Reliability Engineering


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Reliability Engineering

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Reliability Engineering

  1. 1. Reliability engineering 1 Reliability engineering Reliability engineering is 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 engineering is a sub-discipline within systems engineering. Reliability is theoretically defined as the probability of failure, the frequency of failures, or in terms of availability, a probability derived from reliability and maintainability. Maintainability and maintenance may be defined as a part of reliability engineering. Reliability plays a key role in cost-effectiveness of systems. Although reliability is defined and affected by stochastic parameters, according to some acknowledged specialists, quality, reliability and safety are not achieved by mathematics and statistics. Nearly all teaching and literature on the subject emphasizes these aspects, and ignores the reality that the ranges of uncertainty involved largely invalidate quantitative methods for prediction and measurement. [2] Reliability engineering for complex systems requires a different, more elaborate systems approach than for non-complex systems. Reliability engineering may involve the creation of proper use studies and requirements specification, hardware & software design, functional (failure) analysis, testing and analyzing manufacturing, maintenance, transport, storage, spare parts stocking, operations research, human factors and technical documentation. Also data and information acquisition / organisation may be of importance. 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, like: tribology-, stress / fracture mechanics -, fatigue-, thermal-, shock-, electrical- and chemical "engineering". Reliability engineering is closely related to safety engineering and 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. The focus of safety engineering is normally not on cost, but on preserving life and nature, and therefore deals only with particular dangerous system failure modes. High reliability (safety) levels are also here the result of good engineering, attention to detail and almost never the result of only re-active failure management (Reliability Accounting / Statistics). [3] "Reliability is, after all, engineering in its most practical form" as once stated by James R. Schlesinger, Former US Secretary of Defense. Overview 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. Many engineering techniques are used in reliability engineering, such as reliability hazard analysis, failure mode and effects analysis (FMEA), failure modes, mechanisms, and effects analysis (FMMEA), [4] fault tree analysis (FTA), material stress and wear calculations, fatigue and creep analysis, finite element analysis, reliability prediction, thermal (stress) analysis, corrosion analysis, human error analysis, reliability testing, statistical uncertainty estimations, Monte Carlo simulations, design of experiments, reliability centered maintenance (RCM), failure reporting and corrective actions management. 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
  2. 2. Reliability engineering 2 plan to specify the reliability tasks that will be performed for that specific system. Consistent with the creation of safety cases, for example ARP4761, the goal 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 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, 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 the combination of probability and severity of the failure incident (scenario) occurring. In a deminimus 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). What is acceptable is determined by the managing authority or customers or the effected 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. Reliability and availability program plan 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 systems 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 on focusing on increasing testability & maintainability and not on reliability. Improving maintainability is generally easier than reliability. Maintainability estimates (Repair rates) are also generally more accurate. However, because the uncertainties in the reliability estimates are in most cases very large, it is likely to dominate the availability (prediction uncertainty) problem; even in the case maintainability levels are very high. When reliability is not under control more complicated issues may arise, like manpower (maintainers / customer service capability) shortage, 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. Only focusing on maintainability is therefore not enough. If failures are prevented, none of the others 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 cost of ownership (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 down-stream liability costs when reliability calculations do not sufficiently or accurately address customers' personal bodily risks. Often a trade-off is
  3. 3. Reliability engineering 3 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 this 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 in this case for reliability, availability, maintainability/maintenance and testability in context to the customer needs. Reliability requirements For any system, one of the first tasks of reliability engineering is to adequately specify the reliability and maintainability requirements derived from the overall availability needs and more importantly, from proper failure analysis or preliminary test results. Setting only availability targets is not appropriate. 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. Provision of only quantitative minimum targets (e.g. MTBF values/ Failure rates) is not sufficient for different reasons. One reason is that a full validation (related to correctness and verifiability in time) of an 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 probabalistic and 2) The high level of uncertainties involved for showing compliance with all these probabalistic requirements 3) Good estimates of a (probabalistic) reliability number per item are available only very late in the project, sometimes even only many years after in-service use. Compare this problem with the continues (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 % and this data is non-probabalistic and available already in CAD models. In case of reliability, the levels of unreliability (failure rates) may change with factors of decades (1000's of %)as result of very minor deviations in design, process or anything else. 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, wich 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 only depending 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 to make some predictions, this could potentially distract the engineering effort to a kind of accounting work. A design requirement should be so 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. A test requirement should be detailed and could be derived from failure analysis (FEM) or other lower part or material level reliability tests, e.g. required overload loads (or 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. The design requirements shall be part of the output from functional or other failure analysis or tests. These requirements (often design constraints) are in this way derived from failure analysis or preliminary tests.
