26.1 Introduction

The objective of this chapter is to describe statistical methods for reliability data analysis, in a manner which gives the flavor of modern approaches. The chapter commences with a description of five examples of different forms of data encountered in reliability studies. These examples are from recently published papers in reliability journals and include right censored data, accelerated failure data, and data from repairable systems. However, before commencing any discussion of statistical methods, a formal definition of reliability is required. The reliability of a system (or component) is defined as the probability that the system operates (performs a function under stated conditions) for a stated period of time. Usually the period of time is the initial interval of length t, which is denoted by [0, t). In this case the reliability is a function of t, so that the reliability function R(t) can be defined as:

where P(A) denotes the probability of an event A, say. This enables the various features of continuous distributions, which are used to model failure times, to be introduced. The relationships between the reliability function, the probability density function, and the hazard function are detailed. Then there is an account of statistical methods and how they may be used in achieving the objectives of a reliability study. This covers the use of parametric, semi-parametric, and non-parametric models.

26.2 Nature of Reliability Data

To achieve the objectives of a reliability study, it is necessary...