STATISTICAL INFERENCE ABOUT AVAILABILITY OF SYSTEM WITH GAMMA LIFETIME AND REPAIR TIME

Abstract

Availability is an important measure of performance of repairable system. The steady state system availability has special importance since it demonstrates the performance of a system after it has been operated for long. The statistical inference about the steady state availability are particularly useful for practitioners. Much work has been done in this regard. Most of these researches proposed certain pivotal quantities for constructing confidence intervals of the steady state availability. Assuming both the lifetime and repair time follow gamma distribution with known shape parameters and unknown scale parameters, we propose a pivotal quantity for making inferences, and further derive the likelihood ratio tests. Tables of critical values are given for the convenience of applying the two-sided likelihood ratio test. Confidence intervals are also obtained by converting the acceptance regions.