  4. 4. Reliability engineering 4 The maintainability requirements address the costs of repairs as well as repair time. Testability 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, test, 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 Practically, most failures can in the end be traced back to a root causes of the type of human errors of any kind. For example, human errors in: •• Use studies •• Requirement analysis / setting •• Configuration control •• Assumptions •• Calculations / simulations / FEM analysis •• Design •• Design drawings •• Testing (incorrect load settings or failure measurement) •• Statistical analysis •• Manufacturing •• Quality control •• Maintenance •• Maintenance manuals •• Incorrect feedback of information •• etc. However, humans are also very good in detection of (the same) failures, correction of failures and improvising when abnormal situations occur. The policy that human actions should be completely ruled out of any design and production process to improve reliability may not be effective therefore. Some tasks are better performed by humans and some are better performed by machines. Furthermore, human errors in management and 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 sense as having a "safety culture" is paramount in the development of safety critical systems.
  5. 5. Reliability engineering 5 Design for reliability Reliability design begins with the development of a (system) model. Reliability and availability models use block diagrams and fault trees 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 MTTR, are other inputs for these 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 and practical performance and reliability requirements should be provided to designers so 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 and verification for reliability "performance" by testing may be needed. A Fault Tree Diagram 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 / items is often not available or extremely expensive to obtain. By creating redundancy, together with a high level of failure monitoring and the avoidance of common cause failures, even a system with relative bad single channel (part) reliability, can be made highly reliable (mission reliability) on system level. No testing of reliability has to be required for this. Furthermore, by using redundancy and the use of dissimilar design and manufacturing processes (different suppliers) for the single independent channels, less sensitivity for quality issues (early childhood failures) is created and very high levels of reliability can be achieved at all moments of the development cycles (early life times and 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 design technique to prevent failures is 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 leading to failure at high level of detail, possible with use of modern finite element method (FEM) software programs that may handle complex geometries and mechanisms like 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 variation. Another common design technique is component derating: Selecting components whose tolerance significantly exceeds the expected stress, as using a heavier gauge wire that exceeds the normal specification for the expected electrical current. Another effective way to deal with unreliability issues is to perform analysis to be able to predict degradation and being able to prevent unscheduled down events / failures from occurring. RCM (Reliability Centered Maintenance) programs can be used for this. Many tasks, techniques and analyses are specific to particular industries and applications. Commonly these include: •• Built-in test (BIT) (testability analysis)
  6. 6. Reliability engineering 6 • Failure mode and effects analysis (FMEA) • Reliability hazard analysis •• Reliability block-diagram analysis • Dynamic Reliability block-diagram analysis [5] •• Fault tree analysis •• Root cause analysis •• Sneak circuit analysis •• Accelerated testing •• Reliability growth analysis • Weibull analysis • Thermal analysis by finite element analysis (FEA) and / or measurement • Thermal induced, shock and vibration fatigue analysis by FEA and / or measurement •• Electromagnetic analysis •• Statistical interference • Avoidance of single point of failure •• Functional analysis and functional failure analysis (e.g., function FMEA, FHA or FFA) •• Predictive and preventive maintenance: reliability centered maintenance (RCM) analysis •• Testability analysis •• Failure diagnostics analysis (normally also incorporated in FMEA) •• Human error analysis •• Operational hazard analysis / •• Manual screening •• Integrated logistics support Results are presented during the system design reviews and logistics reviews. Reliability is just one requirement among many system requirements. Engineering trade studies are used to determine the optimum balance between reliability and other requirements and constraints. Reliability prediction and improvement Reliability prediction is the combination of the creation of a proper reliability model together with estimating (and justifying) the input parameters for this model (like failure rates for a particular failure mode or event and the mean time to repair the system for a particular failure) and finally to provide a system (or part) level estimate for the output reliability parameters (system availability or a particular functional failure frequency). 