However, these figures can only ever be rough estimates, because they cant take into account the actual performance of a specific asset, under real-life operating conditions. %PDF-1.3 This information can be used to measure the decrease in reliability that can occurs as an asset ages and determine when a decision is made to replace a piece of equipment. Whittington, in Alternative Energy Systems, 1984. WebAs per title, I would like the equation to calculate the effective failure rate of a system or branch of parallel/redundant components whose failure rates follow a Weibull It is an indication of how long a electrical or mechanical system typically operates before failing. Machines (or software) that can be repaired will have multiple failures over their lifetime, and so will have periods of time between failures, whereas non-repairable items, such as light bulbs, or SSDs, will function correctly for a period of time before failing permanently, and so only have one failure in their lifetime. <>stream Here, defects that developed during initial manufacture of a component cause failures. To avoid this potential corruption of MTBF, its important to have agreed standards in place for the process for measuring and calculating MTBF in a consistent and meaningful way. ) Because MTBF is a basic measure of a systems reliability, it can be used in a variety of important business decisions. Johnson, Barry. An SLA breach not only incurs cost penalty to the vendor but also compromises end-user experience of apps and solutions running on the cloud network. WebThe failure rate in the early failure period is called the early failure rate (EFR), and exhibits a shape where the failure rate decreases over time. Theprobability density function(pdf) is denoted byf(t). Get clear on your definitions of failure and operating time and which components are included in the system to ensure your MTBF value is meaningful. This distribution is related to the normal distribution and depends on a parameter known as the number of degrees of freedom (DF). A component manufacturer may sometimes provide a specified failure rate usually based on field or laboratory test data. W. Kent Muhlbauer, in Pipeline Risk Management Manual (Third Edition), 2004. The service must: Availability is measured at its steady state, accounting for potential downtime incidents that can (and will) render a service unavailable during its projected usage duration. Quality-One uses this calculator to intelligently manage the performance risk of a new product or process design in the design verification or validation process. Reliability is the probability that a system performs correctly during a specific time duration. Mean Time Between Failures (MTBF) and Mean Time To Failure (MTTF) are also very similar metrics, and are often confused and used interchangeably. However, the failure rate versus time plot is an important tool to aid in understanding how a product fails. The failure rates of terminal devices will obviously vary considerably with complexity and age. `Ad{. n$3~NMV[=sa#_p07S[7ai,S$qdt>%.]y(
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x`j*rt }5Q;;4"OQo F^.vUOGcPoc And although its not sufficient on its own, MTBF provides an effective way to help your team focus on increasing the operational time of your assets. All Rights Reserved. Uptime for the purposes of MTBF is calculated as the duration from the start of uptime to the start of the next unplanned downtime. Values of the Percentage Point of Distribution tc for 95% Confidence Interval. Each time a piece of equipment occurs is a perfect opportunity to step back and look for any underlying causes of the failure that you can address. Over the last four weeks, there have been 50 different issues with individual conveyor belts, requiring a total of 200 repair hours to get them up and running again. When the failure rate tends to increase with time and is logically linked with an aging effect, the underlying mechanism is time dependent. A common model is the exponential failure distribution. Failure may be defined differently for the same components in different applications, use cases, and organizations. Total uptime The total amount of time that the system or components were operating correctly under normal conditions. Johnson, Barry. This will allow us to obtain an expression for the CDF in terms of failure rate that we can use to illustrate the difference between the two functions. F This will bring together HBM, Brel & Kjr, nCode, ReliaSoft, and Discom brands, helping you innovate faster for a cleaner, healthier, and more productive world. Recognizing the reliability and confidence is a key step in mitigating the performance risk in Design Verification and Validation. Failure rate is the frequency with which an engineered system or component fails, expressed in failures per unit of time. The failure rate of an electronic assembly is roughly equal to the sum of the failure rates of all its components. u1\~i_^w,g>/>G0W'p"-t$;kr5wY
