Content-Corrected Tolerance Limits Based on the Bootstrap

Abstract

This article considers k-factor tolerance limits in which the p-content is data dependent. The proposed content-corrected method is based on a bootstrap estimate of the given content and is shown to be robust in the sense of preserving the confidence coefficient for a variety of distributions for small or moderate sample sizes to all large samples. We develop the theoretical basis for the asymptotic results and prove both asymptotic normality and weak consistency of the corresponding bootstrap statistic. The method is shown to be asymptotically accurate with respect to the confidence coefficient for a wide class of distributions. Several simulations and two examples show the advantage of this method when the normality of the data cannot be assumed.

KEY WORDS :

• Asymptotic normality
• Bootstrap
• Corrected content
• Hadamard derivatives
• Tolerance limits
• Weak consistency