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 and more effort should be devoted to the prevention of failure (reliability improvement). Failures can and should be prevented in the first place for most cases. The emphasis on quantification and target setting in terms of (e.g.) MTBF might provide the idea that there is a limit to the amount of reliability that can be achieved. In theory there is no inherent limit and higher reliability does not need to be more costly in development. Another of their arguments is that prediction of reliability based on historic data can be very misleading, as a comparison is only valid for exactly the same designs, products, manufacturing processes and maintenance under exactly the same loads and environmental context. Even a minor change in detail in any of these could have major effects on reliability. Furthermore, normally the most unreliable and important items (most interesting candidates for a reliability investigation) are most often subjected to many modifications and changes. Engineering designs are in most industries updated frequently. This is the reason why the standard (re-active or pro-active) statistical methods and processes as used in the medical industry or insurance branch are not as effective for engineering. Another surprising but logical argument is that to be able to accurately predict reliability by testing, the exact mechanisms of failure must have been known in most cases and therefore – in most cases – can
  7. 7. Reliability engineering 7 be prevented! Following the incorrect route by trying to quantify and solving a complex reliability engineering problem in terms of MTBF or Probability and using the re-active approach is referred to by Barnard as "Playing the Numbers Game" and is regarded as bad practise. For existing systems, it is arguable that responsible programs would directly analyse and try to correct the root cause of discovered failures and thereby may render the initial MTBF estimate fully invalid as new assumptions (subject to high error levels) of the effect of the patch/redesign must be made. Another practical issue concerns a general lack of availability of detailed failure data and not consistent filtering of failure (feedback) data or igoring statistical errors, which are very high for rare events (like reliability related failures). Very clear guidelines must be present to be able 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 type 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 may be very expensive if done by testing. On part level, results can be obtained often with higher confidence as many samples might be used for the available testing financial budget, however unfortunately these tests might lack validity on system level due to the assumptions that had to be made for part level testing. These authors argue that it can not be emphasized enough that testing for reliability should be done to create failures in the first place, learn from them and to improve the system / part. The general conclusion is drawn that an accurate and an absolute prediction – by field data comparison or testing – of reliability is in most cases not possible. An exception might be failures due to wear-out problems like fatigue failures. In the introduction of MIL-STD-785 it is written that reliability prediction should be used with great caution if not only used for comparison in trade-off studies. See also: Risk Assessment#Quantitative risk assessment – Critics paragraph Reliability theory 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: 1.1. 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. Units other than time may sometimes be used. 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.
  8. 8. Reliability engineering 8 Quantitative system reliability parameters – theory 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 are very useful for systems that are operated frequently, such as most 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. 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 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 – which actually is an unavailability number. This 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 and 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 modelling Reliability modelling 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 availability (including effects from logistics issues like spare part provisioning, transport and manpower) behavior are fault tree analysis and reliability block diagrams. On component level the same type of analysis can be used together with others. The input for the models can come from many sources: Testing, Earlier operational experience field data or data handbooks from the same or mixed industries can be used. In all cases, the data must be used with great caution as predictions are only valid in case the same product in the same context is used. Often predictions are only made to compare alternatives. A reliability block diagram showing a 1oo3 (1 out of 3) redundant designed subsystem 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 modelling 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 it is a considerable component to system functionality.
  9. 9. Reliability engineering 9 Reliability test requirements 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. Reliability testing A reliability sequential test plan 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 [6] . (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.
  10. 10. Reliability engineering 10 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 an 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. Accelerated testing 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
  11. 11. Reliability engineering 11 Software reliability 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.
