Application of Bayesian decision theory to the reliability of standby systems

Since many safety systems are standby systems, they remain idle during most of their useful lifetime. There is a certain possibility that the equipment in these systems may fail prior to demand and make the systems inoperable. To avoid such a situation one may periodically check a standby system to see whether it is operable (good) or inoperable (bad). The likelihood that the system will be unavailable upon demand may be decreased by periodic testing. Moreover, the test interval becomes an important parameter that can be readily adjusted to meet reliability specifications.;In this work a method for making an assessment of safety for standby system using techniques of Bayesian decision theory is presented. When selecting a functional test interval, one would like to determine the optimal number of tests that will meet the reliability goal with a given level of assurance. This analysis concentrates on the reliability of the standby systems that are normally inactive, and deteriorate with time according to the Weibull model. Two questions are considered: (a) What is the probability that the believed reliability is greater than some threshold value, ;In this dissertation, a closed form is derived for the r;Application of preposterior analysis to both modes with the exponential and Weibull models has shown that no functional testing program can ensure a satisfactory reliability system for the transitory mode. However, a satisfactory program is feasible for the persistent failure mode. For the transitory mode, a periodic preventive maintenance program is required when the system reliability is assumed to be exponential. But, when the system reliability follows a Weibull model, a change of parts, redesign, or a new system is required.