On the assessment of tolerance limits under inverse Gaussian distribution
Inverse Gaussian distribution has been used in a wide range of applications in modeling duration and failure phenomena. In these applications, one-sided lower tolerance limits are employed, for instance, for designing safety limits of medical devices, Tang and Chang (1994) proposed lowersided tolerance limits via Bonferroni inequality when parameters in the inverse Gaussian distribution are unknown. However, their simulation results showed conservative coverage probabilities, and consequently larger interval width. In their paper, they also proposed an alternative to construct lesser conservative limits. But simulation results yielded unsatisfactory coverage probabilities in many cases. In this article, the exact lower-sided tolerance limit is proposed. The proposed limit has a similar form to that of the confidence interval for mean under inverse Gaussian. The comparison between the proposed limit and Tang and Chang's method is compared via extensive Monte Carlo simulations. Simulation results suggest that the proposed limit is superior to Tang and Chang's method in terms of narrower interval width and approximate to nominal level of coverage probability Similar argument can be applied to the formulation of two-sided tolerance limits, A summary and conclusion of the proposed limits is included.
tolerance limit bonferroni inequality confidence interval monte carlo simulation