  12. 12. Reliability engineering 12 Reliability engineering vs safety engineering Reliability engineering differs from safety engineering with respect to the kind of hazards that are considered. Reliability engineering is in the end only concerned with cost. It relates to all Reliability hazards that could transform into incidents with a particular level of loss of revenue for the company or the customer. These can be cost due to loss of production due to system unavailability, unexpected high or low demands for spares, repair costs, man hours, (multiple) re-designs, interruptions on normal production (e.g. due to high repair times or due to unexpected demands for non-stocked spares) and many other indirect costs. Safety engineering, on the other hand, is more specific and regulated. It relates to only very specific and system safety hazards that could potentially lead to severe accidents and is primarily concerned with loss of life, loss of equipment, or environmental damage. The related system functional reliability requirements are sometimes extremely high. It deals with unwanted dangerous events (for life, property, and environment) in the same sense as reliability engineering, but does normally not directly look at cost and is not concerned with repair actions after failure / accidents (on system level). Another difference is the level of impact of failures on society and the control of governments. Safety engineering is often strictly controlled by governments (e.g. nuclear, aerospace, defense, rail and oil industries). Furthermore, safety engineering and reliability engineering may even have contradicting requirements. This relates to system level architecture choices .Wikipedia:Citation needed For example, in train signal control systems it is common practice to use a fail-safe system design concept. In this concept the Wrong-side failure need to be fully controlled to an extreme low failure rate. These failures are related to possible severe effects, like frontal collisions (2* GREEN lights). Systems are designed in a way that the far majority of failures will simply result in a temporary or total loss of signals or open contacts of relays and generate RED lights for all trains. This is the safe state. 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 full or temporary, intermittent failure is quickly latched in a shut-down (safe)state. Different solutions are available for this issue. See chapter Fault Tolerance below. Fault tolerance Reliability can be increased here by using a 2oo2 (2 out of 2) redundancy on part or system level, but this does in turn lower the safety levels (more possibilities for Wrong Side and undetected dangerous Failures). Fault tolerant voting systems (e.g. 2oo3 voting logic) can increase both reliability and safety on a system level. In this case the so-called "operational" or "mission" reliability as well as the safety of a system can be increased. This is also common practice in Aerospace systems that need continued availability and do not have a fail safe mode (e.g. flight computers and related electrical and / or mechanical and / or hydraulic steering functions need always to be working. There are no safe fixed positions for rudder or other steering parts when the aircraft is flying). Basic reliability and mission (operational) reliability 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 refers to all failures, including those that might not result in system failure, but do result in maintenance repair actions, logistic cost, use of spares, etc. For example, the replacement or repair of 1 channel in a 2oo3 voting system that is still operating with one failed channel (which in this state actually has become a 1oo2 system) is contributing to basic unreliability but not mission unreliability. Also, for example, the failure of the taillight of an aircraft is not considered as a mission loss failure, but does contribute to the basic unreliability.
  13. 13. Reliability engineering 13 Detectability and common cause failures When using fault tolerant (redundant architectures) systems or systems that are equipped with protection functions, detectability of failures and avoidance of common cause failures become paramount for safe functioning and/or mission reliability. Reliability operational assessment After a system is produced, reliability engineering monitors, assesses and corrects deficiencies. Monitoring includes electronic and visual surveillance of critical parameters identified during the fault tree analysis design stage. The data are constantly analyzed using statistical techniques, such as Weibull analysis and linear regression, to ensure the system reliability meets requirements. Reliability data and estimates are also key inputs for system logistics. Data collection is highly dependent on the nature of the system. Most large organizations have quality control groups that collect failure data on vehicles, equipment and machinery. Consumer product failures are often tracked by the number of returns. For systems in dormant storage or on standby, it is necessary to establish a formal surveillance program to inspect and test random samples. Any changes to the system, such as field upgrades or recall repairs, require additional reliability testing to ensure the reliability of the modification. Since it is not possible to anticipate all the failure modes of a given system, especially ones with a human element, failures will occur. The reliability program also includes a systematic root cause analysis that identifies the causal relationships involved in the failure such that effective corrective actions may be implemented. When possible, system failures and corrective actions are reported to the reliability engineering organization. One of the most common methods to apply to a reliability operational assessment are failure