Tolerance Intervals for the Distribution of the Difference Between Two Independent Normal Random Variables

Abstract

The problem of constructing tolerance interval for the distribution of the difference between two independent normal random variables possibly with different variances is considered. Assuming that the variance ratio is known, an exact method and a simple approximate method for constructing tolerance factor are presented. Also, approximate methods for obtaining tolerance interval are provided when the variances are unknown and arbitrary. The coverage probabilities of the approximate methods and an available approximate method are evaluated via Monte Carlo simulation study. Simulation study indicates that the approximate tolerance intervals are quite satisfactory even when the sample sizes are small whereas the existing method is conservative for small to moderate samples. The proposed tolerance interval can be used safely for practical applications. The methods are illustrated using an example.

Keywords:

• Coverage probability
• Lognormal distribution
• Moment approximation
• Stress-strength reliability

Mathematics Subject Classification:

• 62F03
• 62F25