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Confidence Bounds on Reliability for the Inverse Gaussian Model

The inverse Gaussian distribution is considered as a lifetime model. First, the MLEs of the mean and shape parameters of the inverse Gaussian model are discussed, and s-confidence bounds for those parameters are given. Then the problem of obtaining s-confidence bounds for the reliability is considered for two cases: i) When the shape parameter is known and mean is unknown, s-confidence intervals for reliability are relatively easily derived. ii) If the shape parameter is unknown and mean is known, then lower s-confidence bounds (LCBs) on reliability must be approximated for time > mean due to the fact that the reliability function is not monotone increasing in shape parameter for those values of time. The performance of the approximate LCBs is investigated by computer simulation. The measure of performance is the relative frequency of computed LCBs that are actually less than the true reliability in the simulations. Also, the average LCB (ALB) at each time t is computed. The relative frequency and ALB both indicate very good performance of the approximate bounds.