Some basic properties of the Failure Rate of Redundant Reliability Systems in Industrial Electronics Applications

The paper discusses some common reliability architectures, such as "parallel" and "k-out-of-n" systems, adopted to add redun-dancy in many modern industrial systems, such as parallel-inverter systems. The focus is on some crucial properties of the failure rate of such systems, motivated by the fact that, in applied literature, the system failure rate is often simply evaluated as the reciprocal of the "Mean Time To Failure" of the system. Howev-er, this relationship is valid if, and only if, the system has a "se-ries" reliability architecture. This is indeed the only case in which also the system has a constant failure rate, i.e. an Exponential lifetime distribution. Instead, the system failure rate of redundant systems is a func-tion of time, which can never be constant. It is simply shown in-deed that the failure rate of a parallel system with constant fail-ure rate components is an increasing, or "first increasing, then decreasing" function of time, eventually reaching the value of the smallest failure rate. These results are extended to "k-out-of-n" reliability systems, and also to more general reliability models with non-constant failure rate, such as the Weibull or the "bath-tub" model.