy to address this issue is to use a scoring conference process. A scoring conference includes representatives from the customer, the developer, the test organization, the reliability organization, and sometimes independent observers. The scoring conference process is defined in the statement of work. Each test case is considered by the group and "scored" as a success or failure. This scoring is the official result used by the reliability engineer.

As part of the requirements phase, the reliability engineer develops a test strategy with the customer. The test strategy makes trade-offs between the needs of the reliability organization, which wants as much data as possible, and constraints such as cost, schedule and available resources. Test plans and procedures are developed for each reliability test, and results are documented.

Reliability testing is common in the Photonics industry. Examples of reliability tests of lasers are life test and burn-in. These tests consist of the highly accelerated ageing, under controlled conditions, of a group of lasers. The data collected from these life tests are used to predict laser life expectancy under the intended operating characteristics.[24]

Reliability test requirements[edit]

Reliability test requirements can follow from any analysis for which the first estimate of failure probability, failure mode or effect needs to be justified. Evidence can be generated with some level of confidence by testing. With software-based systems, the probability is a mix of software and hardware-based failures. Testing reliability requirements is problematic for several reasons. A single test is in most cases insufficient to generate enough statistical data. Multiple tests or long-duration tests are usually very expensive. Some tests are simply impractical, and environmental conditions can be hard to predict over a systems life-cycle.

Reliability engineering is used to design a realistic and affordable test program that provides empirical evidence that the system meets its reliability requirements. Statistical confidence levels are used to address some of these concerns. A certain parameter is expressed along with a corresponding confidence level: for example, an MTBF of 1000 hours at 90% confidence level. From this specification, the reliability engineer can, for example, design a test with explicit criteria for the number of hours and number of failures until the requirement is met or failed. Different sorts of tests are possible.

The combination of required reliability level and required confidence level greatly affects the development cost and the risk to both the customer and producer. Care is needed to select the best combination of requirements—e.g. cost-effectiveness. Reliability testing may be performed at various levels, such as component, subsystem and system. Also, many factors must be addressed during testing and operation, such as extreme temperature and humidity, shock, vibration, or other environmental factors (like loss of signal, cooling or power; or other catastrophes such as fire, floods, excessive heat, physical or security violations or other myriad forms of damage or degradation). For systems that must last many years, accelerated life tests may be needed.

Accelerated testing[edit]

The purpose of accelerated life testing (ALT test) is to induce field failure in the laboratory at a much faster rate by providing a harsher, but nonetheless representative, environment. In such a test, the product is expected to fail in the lab just as it would have failed in the field—but in much less time. The main objective of an accelerated test is either of the following:

  • To discover failure modes
  • To predict the normal field life from the high stress lab life

An Accelerated testing program can be broken down into the following steps:

  • Define objective and scope of the test
  • Collect required information about the product
  • Identify the stress(es)
  • Determine level of stress(es)
  • Conduct the accelerated test and analyze the collected data.

Common way to determine a life stress relationship are

  • Arrhenius model
  • Eyring model
  • Inverse power law model
  • Temperature–humidity model
  • Temperature non-thermal model

Software reliability[edit]

Further information: Software reliability

Software reliability is a special aspect of reliability engineering. System reliability, by definition, includes all parts of the system, including hardware, software, supporting infrastructure (including critical external interfaces), operators and procedures. Traditionally, reliability engineering focuses on critical hardware parts of the system. Since the widespread use of digital integrated circuit technology, software has become an increasingly critical part of most electronics and, hence, nearly all present day systems.

There are significant differences, however, in how software and hardware behave. Most hardware unreliability is the result of a component or material failure that results in the system not performing its intended function. Repairing or replacing the hardware component restores the system to its original operating state. However, software does not fail in the same sense that hardware fails. Instead, software unreliability is the result of unanticipated results of software operations. Even relatively small software programs can have astronomically large combinations of inputs and states that are infeasible to exhaustively test. Restoring software to its original state only works until the same combination of inputs and states results in the same unintended result. Software reliability engineering must take this into account.

