Some Basic Properties of the Failure Rate of Redundant Reliability Systems in Industrial Electronics Applications

This paper discusses some common reliability architectures, such as “parallel” and “k out of n” systems, adopted to add redundancy in many modern industrial systems, such as parallel-inverter systems. The focus is on some crucial properties of the failure rate (FR) of such systems, motivated by the fact that, in applied literature, the system FR is often simply evaluated as the reciprocal of the “Mean Time To Failure” of the system. However, this relationship is valid if, and only if, the system has a “series” reliability architecture. This is indeed the only case in which also the system has a constant FR, i.e., an Exponential lifetime distribution. Instead, the system FR of redundant systems is a function of time, which can never be constant. It is simply shown indeed that the FR of a parallel system with constant FR components is an increasing, or “first increasing, then decreasing” function of time, eventually reaching the value of the smallest FR. These results are extended to k out of n reliability systems, and also to more general reliability models with nonconstant FR, such as the Weibull or the “bathtub” model.