CONFIDENCE INTERVAL FOR THE CRITICAL TIME OF INVERSE GAUSSIAN FAILURE RATE

Abstract

Critical time is the point at which the failure rate attains its maximum and then decreases. For the inverse Gaussian distribution, the critical time always exists and can be used as a guide for conducting burn-in. In this paper, we use two different reparametrization schemes to establish monotonicity property of critical time. This property is then used to obtain exact confidence intervals for the critical time when either one of the parameters of the inverse Gaussian distribution is known. When both parameters are unknown we construct an analytically exact confidence interval for the critical time that guarentees the desired coverage probability. An approximate confidence interval, motivated by conservative nature of the above bound, is also proposed. Monte-Carlo simulation is conducted to investigate the performance of the two confidence intervals in terms of the their coverage probability and average width. Finally, a numerical example on repair time data is provided to illustrate the procedure.