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52 Main articles: reliability theory, failure rate.

80 Furthermore, based on latest insights in Reliability centered maintenance (RCM), most (complex) system failures do no occur due to wear-out issues (e.g. a number of 4% has been provided, refer to RCM page). The failures are often a result of combinations of more and multi-type events or failures. The results of these studies have shown that the majority of failures follow a constant failure rate model, for which prediction of the value of the parameters is often problematic and very time consuming (for a high level reliability - part level). Testing these constant failure rates at system level, by for example mil. handbook 781 type of testing, is not practical and can be extremely misleading.

98 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.

101 For such systems, the probability of failure on demand (PFD) is the reliability measure - which actually is a 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.

109 Early failure rate studies determine the distribution with a decreasing failure rate over the first part of the bathtub curve. (The bathtub curve only holds for hardware failures, not software.) Here in general only moderate stress is necessary. The stress is applied for a limited period of time in what is called a censored test. Therefore, only the part of the distribution with early failures can be determined.

110 In so-called zero defect experiments, only limited information about the failure distribution is acquired. Here the stress, stress time, or the sample size is so low that not a single failure occurs. Due to the insufficient sample size, only an upper limit of the early failure rate can be determined. At any rate, it looks good for the customer if there are no failures.

112 It is a general praxis to model the early (hardware) failure rate with an exponential distribution. This less complex model for the failure distribution has only one parameter: the constant failure rate. In such cases, the Chi-squared distribution can be used to find the goodness of fit for the estimated failure rate. Compared to a model with a decreasing failure rate, this is quite pessimistic (important remark: this is not the case if less hours

113 load cycles are tested than service life in a wear-out type of test, in this case the opposite is true and assuming a more constant failure rate than it is in reality can be dangerous). Sensitivity analysis should be conducted in this case.

163 The purpose of accelerated life testing 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:

stress

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