A Two-Sample Test for Reliability Comparison

Abstract

A new test for the comparison of reliabilities of two populations is proposed. The test statistic uses only the number of failures in each sample. The test procedure is conditional in the sense that the unknown parameter p, the probability of failure during the test period, under the null hypothesis is estimated first by the pooled sample proportion. Critical values are tabulated for several equal sample size cases and asymptotic properties are obtained. The use of this test in practice is illustrated by several examples. It is shown that the power of the proposed test is larger than that of Fisher's exact test for the cases considered. Applications in survival analysis are also studied, and the power of the test procedure is compared with those of other tests, which are based on failure times in addition to failure counts.

Keywords:

• Reliability comparison
• Life testing
• Censored data
• Binomial distribution
• Two-sample test
• Power
• Failure times
• Conditional distribution