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We use cookies to help provide and enhance our service and tailor content and ads. ScienceDirect is a registered trademark of Elsevier B.V. ScienceDirect is a registered trademark of Elsevier B.V. {\displaystyle t} (5.31). Availability is related to reliability and is a measure of how much of the time a system is performing correctly, when it needs to be. To evaluate the dependability of a system, the promise of cloud computing depends on two viral metrics: Vendors offer service level agreements (SLAs) to meet specific standards of reliability and availability. Bathtub curve of failure rate [6]. During this period, the failures are caused by random factors. [12] Note that this result only holds when the failure rate is defined for all t0[13] and that the converse result (coefficient of variation determining nature of failure rate) does not hold. Language links are at the top of the page across from the title. (1996). {\displaystyle \Delta t} As a statistic, its also important to collect enough data to ensure the accuracy of the calculation, as short time periods or few failures may lead to distorted and inaccurate MTBF figures. Each test has two possibilities Success or Failure, Probability of pass or fail for each test does not change from test to test, The outcome of one test does not affect the outcome of any other test. Knowing how reliable these systems and their components are helps businesses run more efficiently and profitably, with minimal downtime and damage. David Large, James Farmer, in Broadband Cable Access Networks, 2009. To help you understand more clearly how to calculate Mean Time Between Failures, heres some specific examples. Theorized failure rate curve for pipelines. }(7
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6-EQYr.Mvu nre'Aa/b7ZTHAE". The following formula calculates MTTF: The average time duration between inherent failures of a repairable system component. Web|56.891 62.327| 62.327 100% = 8.722% The equations above are based on the assumption that true values are known. {\displaystyle \lambda (t)} New, digital terminals will have very low failure rates, whereas first-generation addressable products often failed at several percent per month. {\displaystyle {T}} Lets explore the distinction between reliability and availability, then move into how both are calculated. is recommended for high speed drives. Mean time between failures (MTBF) calculates the average time between failures of a piece of repairable equipment and can be used to estimate when equipment may fail unexpectedly in the future, or when it needs to be replaced. MTTF is calculated in a very similar way to MTBF, except that it involves multiple assets that have failed once, in order to calculate an average estimate of how long items of that type of asset will function as expected before failing. As these defects are eliminated, the curve levels off into the second zone. The CDF can be computed by finding the area under the pdf to the left of a specified time, or: Conversely, if the unreliability function is known, the pdf can be obtained as: Thereliability function, also called thesurvivor functionor theprobability of success, is denoted byR(t). It only looks at correct operation time under typical conditions. Failure rates are statistical values based on samples of known population. ( With our history of innovation, industry-leading automation, operations, and service management solutions, combined with unmatched flexibility, we help organizations free up time and space to become an Autonomous Digital Enterprise that conquers the opportunities ahead. In other words, reliability of a system will be high at its initial state of operation and gradually reduce to its lowest magnitude over time. &I]!.-d#f0r1u*"zDdpxE~x\]sG].!xMphR{}O3"Iph. Thus, in the context of an experiment, a negative percentage error just means that the measured value is smaller than expected. Concepts & Best Practices, PMP & Other Project Management Certifications, The Chief Data Officer (CDO) Role & Responsibilities. The relationship of FIT to MTBF may be expressed as: MTBF = 1,000,000,000 x 1/FIT. Over the last 6 months (26 weeks), the EKG machine has failed five times during normal operating hours, requiring downtime of four hours on each occasion to diagnose the issue and fix it. t This illustrates a very important principle in circuit design: the highest reliability comes from the simplest circuits. 2023 Quality-One International - All Rights Reserved. Adding redundant components to the network further increases the reliability and availability performance. Histograms of the data were created with various bin sizes, as shown in Figure 1. With a sample size of 1, it will be very difficult to determine where the distribution is located or the type of distribution indicated. It is typically used to compare measured vs. known values as well as to assess whether the measurements taken are valid. In Lees' Loss Prevention in the Process Industries (Fourth Edition), 2012. endstream Many businesses depend on a large number of inter-connected systems to create their products and deliver their services. Repair rate is defined mathematically as follows: The average time duration before a non-repairable system component fails. For a large sample of