Despite this difference in the source of failure between software and hardware, several software reliability models based on statistics have been proposed to quantify what we experience with software: the longer software is run, the higher the probability that it will eventually be used in an untested manner and exhibit a latent defect that results in a failure (Shooman 1987), (Musa 2005), (Denney 2005).

As with hardware, software reliability depends on good requirements, design and implementation. Software reliability engineering relies heavily on a disciplined software engineering process to anticipate and design against unintended consequences. There is more overlap between software quality engineering and software reliability engineering than between hardware quality and reliability. A good software development plan is a key aspect of the software reliability program. The software development plan describes the design and coding standards, peer reviews, unit tests, configuration management, software metrics and software models to be used during software development.

A common reliability metric is the number of software faults, usually expressed as faults per thousand lines of code. This metric, along with software execution time, is key to most software reliability models and estimates. The theory is that the software reliability increases as the number of faults (or fault density) decreases or goes down. Establishing a direct connection between fault density and mean-time-between-failure is difficult, however, because of the way software faults are distributed in the code, their severity, and the probability of the combination of inputs necessary to encounter the fault. Nevertheless, fault density serves as a useful indicator for the reliability engineer. Other software metrics, such as complexity, are also used. This metric remains controversial, since changes in software development and verification practices can have dramatic impact on overall defect rates.

Testing is even more important for software than hardware. Even the best software development process results in some software faults that are nearly undetectable until tested. As with hardware, software is tested at several levels, starting with individual units, through integration and full-up system testing. Unlike hardware, it is inadvisable to skip levels of software testing. During all phases of testing, software faults are discovered, corrected, and re-tested. Reliability estimates are updated based on the fault density and other metrics. At a system level, mean-time-between-failure data can be collected and used to estimate reliability. Unlike hardware, performing exactly the same test on exactly the same software configuration does not provide increased statistical confidence. Instead, software reliability uses different metrics, such as code coverage.

Eventually, the software is integrated with the hardware in the top-level system, and software reliability is subsumed by system reliability. The Software Engineering Institute's capability maturity model is a common means of assessing the overall software development process for reliability and quality purposes.

Comparison to safety engineering[edit]

Reliability engineering is concerned with overall minimisation of failures that could lead to financial losses for the responsible entity, whereas safety engineering focuses on minimising a specific set of failure types that in general could lead to large scale, widespread issues beyond the responsible entity.

Reliability hazards could transform into incidents leading to a loss of revenue for the company or the customer, for example due to direct and indirect costs associated with: loss of production due to system unavailability; unexpected high or low demands for spares; repair costs; man-hours; (multiple) re-designs; interruptions to normal production etc.[25]

Safety engineering is often highly specific, relating only to certain tightly regulated industries, applications, or areas. It primarily focuses on system safety hazards that could lead to severe accidents including: loss of life; destruction of equipment; or environmental damage. As such, the related system functional reliability requirements are often extremely high. Although it deals with unwanted failures in the same sense as reliability engineering, it however has less of a focus on direct costs, and is not concerned with post failure repair actions. Another difference is the level of impact of failures on society, leading to a tendency for strict control by governments or regulatory bodies (e.g. nuclear, aerospace, defense, rail and oil industries).[25]

This can occasionally lead to safety engineering and reliability engineering having contradictory requirements or conflicting choices at a system architecture level.[citation needed] For example, in train signal control systems it is common practice to use a "fail-safe" system design concept. In this example, a wrong-side failure needs an extremely low failure rate as such failures can lead to such severe effects, like frontal collisions of two trains where a signalling failure leads to two oncoming trains on the same track being given GREEN lights. Such systems should be (and thankfully are) designed in a way that the vast majority of failures (e.g. temporary or total loss of signals or open contacts of relays) will generate RED lights for all trains. This is the safe state. This means in the event of a failure, all trains are stopped immediately. This fail-safe logic might unfortunately lower the reliability of the system. The reason for this is the higher risk of false tripping, as any failure whether temporary or not may be trigger such a safe – but costly – shut-down state. Different solutions can be applied for similar issue. See the section on fault tolerance below.

