On the Determination of a Safe Life for Distributions Classified by Failure Rate

If the distribution of life length is a member of a specified subset of distributions which have increasing failure rates, we find a method of determining functions of the sample data which can be used to provide lower tolerance bounds of given confidence or a service life with specified assurance of no failures among a given number of items to be produced. The method of finding such functions of the observations is shown to be optimal in a sense and the calculation of a lower bound for the probability of no failure in the future production is carried out when such functions are used. The confidence in the tolerance bound and the assurance of no failure in a production lot of specified size are compared when using bounds obtained from these functions.