reporting, analysis and corrective action systems (FRACAS). This systematic approach develops a reliability, safety and logistics assessment based on Failure / Incident reporting, management, analysis and corrective/preventive actions. Organizations today are adopting this method and utilize commercial systems such as a Web based FRACAS application enabling an organization to create a failure/incident data repository from which statistics can be derived to view accurate and genuine reliability, safety and quality performances. It is extremely important to have one common source FRACAS system for all end items. Also, test results should be able to be captured here in a practical way. Failure to adopt one easy to handle (easy data entry for field engineers and repair shop engineers)and maintain integrated system is likely to result in a FRACAS program failure. Some of the common outputs from a FRACAS system includes: Field MTBF, MTTR, Spares Consumption, Reliability Growth, Failure/Incidents distribution by type, location, part no., serial no, symptom etc. The use of past data to predict the reliability of new comparable systems/items can be misleading as reliability is a function of the context of use and can be affected by small changes in the designs/manufacturing. Reliability organizations Systems of any significant complexity are developed by organizations of people, such as a commercial company or a government agency. The reliability engineering organization must be consistent with the company's organizational structure. For small, non-critical systems, reliability engineering may be informal. As complexity grows, the need arises for a formal reliability function. Because reliability is important to the customer, the customer may even specify certain aspects of the reliability organization. There are several common types of reliability organizations. The project manager or chief engineer may employ one or more reliability engineers directly. In larger organizations, there is usually a product assurance or specialty engineering organization, which may include reliability, maintainability, quality, safety, human factors, logistics, etc. In such case, the reliability engineer reports to the product assurance manager or specialty engineering manager. In some cases, a company may wish to establish an independent reliability organization. This is desirable to ensure that the system reliability, which is often expensive and time consuming, is not unduly slighted due to budget and
  14. 14. Reliability engineering 14 schedule pressures. In such cases, the reliability engineer works for the project day-to-day, but is actually employed and paid by a separate organization within the company. Because reliability engineering is critical to early system design, it has become common for reliability engineers, however the organization is structured, to work as part of an integrated product team. Certification The American Society for Quality has a program to become a Certified Reliability Engineer, CRE. Certification is based on education, experience, and a certification test: periodic re-certification is required. The body of knowledge for the test includes: reliability management, design evaluation, product safety, statistical tools, design and development, modeling, reliability testing, collecting and using data, etc. Another highly respected certification program is the CRP [7] (Certified Reliability Professional). To achieve certification, candidates must complete a series of courses focused on important Reliability Engineering topics, successfully apply the learned body of knowledge in the workplace and publicly present this expertise in an industry conference or journal. Reliability engineering education Some universities offer graduate degrees in reliability engineering. Other reliability engineers typically have an engineering degree, which can be in any field of engineering, from an accredited university or college program. Many engineering programs offer reliability courses, and some universities have entire reliability engineering programs. A reliability engineer may be registered as a professional engineer by the state, but this is not required by most employers. There are many professional conferences and industry training programs available for reliability engineers. Several professional organizations exist for reliability engineers, including the IEEE Reliability Society, the American Society for Quality (ASQ) [8] , and the Society of Reliability Engineers (SRE) [9] . References [1][1] Institute of Electrical and Electronics Engineers (1990) IEEE Standard Computer Dictionary: A Compilation of IEEE Standard Computer Glossaries. New York, NY ISBN 1-55937-079-3 [2] O'Connor, Patrick D. T. (2002), Practical Reliability Engineering (Fourth Ed.), John Wiley & Sons, New York. ISBN 978-0-4708-4462-5. [3] [4] Using Failure Modes, Mechanisms, and Effects Analysis in Medical Device Adverse Event Investigations, S. Cheng, D. Das, and M. Pecht, ICBO: International Conference on Biomedical Ontology, Buffalo, NY, July 26–30, 2011, pp. 340–345 [5][5] Salvatore Distefano, Antonio Puliafito: Dependability Evaluation with Dynamic Reliability Block Diagrams and Dynamic Fault Trees. IEEE Trans. Dependable Sec. Comput. 6(1): 4-17 (2009) [6] [7] [8] [9] Further reading • Blanchard, Benjamin S. (1992), Logistics Engineering and Management (Fourth Ed.), Prentice-Hall, Inc., Englewood Cliffs, New Jersey. • Breitler, Alan L. and Sloan, C. (2005), Proceedings of the American Institute of Aeronautics and Astronautics (AIAA) Air Force T&E Days Conference, Nashville, TN, December, 2005: System Reliability Prediction: towards a General Approach Using a Neural Network. • Ebeling, Charles E., (1997), An Introduction to Reliability and Maintainability Engineering, McGraw-Hill Companies, Inc., Boston.