Fault tolerance[edit]

Main article: Fault tolerance

Reliability can be increased by using "1oo2" (1 out of 2) redundancy at a part or system level. However, if both redundant elements disagree it can be difficult to know which is to be relied upon. In the previous train signalling example this could lead to lower safety levels as there are more possibilities for allowing "wrong side" or other undetected dangerous failures. Fault tolerant systems often rely on additional redundancy (e.g. 2oo3 voting logic) where multiple redundant elements must agree on a potentially unsage action before it is performed. This increases both reliability and safety at a system level and is often used for so-called "operational" or "mission" systems. This is common practice in Aerospace systems that need continued availability and do not have a fail-safe mode. For example, aircraft may use triple modular redundancy for flight computers and control surfaces (including occasionally different modes of operation e.g. electrical/mechanical/hydraulic) as these need to always be operational, due to the fact that there are no "safe" default positions for control surfaces such as rudders or ailerons when the aircraft is flying.

Basic reliability and mission (operational) reliability[edit]

The above example of a 2oo3 fault tolerant system increases both mission reliability as well as safety. However, the "basic" reliability of the system will in this case still be lower than a non redundant (1oo1) or 2oo2 system. Basic reliability engineering covers all failures, including those that might not result in system failure, but do result in additional cost due to: maintenance repair actions; logistics; spare parts etc. For example, replacement or repair of 1 faulty channel in a 2oo3 voting system, (the system is still operating, although with one failed channel it has actually become a 2oo2 system) is contributing to basic unreliability but not mission unreliability. As an example, the failure of the tail-light of an aircraft will not prevent the plane from flying (and so is not considered a mission failure), but it does need to be remedied (with a related cost, and so does contribute to the basic unreliability levels).

Detectability and common cause failures[edit]

When using fault tolerant (redundant architectures) systems or systems that are equipped with protection functions, detectability of failures and avoidance of common cause failures becomes paramount for safe functioning and/or mission reliability.

Reliability versus quality (Six Sigma)[edit]

Six Sigma has its roots in manufacturing. Reliability engineering is a specialty engineering part of systems engineering. The systems engineering process is a discovery process that is quite unlike a manufacturing process. A manufacturing process is focused on repetitive activities that achieve high quality outputs with minimum cost and time. The systems engineering process must begin by discovering a real (potential) problem that needs to be solved; the biggest failure that can be made in systems engineering is finding an elegant solution to the wrong problem[26] (or in terms of reliability: "providing elegant solutions to the wrong root causes of system failures").

The everyday usage term "quality of a product" is loosely taken to mean its inherent degree of excellence. In industry, a more precise definition of quality as "conformance to requirements or specifications at the start of use" is used. Assuming the final product specification adequately captures the original requirements and customer/system needs, the quality level can be measured as the fraction of product units shipped that meet specifications.[27]

Variation of this static output may affect quality and reliability, but this is not the total picture. More inherent aspects may play a role, and in some cases these may not be readily measured or controlled by any means. At a part level microscopic material variations such as unavoidable micro-cracks and chemical impurities may over time (due to physical or chemical "loading") become macroscopic defects. At a system level, systematic failures may play a dominant role (e.g. requirement errors or software or software compiler or design flaws).

Furthermore, for more complex systems it should be questioned if derived or lower-level requirements and related product specifications are truly valid and correct? Will these result in premature failure due to excessive wear, fatigue, corrosion, and debris accumulation, or other issues such as maintenance induced failures? Are there any interactions at a system level (as investigated by for example Fault Tree Analysis)? How many of these systems still meet function and fulfill the needs after a week of operation? What performance losses occurred? Did full system failure occur? What happens after the end of a one-year warranty period? And what happens after 50 years (a common lifetime for aircraft, trains, nuclear systems, etc.)? That is where "reliability" comes in. These issues are far more complex and can not be controlled only by a standard "quality" (six sigma) way of working. They need a systems engineering

Risk vs Cost/Complexity.[14]
A reliability block diagram showing a "1oo3" (1 out of 3) redundant designed subsystem

I've failed many times. I failed recently and it feels awful. How about you? When was the last time you failed?

