A Simple Approach of Computing Tolerance Limits and Assessing Stress-Strength Reliability

Music City Center 

The problem of testing and interval estimating the reliability parameter R=P( Y1>Y2), where Y1 and Y2 are independent normal random variables with unknown means and variances, is considered. We first observe that the problem of estimating R is equivalent to estimating the coefficient of variation of the distribution of Y1-Y2. On the basis of this relation, we propose an improved approximate method to make inference on R and compare it with two existing approximate methods and a fiducial method. Approximate closed-form confidence bounds for the reliability parameter are provided. Approximate tolerance intervals for Y1-Y2 are also given. The results are extended to the case where Y1 and Y2 depend on some explanatory variables. Examples with real data are given to illustrate the methods and some recommendations are made for applications.

fiducial test

parametric bootstrap

quantile

Satterthwaite approximation

tolerance limits 

Section on Statistical Computing