** Accession Number : **AD0003584

**Title : **SOME RESULTS ON TRUNCATED LIFE TESTS IN THE EXPONENTIAL CASE

**Descriptive Note : **Technical rept.

**Corporate Author : **WAYNE STATE UNIV DETROIT MI

** Personal Author(s) : **Epstein, Benjamin

**Full Text : **https://apps.dtic.mil/dtic/tr/fulltext/u2/003584.pdf

**Report Date : **15 Feb 1953

**Pagination or Media Count : **24

**Abstract : **Life tests are considered which are truncated so that n items a re placed on test; an advance decision requires that the experiment be terminated at min (X sub r sub o, sub n, T sub o), where X sub r sub o, sub n is a random variable equal to the time at which the r sub o 'th failure occurs and T sub o is a truncation time beyond which the experiment will not run. Both r sub o and T sub o are assigned before experimentation starts. If the experiment is terminated at X sub r sub o, sub n (r sub o failures occur before time T sub o) or at time T sub o (the r sub o 'th failure occurs after time T sub o) then the action in terms of hypothesis testing is the rejection or acceptance, respectively, of some specified null hypothesis. While truncated procedures can be considered for any life distribution, restrictions are made to the case where the underlying life distribution is specified by a pdf (probability distribution function) of the exponential form, f(x; theta) = 1/theta sub e to the -x power/theta, x 0, theta 0. Two situations are considered. The first is the nonreplacement case where a failure which occurs during the test is not replaced by a new item. The second is the replacement case where failed items are replaced at once by new items drawn at random from the same pdf as the original n items. Formulas are given for E sub theta (r), the expected number of observations to come to a decision; E sub theta (T), the expected waiting time for reaching a decision; and L (theta), the probability of accepting the hypothesis that theta = theta sub o (theta sub o being the value associated with the null hypothesis) when theta is the true value. Procedures are worked out for finding truncated tests meeting specified conditions.

**Descriptors : **
*PROBABILITY DISTRIBUTION FUNCTIONS
,
*LIFE TESTS
,
TEST AND EVALUATION
,
LIFE EXPECTANCY(SERVICE LIFE)
,
TIME
,
REPLACEMENT
,
NULLS(AMPLITUDE)
,
HYPOTHESES
,
TRUNCATION

** Subject Categories : **Statistics and Probability

Operations Research

**Distribution Statement : **APPROVED FOR PUBLIC RELEASE