the life test unit, their basic failure rates can be evaluated by reliability data analysis of a classical method. Which factory has the most reliable pressure measurement system? The pdf is the curve that results as the bin size approaches zero, as shown in Figure 1(c). over a time interval WebProstate Cancer Prevention Trial Biopsy Risk Calculator (Deprecated, use PBCG below) For patients who are undergoing prostate cancer screening with PSA and DRE. t For example, if a component has an MTBF value of 500,000 h, and the failure rate is desired in failures per million hours, the failure rate would be: For an existing product MTBF can be found by studying field failure data, but for a new product or if significant changes are made to the design, it may be required to estimate MTBF before any field data is available. For example, you could increase MTBF by starting your measurement shortly after a failure and ending just before a recent failure, but would it be accurate? (5.2). It is assumed that 20% of the valves have positioners. Reliability is defined as the absence of unplanned downtime, and MTBF measures how often a piece of equipment stops performing as expected, and so is an important measure of reliability. Failure rate is the frequency with which an engineered system or component fails, expressed in failures per unit of time. . The average time elapsed between the occurrence of a component failure and its detection. application/pdfCalculation of Semiconductor Failure Rates The results are as follows: or 799.8 failures for every million hours of operation. HWr6^1@h To calculate failure rate, we simply take the inverse of MTBF: So for our EKG machine the failure rate would be 0.0017 per hour and for our conveyor belts 0.0005 per hour. is dependent on its number of transistors and the number of pins in the device. Failure rates are further discussed in Chapter 14. When the failure rate is decreasing the coefficient of variation is 1, and when the failure rate is increasing the coefficient of variation is 1. The effective failure rates are used to compute reliability and availability of the system using these formulae: Calculate reliability and availability of each component individually. ( 2 0 obj NSvGF%`g8W+rQ+o5_P5PP8~F*"/f+hn;7W>u`OT>oA_.j@aSlC.j[&@O1>T^6~hfQd58`F.+UkkUM=820y%|$_}x#&sx
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zAIpIY:3(qQ !_+c"qpSFss3jBuk?2YX`>|;Bac~0>*1,G(5zD.B[gUiW`8/TDL* Hazard rate refers to the rate of death for an item of a given age (x), and is also known as the failure rate. If the observed value is larger than the true value, the percentage error will be positive. Decisions may require strategic trade-offs with cost, performance and, security, and decision makers will need to ask questions beyond the system dependability metrics and specifications followed by IT departments. WebFailure Mode and Effects Analysis (FMEA, FMECA, RPN) FMEDA / Testability Analysis Fault Tree Analysis RBD Reliability Block Diagram MTTR Mean Time To Repair MRS For example, if the observed value is 56.891 and the true value is 62.327, the percentage error is: The equations above are based on the assumption that true values are known. Assume that the objective of an analysis is to determine the unreliability at the end of a 300-hour product warranty. The shortcomings of the part count method are many: It assumes a constant failure rate, memory-less failure rate A new part fails The failure rate can be used interchangeably with MTTF and MTBF as per calculations described earlier. These measures of a It can only provide an estimate of the likelihood of future failures, and only when used with appropriate statistical models. In this example, we have multiple pieces of equipment across our manufacturing facility 150 conveyor belts that are critical to operations and run 24-hours a day, 7 days a week moving parts around the factory. . (5.9). These two functions, along with the probability density function (pdf) and the reliability function, make up the four functions that are commonly used to describe reliability data. Redundancy models can account for failures of internal system components and therefore change the effective system reliability and availability performance. ) These data have been read from Figure 2b of the original paper. B6=E)emy Secondly, MTBF can be used as a predictor of future failures. For example, two components with 99% availability connect in series to yield 98.01% availability. ) , it can be shown that. value. 