Hazard Functions, Renewal Rates and Peril Rates

Reliability models appropriate to 1) non-repairable parts, 2) sockets and 3) repairable systems are presented. It is shown that a renewal process is usually appropriate as a model for a socket but generally is implausible as a repairable system model. Several models for repairable systems are proposed. These include a model where system state depends only on the total age of the system and models where system state is a function of total age and the total number of part replacements. Then, it is shown that the applicability of any given probabilistic model to a given system is questionable because of many “real world” factors which are difficult to treat probabilistically. Therefore, it is proposed that the statistical approach is the proper one in determining how real systems behave. The reliability community is called upon to present all available data and appropriate analyses in order to establish a firm empirical foundation for repairable system reliability.

In Appendix A the distribution of the interarrival time to second system failure of a two part system is derived. Based on this result, Appendices B and C demonstrate that (when nothing is known about the first failure) the interarrival times to first and second system failures will be independently and identically distributed if, and only if, both parts have constant hazard functions. Relaxation of the constant hazard function requirement when information about the first failure is available is discussed in Appendix B.