Confidence Intervals for Reliability and Quantile Functions With Application to NASA Space Flight Data

Abstract

This paper considers the construction of confidence intervals for a cumulative distribution function F(z), and its inverse quantile function F-1(u), at some fixed points z, and u on the basis of an i.i.d. sample Xlowbar={Xi}i=1 n, where n is relatively small. The sample is modeled as having a flexible, generalized gamma distribution with all three parameters being unknown. Hence, the technique can be considered as an alternative to nonparametric confidence intervals, when X is a continuous random variable. The confidence intervals are constructed on the basis of Jeffreys noninformative prior. Performance of the resulting confidence intervals is studied via Monte Carlo simulations, and compared to the performance of nonparametric confidence intervals based on binomial proportion. It is demonstrated that the confidence intervals are robust; when data comes from Poisson or geometric distributions, confidence intervals based on a generalized gamma distribution outperform nonparametric confidence intervals. The theory is applied to the assessment of the reliability of the Pad Hypergol Servicing System of the Shuttle Orbiter