  15. 15. Reliability engineering 15 • Denney, Richard (2005) Succeeding with Use Cases: Working Smart to Deliver Quality. Addison-Wesley Professional Publishing. ISBN . Discusses the use of software reliability engineering in use case driven software development. •• Gano, Dean L. (2007), "Apollo Root Cause Analysis" (Third Edition), Apollonian Publications, LLC., Richland, Washington • Holmes, Oliver Wendell, Sr. The Deacon's Masterpiece • Kapur, K.C., and Lamberson, L.R., (1977), Reliability in Engineering Design, John Wiley & Sons, New York. •• Kececioglu, Dimitri, (1991) "Reliability Engineering Handbook", Prentice-Hall, Englewood Cliffs, New Jersey • Trevor Kletz (1998) Process Plants: A Handbook for Inherently Safer Design CRC ISBN 1-56032-619-0 • Leemis, Lawrence, (1995) Reliability: Probabilistic Models and Statistical Methods, 1995, Prentice-Hall. ISBN 0-13-720517-1 • Frank Lees (2005). Loss Prevention in the Process Industries (3rdEdition ed.). Elsevier. ISBN 978-0-7506-7555-0. • MacDiarmid, Preston; Morris, Seymour; et al., (1995), Reliability Toolkit: Commercial Practices Edition, Reliability Analysis Center and Rome Laboratory, Rome, New York. •• Modarres, Mohammad; Kaminskiy, Mark; Krivtsov, Vasiliy (1999), "Reliability Engineering and Risk Analysis: A Practical Guide, CRC Press, ISBN 0-8247-2000-8. •• Musa, John (2005) Software Reliability Engineering: More Reliable Software Faster and Cheaper, 2nd. Edition, AuthorHouse. ISBN •• Neubeck, Ken (2004) "Practical Reliability Analysis", Prentice Hall, New Jersey • Neufelder, Ann Marie, (1993), Ensuring Software Reliability, Marcel Dekker, Inc., New York. • O'Connor, Patrick D. T. (2002), Practical Reliability Engineering (Fourth Ed.), John Wiley & Sons, New York. ISBN 978-0-4708-4462-5. • Shooman, Martin, (1987), Software Engineering: Design, Reliability, and Management, McGraw-Hill, New York. • Tobias, Trindade, (1995), Applied Reliability, Chapman & Hall/CRC, ISBN 0-442-00469-9 • Springer Series in Reliability Engineering ( • Nelson, Wayne B., (2004), Accelerated Testing – Statistical Models, Test Plans, and Data Analysis, John Wiley & Sons, New York, ISBN 0-471-69736-2 • Bagdonavicius, V., Nikulin, M., (2002), "Accelerated Life Models. Modeling and Statistical analysis", CHAPMAN&HALL/CRC, Boca Raton, ISBN 1-58488-186-0 US standards, specifications, and handbooks • Aerospace Report Number: TOR-2007(8583)-6889 ( TOR2007-8583-6889_14232/) Reliability Program Requirements for Space Systems, The Aerospace Corporation (10 Jul 2007) • DoD 3235.1-H (3rd Ed) ( Test and Evaluation of System Reliability, Availability, and Maintainability (A Primer), U.S. Department of Defense (March 1982) . • NASA GSFC 431-REF-000370 ( GSFC_431_REF_000370_2297/) Flight Assurance Procedure: Performing a Failure Mode and Effects Analysis, National Aeronautics and Space Administration Goddard Space Flight Center (10 Aug 1996). • IEEE 1332–1998 ( IEEE Standard Reliability Program for the Development and Production of Electronic Systems and Equipment, Institute of Electrical and Electronics Engineers (1998). • JPL D-5703 ( Reliability Analysis Handbook, National Aeronautics and Space Administration Jet Propulsion Laboratory (July 1990).
