What is a typical approach to modeling the reliability of a repairable system?

As an example, Figure 1 presents a simple reliability block diagram of a system and Table 1 summarizes a hypothetical assembly level set of failure rate data.  Failure rates for the individual “boxes” of the model can be derived from field failure rate data on exact or similar hardware.  If actual field data is unavailable from fielded systems, failure rates can be developed from published values for electronic components in handbooks such as Reliability Analysis Center (RAC) data books, RAC PRISM software, Bellcore, or MIL-HDBK-217 (Reliability Prediction of Electronic Equipment). These component level failure rates are summed to estimate expected “box” level failure rates.  

It should be noted that a limitation of using published data is that it becomes outdated quickly as technological advancements are made to improve component designs and manufacturing processes.  Never the less, published data from handbooks such as MIL-HDBK-217 are periodically updated and provide a starting point for system analysis when no other data sources exist.  

For this discussion, it should be noted that these failure rates are assumed to represent randomly occurring failures in the useful life portion of the bathtub curve.  Adjustments shown in Table 1 are to account for the application environment (i.e., aircraft versus ground).  Other adjustments can be made to account for different conditions, such as duty cycle, temperature and part screening.  common adjustment factors for a component’s electrical, thermal and mechanical stresses exist in MIL-HDBK-217.  Thus for this example, the series failure rate, which is simply every “box” in series (all must work) is 259 failures per million hours (FPMH).  Taking the reciprocal of this results in a mean-time-between-failure (MTBF) of 3861 hours.   The modeling of redundant configurations will be discussed elsewhere in these FAQ.

Figure 1 - Hypothetical Personal Computer System Model

Table 1 - Summary of Failure Rates (FPMH = Failures per Million Hours)