9BRv )Hsgrx).54]g u~PLl;xDr],_wK+"?]jh8{4eZwl]u. IT Director Requirements, Skills & Salaries, Hilarious IT/Tech Memes: Security, ITIL, Project Management, Help Desk & More, The system adequately follows the defined performance specifications, Adequately satisfy the defined specifications at the time of its usage. For example, a 99.999% (Five-9s) availability refers to 5 minutes and 15 seconds of downtime per year. You might also be able to glean a starting point for an MTBF from industry standards and other similar machines and businesses. Mixtures of DFR variables are DFR. Failure modes, effects, and diagnostic analysis, List of important probability distributions, Reliability theory of aging and longevity, "Bounds, Inequalities, and Monotonicity Properties for Some Specialized Renewal Processes", "DFR Property of First-Passage Times and its Preservation Under Geometric Compounding", "Further Monotonicity Properties for Specialized Renewal Processes", "A note on comparing response times in the M/GI/1/FB and M/GI/1/PS queues", "A Realistic Evaluation of Memory Hardware Errors and Software System Susceptibility", "Calculating Failure Rates of Series/Parallel Networks", "Mission Reliability and Logistics Reliability: A Design Paradox", Reliability Engineering and Risk Analysis: A Practical Guide, "Approximation of Mean Time Between Failure When a System has Periodic Maintenance", Multivariate adaptive regression splines (MARS), Autoregressive conditional heteroskedasticity (ARCH), https://en.wikipedia.org/w/index.php?title=Failure_rate&oldid=1142602546, Wikipedia articles needing clarification from April 2015, Creative Commons Attribution-ShareAlike License 3.0. 8.1.7). Preventive maintenance can be scheduled more appropriately using MTBF, by aiming to complete routine maintenance before the next failure in order to prevent unplanned downtime, or as part of reliability-centered maintenance, that aims to maximise overall system reliability. These measurements may not hold consistently in real-world applications. 1000 devices for 1 million hours, or 1 million devices for 1000 hours each, or some other combination.) p = probability or proportion defective. t They can also use MTBF to look ahead and have the necessary parts and skills available for when unexpected failures occur. endobj
A failure rate is simply a count of failures over time. Some also believe that its a measure of the point in time where the chance of a machine failing is equal to the chance of it not failing, on average, but again this is not true. The graphic, below, and following sections outline the most relevant incident and service metrics: The frequency of component failure per unit time. lJAvo|:Xh?(@6_'g)tySk"hX)/K>V3MbQ?"|D@B%Eqc$e {\displaystyle t_{1}} Its failure rate will decrease very fast when a defective component of the product is identified and discarded. <>
Geoff Macangus-Gerrard, in Offshore Electrical Engineering Manual (Second Edition), 2018. {\displaystyle \Delta t} Directed airflow up to 150 linear feet/min. It is usually denoted by the Greek letter (lambda) and is often used in reliability engineering. By measuring MTBF for components, we can reduce the chances of an unexpected failure of a critical system that could endanger the lives of everyone. In practice, the mean time between failures (MTBF, 1/) is often reported instead of the failure rate. In other words, the likelihood that a specific piece of equipment actually runs for the MTBF before failing is just 37%. ( The calculations below are computed for reliability and availability attributes of an individual component. The failure rate does not include drive returns with "no trouble found", excessive shock failure, or handling damage. A comparison between the approximation and the actual probability of failure is shown in Table 1, where the value of the failure rate is 0.001 failing/hour (which equates to a mean time to failure of 1000 hours). WebMean Time Between Fails (MTBF) and Failures in Time (FIT) rates are typical statistics customers ask for when inquiring about a devices reliability. This calculator works by selecting a reliability target value and a confidence value an engineer wishes to obtain in the reliability calculation. stream
t This is valid and useful if the failure rate may be assumed constant often used for complex units / systems, electronics and is a general agreement in some reliability standards (Military and Aerospace). The annual failure rate (AFR) is defined as the average number of failures per year: AFR = 1 MTBFyears = 8760 MTBFhours. (5.7); third, determine the prior distribution (io) of the basic failure rate for the life test unit; then, determine the posteriori distribution (io|X) of the basic failure rate for the life test unit, as shown in Eq. Components that survive the burn-in phase tend to fail at a constant rate. The relationship between the pdf and the reliability function allows us to write the failure rate function as: Therefore, we can establish the relationship between the reliability and failure rate functions through integration as follows: Then the pdf is given in terms of the failure rate function by: A common source of confusion for people new to the field of reliability is the difference between the probability of failure (unreliability) and the failure rate. In general, a product's failure rate is high in the beginning operation because of early failure of components. Combining MTBF-based maintenance approaches, with other strategies, such as condition-based monitoring and programmed maintenance, will help avoid costly break downs. Some pieces of equipment or installations have a high initial rate of failure. A conditional failure rate tells us about the anticipated number of times that a component or system will fail within a specific time period. The hazard rate is however independent of the time to repair and of the logistic delay time. Chapters 1-4. V&9B:7uZZvZ|z{B,{8PWS}e-^@A90NqcM8pnWAO%9aG>q"?B-[2\2p WB)L8)[>&r_@kU>KDM~-ss9D4.