  16. 16. Reliability engineering 16 • MIL-STD-785B ( Reliability Program for Systems and Equipment Development and Production, U.S. Department of Defense (15 Sep 1980). (*Obsolete, superseded by ANSI/GEIA-STD-0009-2008 titled Reliability Program Standard for Systems Design, Development, and Manufacturing, 13 Nov 2008) • MIL-HDBK-217F ( MIL-HDBK-217F_14591/) Reliability Prediction of Electronic Equipment, U.S. Department of Defense (2 Dec 1991). • MIL-HDBK-217F (Notice 1) ( MIL-HDBK-217F_NOTICE-1_14589/) Reliability Prediction of Electronic Equipment, U.S. Department of Defense (10 Jul 1992). • MIL-HDBK-217F (Notice 2) ( MIL-HDBK-217F_NOTICE-2_14590/) Reliability Prediction of Electronic Equipment, U.S. Department of Defense (28 Feb 1995). • MIL-STD-690D ( Failure Rate Sampling Plans and Procedures, U.S. Department of Defense (10 Jun 2005). • MIL-HDBK-338B ( MIL-HDBK-338B_15041/) Electronic Reliability Design Handbook, U.S. Department of Defense (1 Oct 1998). • MIL-HDBK-2173 ( MIL-HDBK-2173_15046/) Reliability-Centered Maintenance (RCM) Requirements for Naval Aircraft, Weapon Systems, and Support Equipment, U.S. Department of Defense (30 JAN 1998); (superseded by NAVAIR 00-25-403 ( • MIL-STD-1543B ( Reliability Program Requirements for Space and Launch Vehicles, U.S. Department of Defense (25 Oct 1988). • MIL-STD-1629A ( Procedures for Performing a Failure Mode Effects and Criticality Analysis, U.S. Department of Defense (24 Nov 1980). • MIL-HDBK-781A ( MIL_HDBK_781A_1933/) Reliability Test Methods, Plans, and Environments for Engineering Development, Qualification, and Production, U.S. Department of Defense (1 Apr 1996). • NSWC-06 (Part A & B) ( NSWC-06_RELIAB_HDBK_2006_15051/) Handbook of Reliability Prediction Procedures for Mechanical Equipment, Naval Surface Warfare Center (10 Jan 2006). • SR-332 ( TITLE=&DOCUMENT=sr-332&DATE=&CLASS=&COUNT=1000) Reliability Prediction Procedure for Electronic Equipment, Telcordia Technologies (January 2011). • FD-ARPP-01 ( KEYWORDS=&TITLE=&DOCUMENT=fd-arpp-01&DATE=&CLASS=&COUNT=1000) Automated Reliability Prediction Procedure, Telcordia Technologies (January 2011).
  17. 17. Reliability engineering 17 UK standards In the UK, there are more up to date standards maintained under the sponsorship of UK MOD as Defence Standards. The relevant Standards include: DEF STAN 00-40 Reliability and Maintainability (R&M) •• PART 1: Issue 5: Management Responsibilities and Requirements for Programmes and Plans • PART 4: (ARMP-4)Issue 2: Guidance for Writing NATO R&M Requirements Documents • PART 6: Issue 1: IN-SERVICE R & M • PART 7 (ARMP-7) Issue 1: NATO R&M Terminology Applicable to ARMP’s DEF STAN 00-42 RELIABILITY AND MAINTAINABILITY ASSURANCE GUIDES •• PART 1: Issue 1: ONE-SHOT DEVICES/SYSTEMS •• PART 2: Issue 1: SOFTWARE • PART 3: Issue 2: R&M CASE •• PART 4: Issue 1: Testability •• PART 5: Issue 1: IN-SERVICE RELIABILITY DEMONSTRATIONS DEF STAN 00-43 RELIABILITY AND MAINTAINABILITY ASSURANCE ACTIVITY •• PART 2: Issue 1: IN-SERVICE MAINTAINABILITY DEMONSTRATIONS DEF STAN 00-44 RELIABILITY AND MAINTAINABILITY DATA COLLECTION AND CLASSIFICATION • PART 1: Issue 2: MAINTENANCE DATA & DEFECT REPORTING IN THE ROYAL NAVY, THE ARMY AND THE ROYAL AIR FORCE • PART 2: Issue 1: DATA CLASSIFICATION AND INCIDENT SENTENCING – GENERAL • PART 3: Issue 1: INCIDENT SENTENCING – SEA • PART 4: Issue 1: INCIDENT SENTENCING – LAND DEF STAN 00-45 Issue 1: RELIABILITY CENTERED MAINTENANCE DEF STAN 00-49 Issue 1: RELIABILITY AND MAINTAINABILITY MOD GUIDE TO TERMINOLOGY DEFINITIONS These can be obtained from DSTAN ( There are also many commercial standards, produced by many organisations including the SAE, MSG, ARP, and IEE. French standards • FIDES ( The FIDES methodology (UTE-C 80-811) is based on the physics of failures and supported by the analysis of test data, field returns and existing modelling. • UTE-C 80–810 or RDF2000 ( The RDF2000 methodology is based on the French telecom experience. International standards • TC 56 Standards: Dependability (
