Reliability of stochastic systems

INTRODUCTION

The coming decades may well be known for the popularization of the Q word– quality . Phrases like quality circles, total quality management, and total quality integration practically became household words, even though old standbys like quality control and quality assurance have been the subject of study of industrial engineers and statisticians for many of the preceding decades. Intricately related to quality, in fact, a necessary ingredient, is reliability, loosely defined as the probability that a system, subject to random failures, will perform properly over some time span of interest. This definition shall be made more precise in the following. One might be able to have reliability without quality, but one can never have quality without reliability.

The major issue here is a consideration of the probability structure of systems made up of individual components, each with a known lifetime density, say, f _i(t). The two basic combinations of system design are the series...