
Accession Number : AD0617096
Title : TESTS FOR MONOTONE FAILURE RATE.
Descriptive Note : Mathematical note,
Corporate Author : BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH
Personal Author(s) : Proschan,Frank ; Pyke,Ronald
Report Date : MAR 1965
Pagination or Media Count : 47
Abstract : Physical considerations often lead one to expect that a distribution has increasing failure rate, and knowledge of increasing failure rate is mathematically useful in solving a variety of practical problems. In this paper, a nonparametric test to determine whether a sample comes from a population possessing an increasing failure rate is proposed and investigated. The test statistic is based only on the ordering of normalized spacings between the ordered observations. The distribution of the test statistic under the null hypothesis of constant failure rate is known. Suitably normalized, it is shown to be asymptotically normally distributed for a wide class of alternatives. In particular, under mild assumptions, when the underlying distribution has increasing failure rate, the test statistic is asymptotically normally distributed. The test is shown to be unbiased. The criterion of asymptotic relative efficiency is used to compare the test proposed with the likelihood ratio test for Weibull alternatives and with the likelihood ratio test for Gamma alternatives. (Author)
Descriptors : (*STATISTICAL TESTS, FAILURE(MECHANICS)), (*FAILURE(MECHANICS), STATISTICAL TESTS), RELIABILITY, STATISTICAL DISTRIBUTIONS, OPERATIONS RESEARCH
Distribution Statement : APPROVED FOR PUBLIC RELEASE