Reliability bounds and tolerance limits of two inverse Gaussian models

In this paper, we obtain confidence bounds for reliability function of the inverse Gaussian distribution where all the parameters are unknown. We consider two cases where the reliability function is parameterized with two different sets of parameters. In the first case, the parameters arise naturally as the drift and variance parameter of the underlying deterioration process. For the second case, the parameters are the mean and dispersion parameter. We describe the life testing methods where these two different forms of pdf arise. For both cases, we give estimators of these parameters and their respective confidence intervals. We demonstrate how to construct the proposed confidence bounds of the reliability function from the confidence intervals of the parameters. The corresponding β-content tolerance limits can then be derived from these reliability bounds. Finally, a numerical example for each case is provided to illustrate the procedure.