A New Technique of Intelligent Constructing Unbiased Prediction Limits on Future Order Statistics Coming from an Inverse Gaussian Distribution under Parametric Uncertainty

Abstract

This paper provides a new technique for constructing unbiased statistical prediction limits on order statistics of future samples using the results of a previous sample from the same underlying inverse Gaussian distribution. Statistical prediction limits for the inverse Gaussian distribution are obtained from a classical frequentist viewpoint. 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 statistical 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 beta distribution and is conceptually simple and easy to use. The discussion is restricted to one-sided tolerance limits. For illustration, a numerical example is given.