  18. 18. Reliability engineering 18 External links • Prognostics Journal ( is an open access journal that provides an international forum for the electronic publication of original research and industrial experience articles in all areas of systems reliability and prognostics. • Models and methods regarding reliability analysis ( • Structural Safety (
  19. 19. Article Sources and Contributors 19 Article Sources and Contributors Reliability engineering  Source:  Contributors: ABCZzzWriter1, ALD1984, ASQ-Reliability-Div, Academy633, Adamantios1, Aecannon12, Aetheling, Agaran, Akerans, Aldfavoweb, Alexdfromald, Allan McInnes, Allens, Andreas Kaufmann, Anna.nozik, Antosheryl, Ashchori, Atoine85, AxelBoldt, Bassplr19, Bernard S. Jansen, Boreman, Bushsf, CG-Bradley, CasualVisitor, CatherineMunro, ChrisGualtieri, Ckelloug, Cmattison387, Copeland.James.H, CouchSurfer222, Crzer07, DVdm, Damsun, Daniel dulay, Daveplot, David Haslam, David s graff, Deangano, Deedmonds, Deevakar k, Dependability, Dewritech, DexDor, Dougmcdonell, Downsize43, Druzhnik, Dthomsen8, Eclipsed, Edward, Egoadvocate, FMEA Expert, Fa1275, Favonian, Fede.Campana, FeralOink, Frap, Gavrilov, Georgecmu, GoingBatty, Gregbard, Hanwufu, Hertzsprung, Hhhippo, Hlperng, Ibbn, Ingolfson, Inwind, IrfanSha, Itemuk, J.Trew, JLaTondre, JaGa, Jack Greenmaven, Jack4875, JaneningUMD, Johnqtodd, Jonel, Jpbowen, Jr2349, Karada, Kiefer.Wolfowitz, Kokcharov, KrazyKotik, Kuru, Les boys, Levineps, Lfiondella, Longcr, M2OS, MER-C, Macaddct1984, Makki98, Mandarax, Mark Arsten, Matjaz285, Maurice Carbonaro, Maurizio.Cattaneo, Mdd, Melcombe, Mfhall, Michael Hardy, MichaelBillington, Michaeldsuarez, Modarres, Mogism, Monnini1, Mr pand, MrOllie, Mrausand, Musiphil, Nelson50, Niceguyedc, Niemeyerstein en, Noclevername, Nurg,, Petter73, Pharaoh of the Wizards, PhilKnight, Pinecar, Pokeme444, Pqrstuv, Printz150, R'n'B, Reinderien, RichardDenney, Ringbang, Rjackchapman, Rjwilmsi, Rlsheehan, Rockfang, Ronz, Rosenlind, Rp, S2000magician, SamJohnston, Sanya3, Sasuke Sarutobi, Schbrownie, SchreyP, Scwarebang, Seb az86556, Senarvi, Shalom Yechiel, Shreyankh, Silvonen, SjoerdOptLand, Slashme, Sonoma-rich, SouthLake, Spalding, Standardschecker, Sun Creator, SunSw0rd, Sv1xv, Tedernst, Telcoterry, Thine Antique Pen, Thumperward, Tmcgibbo, Tom harrison, Tony1, Tonyshan, Tribaal, Tripodian, Upholder, Uršul, Vasywriter, Vebjorl, Velella, Versageek, Vincentvikram, Vitalikk, WCroslan, WalNi, Wbm1058, WikHead, Woohookitty, Wyatts, Xaviervd, Yocto42, Zzzz12345678, 472 ,‫טבעת-זרם‬ anonymous edits Image Sources, Licenses and Contributors File:Fault tree.png  Source:  License: Public Domain  Contributors: Original uploader was Wyatts at en.wikipedia File:Reliability block diagram.png  Source:  License: Public Domain  Contributors: User:Wyatts File:Reliability sequential test plan.png  Source:  License: Public Domain  Contributors: BenFrantzDale, Sfan00 IMG, Wyatts License Creative Commons Attribution-Share Alike 3.0 //