Predictive inferences for future order statistics coming from an inverse Gaussian distribution

This paper provides procedures for constructing prediction limits on order statistics of future samples using the results of a previous sample from the same underlying inverse Gaussian distribution. Prediction limits are obtained from a point of view of frequentist approach. Bayesian methods are not considered here. The results have direct application in reliability theory, where the time until the first failure in a group of several items in service provides a measure of assurance regarding the operation of the items. The prediction limits are required as specifications on future life for components, as warranty limits for the future performance of a specified number of systems with standby units, and in various other applications. Prediction limit is an important statistical tool in the area of quality control. The lower prediction limits are often used as warranty criteria by manufacturers. The technique used here does not require the construction of any tables. It requires a quantile of the G_θ and F distributions and is conceptually simple and easy to use. The prediction limits obtained in the paper are generalizations of the usual prediction limits on observations or functions of observations of only one future sample. For illustration, a numerical example is given.