ABSTRACT
This chapter considers a homogeneous population of individuals, each having a 'failure time'. It deals with a single nonnegative random variable, T. The chapter examines the general specification of the distribution of T and also considers various special distributions that are useful. Particular forms of distribution may be useful either because they are suggested by some theoretical argument or because they provide flexible empirical representations, preferably with relatively simple statistical analysis. The exponential distribution was widely used in early work on reliability of, for example, electronic components and to a more limited extent in medical studies. The Weibull distribution arises theoretically as a limit law for the smallest of a large number of independent nonnegative random variables, thus generalizing the result already noted for the exponential distribution. J. W. Boag gave several sets of hospital cancer data and showed that the log normal distribution gives a rather better fit than the exponential.