When we're very young we fail a lot. Look at any toddler as they learn to walk. It's pretty well understood that it's through failure and persistence that we learn to do things.

Fast forward a few years, and it becomes increasingly difficult for us to accept failure. We assume that we can't learn and grow at the rate that we could when we were kids. But is that really true? Maybe we stop growing because we're scared of failure.

The core of this essay came out of teaching Search Inside Yourself in France this summer where participants found some of the analogies below very useful.

Measuring Failure

There are several different metrics we can use when measuring system failures. I want to use two of them to contrast ways of thinking about failure. The first is Mean Time Between Failures (MTBF) and the second is Mean Time To Recovery (MTTR).

If you focus on increasing Mean Time Between Failures (or MTBF, the average time between failures), you tend towards building a highly controlled system that stays within safe bounds of operation. You harden your components, control your operating conditions, and are relentless in your pursuit of order.

When I worked at amazon in the early 2000s, both amazon and google were pioneering a slightly different way of thinking about the reliability of computer systems. They began to experiment with the idea of using very cheap components that were known to fail; so "failures" became routine occurrences rather than out-of-the-ordinary events. Then you bind them together with software that expects those failures, and works around them as quickly as possible. You start to focus, then, on the Mean Time to Recovery (MTTR) from a failure -- or the time it takes for the system to come back to being operational after a given failure.

The System of You

Think about what those two approaches mean for the System of You.

If you're reading this, you're probably old enough that you know that failure usually feels like poop. No one likes that feeling. Think of a time when you felt shame, when you let someone down, when you publicly made a mistake. It was probably uncomfortable and you may have resolved never to feel that again.

In other words, we start optimizing for a very long Mean Time Between Failures; possibly by doubling-down on our strengths, avoiding things that are unfamiliar, unknown, or uncomfortable,.

What would it look like to optimize for Mean Time To Recovery? To push the boundaries of the uncomfortable, to embrace failures, to fail fast and fail often (as the startup mantra goes), and to continue to get better at recovering quickly from those failures.

It may sound good in theory, but given how terrible failure feels, how do you actually do this?

Be with what IS.

At the most basic level, we need to learn to be with whatever is.
What will happen hasn't yet happened, so cannot actually harm us in this instant.
What was, by definition, has already manifested, and so cannot be changed.
Even what is happening in this instant is already in the process of unfolding, so cannot be changed.
But we do have a choice as to how we react to what is happening right now.

While it might be possible to accept all that intellectually, it still doesn't change the fact that failure feels awful in the moment. How do we learn to experience the very physical unpleasantness that comes with difficult emotions (like failure)?

This is exactly what we practice when we sit.

After we first train our attention, we learn to bring our attention to physical sensations in all different parts of our body, and observe their characteristics objectively, without labeling them as pleasant or unpleasant. We practice being with unpleasant sensations without pushing them away but instead just really noticing them like a scientist might observe bacteria under a microscope.

Very soon we realize that we need to be skillful not just with the unpleasant, but with the pleasant sensations too.

How could that be important -- isn't it good to feel, well, good?

If we cannot experience pleasant sensations with the same objectivity that we cultivate in the presence of unpleasantness, we quickly go from enjoying them to becoming attached to them. And then the moment they disappear (which they must), we crave them, and we are uncomfortable until we can bring them back.

In a way this is related to Carol Dweck's research on fixed vs. growth mindset, and the importance of praising effort vs. outcome. Praise feels good, and if the praise is for a positive outcome ("good job acing that test!") then we tend to only work on things where we expect to get a positive outcome. If the praise is for effort ("you studied hard for that test!"), then we are more open to working on things where our efforts will be recognized, regardless of the outcome.

In a way what we're talking about here is going one level deeper and weaning ourselves from the need to be praised or recognized -- regardless of whether it's for effort or outcome.

