CONFIDENCE-REGIONS HAVING DIFFERENT SHAPES FOR THE FAILURE DISTRIBUTION FUNCTION

A failure distribution represents an attempt to describe mathematicall y the Most often the possibility remains that the analysts may be hesi tant or unwilling to entertain any well known theoretical failure dist ribution. Therefore, one must rely on actual observations of the time to failure to construct an empirical cumulative failure distribution f unction. We present some useful results in constructing statistical co nfidence regions for the entire failure cumulative distribution functi on (cdf), F(x) from which a random sample has been drawn. The bandwidt h of these regions becomes narrower in some parts of the distribution where we may want to have more precise information about failure cdf t han is afforded by the ordinary Kolmogorov-Smirnov (K-S) confidence re gion. The problem of constructing the best, having minimum risk, confi dence region from a decision theoretic approach is also considered. Il lustrative numerical examples are presented. Published by Elsevier Sci ence Ltd