Chapter 14* Life Testing
14.1 Introduction
In this chapter, we consider a population of items having lifetimes that are assumed to
be independent random variables with a common distribution that is specified up to an
unknown parameter. The problem of interest will be to use whatever data are available to
estimate this parameter.
In Section 14.2, we introduce the concept of the hazard (or failure) rate function — a
useful engineering concept that can be utilized to specify lifetime distributions. In
Section 14.3, we suppose that the underlying life distribution is exponential and show
how to obtain estimates (point, interval, and Bayesian) of its mean under a variety of
sampling plans. In Section 14.4, we develop a test of the hypothesis that two exponen-
tially distributed populations have a common mean. In Section 14.5, we consider two
approaches to estimating the parameters of a Weibull distribution.
14.2 Hazard Rate Functions
Consider a positive continuous random variableX, that we interpret as being the lifetime
of some item, having distribution functionFand densityf. Thehazard rate(sometimes
called thefailure rate) functionλ(t)ofFis defined by
λ(t)=f(t)
1 −F(t)To interpret λ(t), suppose that the item has survived fort hours and we desire
the probability that it will not survive for an additional timedt. That is, consider
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