Interval Estimation of the Stress-Strength Reliability with Independent Normal Random Variables

Pierre Nguimkeu, Marie Rekkas and Augustine Wong

Communications in Statistics - Theory and Methods, 2015, vol. 44, issue 6, 1210-1221

Abstract: This article develops a procedure to obtain highly accurate confidence interval estimates for the stress-strength reliability R = P(X > Y) where X and Y are data from independent normal distributions of unknown means and variances. Our method is based on third-order likelihood analysis and is compared to the conventional first-order likelihood ratio procedure as well as the approximate methods of Reiser and Guttman (1986) and Guo and Krishnamoorthy (2004). The use of our proposed method is illustrated by an empirical example and its superior accuracy in terms of coverage probability and error rate are examined through Monte Carlo simulation studies.

Date: 2015
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DOI: 10.1080/03610926.2012.762399

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