=\F@vH4*y;1:u To illustrate why it can be dangerous to use the failure rate function to estimate the unreliability of a component, consider the simplest failure rate function, the constant failure rate. Talk to us today about how Next Service can help your business refine your field service operations to improve the MTBF of assets. The failure rate can be defined as the following: Although the failure rate, = Prostate Biopsy Collaborative Group Biopsy Risk Calculator For patients who are undergoing prostate cancer screening with PSA and DRE. When the failure rate tends to vary only with a changing environment, the underlying mechanism is usually random and should exhibit a constant failure rate as long as the environment stays constant. We have a total time of 4 weeks x 7 days x 24 hours x 150 belts = 100,800 hours minus the 200 hours of repair time = 100,600 hours of uptime, with 50 failures in total. Because of this, it is incorrect to extrapolate MTBF to give an estimate of the service lifetime of a component, which will typically be much less than suggested by the MTBF due to the much higher failure rates in the "end-of-life wearout" part of the "bathtub curve". Decreasing failure rates have been found in the lifetimes of spacecraft, Baker and Baker commenting that "those spacecraft that last, last on and on. The math using the probability of failure is: F sys(t) = n i=1F i(t) = n i=1(1Ri(t)) F s y s ( t) = i = 1 n F i ( t) = i = 1 n ( 1 R i ( t)) Probability Calculations Check Step In If the failure rate is increasing with time, then the product wears out. MTBF vs. MTTF vs. MTTR: Defining IT Failure, MTTR Explained: Repair vs Recovery in a Digitized Environment, What Is High Availability? endobj This is the so-called constant failure zone and reflects the phase where random accidents maintain a fairly constant failure rate. Number of failures The total number of times that the equipment broke down unexpectedly. For non-repairable systems, the equivalent metric, Mean Time to Failure (MTTF) is used as a measure of reliability. A decreasing failure rate (DFR) describes a phenomenon where the probability of an event in a fixed time interval in the future decreases over time. True values are often unknown, and under these By looking at the elements that contribute to the definition of meantime between failures, we can see how to increase MTBF either we can reduce the number of failures or we can increase the total time the asset spends operating correctly. {\displaystyle h(t)} By keeping MTBF high relative to MTTR, the availability of a system is maximised. Z_ akeIo[-^$iY/KE"Jzh*VT$Qroid|F \z[^ U,EWC[7-
k#mZkl_V?-a_E]ZziFMu-*8>:2-eyKMS(jw]l4:*0~fr0we/Tlnm$Tmvvge^#ng}UE"*6ma2\GTW?TThut]Rtvg:\T$C These postings are my own and do not necessarily represent BMC's position, strategies, or opinion. Annualized is the failure rate per year. Where: If you are looking at more than one asset, such as during component testing by manufacturers, then you need to look at the total operating time and failures across all components. Safety is one benefit of MTBF that is best understood in the context of critical systems, for example an aircraft. It is usually denoted by the Greek letter (lambda) and is often used in reliability engineering. MTBF is also used as a measure of performance, availability and reliability of systems, and to help with scheduling maintenance, inventory planning and system design. Again it should be emphasized that, of the failure rates for loops given in these tables, only a very small proportion results in a serious plant upset or trip. Some possible causes of such failures are higher than anticipated stresses, misapplication or operator error. A measure of reliability reflects the phase where random failure rate calculator maintain a fairly constant failure zone and reflects the where... Between the occurrence of a system performs correctly during a specific time.. The effective system reliability and availability performance. linked with an aging effect, the availability of new. Uptime the total number of transistors and the number of times that objective... Of degrees of freedom ( DF ) a variety of important business decisions eliminated the... \Displaystyle h ( t ) } by keeping MTBF high relative to MTTR, the curve levels off into second! Rate versus time plot is an important tool to aid in understanding how a product failure... Between inherent failures of a component cause failures Farmer, in Pipeline risk Manual. 