Robustness issues regarding content-corrected tolerance limits

Abstract.

This article reviews the content-corrected method for tolerance limits proposed by Fernholz and Gillespie (2001) and addresses some robustness issues that affect the length of the corresponding interval as well as the corrected content value. The content-corrected method for k-factor tolerance limits consists of obtaining a bootstrap corrected value p ^* that is robust in the sense of preserving the confidence coefficient for a variety of distributions. We propose several location/scale robust alternatives to obtain robust corrected-content k-factor tolerance limits that produce shorter intervals when outlying observations are present. We analyze the Hadamard differentiability to insure bootstrap consistency for large samples. We define the breakdown point for the particular statistic to be bootstrapped, and we obtain the influence function and the value of the breakdown point for the traditional and the robust statistics. Two examples showing the advantage of using these robust alternatives are also included.