Sensations and MTTR

Wait a sec. Our goal was to reduce Mean Time to Recovery. Let's suppose you somehow master the art of "being with what is." How and why does that help reduce MTTR?

There are two aspects to this.

I often use the stubbed-toe example when I teach: take a moment to think about, and briefly re-live, a time you stubbed your toe; and the pain you felt...

Did you later say to yourself: "let me kick the table again so I can really remember what that stubbed toe felt like?" I doubt it.

And yet we do that all the time with our emotions. Something happens that causes us grief, and we re-play that incident over and over again in our minds. Each time we re-play it, we feel the grief, and try to push away that unpleasant feeling. And as we try to push it away, we analyze, dissect, and re-play it yet again.

As we get better with objectively observing sensations, the first thing that happens is that it becomes easier to experience the unpleasantness of failure as a passing bodily sensation, just like a stubbed toe. You can notice its onset, experience it in all its unpleasant and gory detail without needing to push it away, and notice as it passes (as everything does). There's no need to continue to relive it. We can see ourselves as a sky with dark clouds currently passing through us, rather than identifying with the darkness.

As we learn to experience our sensations objectively, in finer levels of detail, and without pushing away the unpleasant or grasping for the pleasant -- the second thing that happens is that we develop an ability to also make better cognitive sense of them. For example:

How much of our grief is from some actual impending issue ("my rent is due and I'm broke")?

How much of our grief is from current events not reflecting a mental picture we've created to describe who we are (e.g., traits such kind, conscientious, hard working; and roles like engineer, husband, father)?

And how much of the grief is from worrying about the effect on meticulous PR job we've done our whole life, creating mental pictures in other people's minds ("what will so-and-so think of me when they hear about this?").

Once we can tease apart these factors, the magnitude of the grief we experience is often reduced significantly, and it becomes even easier to recover rather than stew in worry, anger, shame, or other negative emotions.

Why embrace failure?

Backing up a moment -- isn't it good that failure feels terrible? Isn't that what helps drives us to succeed, and navigate away from mistakes?

I'm in no way suggesting a masochistic love of failure.

I love how we talk about self-management in the Search Inside Yourself class as

a shift from compulsion to choice

"Unpleasantness" is an amazing set of data points that we are getting about a situation. Normally we are reacting to the unpleasantness by keeping it at arm's length, we are in effect compelled, trapped or victimized into a course of action by our desire to get rid of that unpleasantness.

I'm advocating learning to integrate these data points into a broader understanding of a situation and then proactively choosing the most skillful course of action.

But like any skill, this too is a skill that needs to be practiced.

Back to the cushion

So as we practice being with the pleasant and unpleasant on the cushion, we get better at recovering from life's setbacks.
As we get better at recovering from life's setbacks, we stop over-indexing on safety and are more open to taking risks and exploring opportunities.
When those pan out, great!
In case they don't, we get more practice at failing (and recovering), and feel even more liberated from the fear of the unknown.

So while you may think of meditators as sedentary and stationary; I believe there's a way in which sustained practice can support a life of great adventure and exploration!

Footnote

In a way I feel vulnerable writing this. You may have read memoirs where the authors celebrate and glorify their failures, while writing from a vantage point of success and subsequent accolades. Part of me is thinking: "What if that high point never comes for me? What if this is as good as it gets?"

However, among the things I'm grateful to have experienced and observed first-hand these past few years is that nobody is spared from the pains of being human. Not the the super-wealthy, not the successful entrepreneurs and executives, not movie stars, not the suits, the hardhats, and no -- not even the monks.

Which is why I'm pretty sure that you too have felt this uncertainty at some point in your life.

And so I wanted to share this post from "the trenches." From a place of peacefully walking through a plateau of not knowing what comes next.

This post originally appeared on the meditation minutes blog.

Follow Hemant Bhanoo on Twitter: www.twitter.com/hbhanoo

One thought on “Mttr Analysis Essay

Leave a comment

L'indirizzo email non verrà pubblicato. I campi obbligatori sono contrassegnati *