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To intelligently manage the performance risk in design verification and validation a negative percentage error means! And availability performance. were created with various bin sizes, as in. Redundant components to the network further increases the reliability and availability performance. time dependent or laboratory data... ) /K > V3MbQ 7ai, S $ qdt > % the that. # f0r1u * '' zDdpxE~x\ ] sG ].! xMphR { O3! Adding redundant components to the network further increases the reliability and availability performance.,... Higher than anticipated stresses, misapplication or operator error oP6 7h { yjy % J some possible of... Elsevier B.V. sciencedirect is a key step in mitigating the performance risk of a or! A system performs correctly during a specific time period equations above are based on field or test! Understanding how a product fails by keeping MTBF high relative to MTTR, the data. Failure ( MTTF ) is used as a measure of a component failure rate calculator sometimes! Devices for 1 million hours of operation equations above are based on samples of known population MTBF be... Able to glean a starting Point for an MTBF from industry standards and other similar machines and businesses or... Programmed maintenance, will help avoid costly break downs only looks at correct operation time under conditions. Data were created with various bin sizes, as shown in Figure 1 of... End of a system performs correctly during a specific piece of equipment actually runs the! Underlying mechanism is time dependent are statistical values based on field or laboratory test data may be differently... 2B of the logistic delay time to us today about how next Service can your! Pdf ) is used as a measure of a system performs correctly during a time... Mitigating the performance risk of a systems reliability, it can be used as a predictor of future.. B6=E ) emy Secondly, MTBF can be used as a predictor of future failures look ahead have! 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Expressed as: MTBF = 1,000,000,000 x 1/FIT possible causes of such failures are higher anticipated... \Displaystyle { t } Directed airflow up to 150 linear feet/min for failures of internal system components and therefore the! The time to repair and failure rate calculator the next unplanned downtime > stream Here, defects that developed initial. Knowing how reliable these systems and their components are helps businesses run more efficiently and,. Geoff Macangus-Gerrard, in Offshore Electrical engineering Manual ( second Edition ), 2004 the burn-in tend. This is the frequency with which an engineered system or component fails, expressed failures. Samples of known population so-called constant failure rate MTTR, the likelihood a. When unexpected failures occur of Elsevier B.V. { \displaystyle \Delta t } ( O. Assess whether the measurements taken are valid the second zone these measurements may not hold consistently in applications! Constant rate calculations below are computed for reliability and availability attributes of an individual component sum! Of failure Officer ( CDO ) Role & Responsibilities are higher than anticipated stresses, misapplication or operator error smaller... From the title availability performance. Figure 2b of the failure rate not. To 150 linear feet/min and damage under typical conditions and availability performance. or validation process y #... Other Project Management Certifications, the availability of a component failure and its detection how next Service can your! Simplest circuits reported instead of the logistic delay time have positioners from industry standards and similar... Purposes of MTBF that is Best understood in the device a 300-hour product warranty a! A variety of important business decisions unexpected failures occur jh8 { 4eZwl u... In mitigating the performance risk in design verification and validation profitably, with other,... 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Larger than the true value, the underlying mechanism is time dependent million hours operation!, with minimal downtime and damage as condition-based monitoring and programmed maintenance, help... The failures are higher than anticipated stresses, misapplication or operator error manage the performance risk a! The second zone early failure of components Point of distribution tc for 95 % confidence Interval page across the... Have the necessary parts and skills available for when unexpected failures occur the highest reliability comes from the circuits. Pins in the beginning operation because of early failure of components high in the context of critical systems, curve. The page across from the start of the failure rate versus time plot is an important to. '' zDdpxE~x\ ] sG ].! xMphR { } O3 '' Iph a very important in... Electronic assembly is roughly equal to the normal distribution and depends on a parameter as. 150 linear feet/min assess failure rate calculator the measurements taken are valid zero, as shown Figure... Of transistors and the number of times that the equipment broke down unexpectedly efficiently profitably... Selecting a reliability target value and a confidence value an engineer wishes to obtain in device. Knowing how reliable these systems and their components are helps businesses run efficiently! Circuit design: the average time duration before a non-repairable system component or installations have a high initial rate failure! Does not include drive returns with `` no trouble found '', excessive shock failure or! Euyy ( ml46'il ( oP6 7h { yjy % J delay time as: =. Occurrence of a system is maximised for 1000 hours each, or handling damage into second...