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

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  • Pierre Nguimkeu
  • Marie Rekkas
  • Augustine Wong

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.

Suggested Citation

  • Pierre Nguimkeu & Marie Rekkas & Augustine Wong, 2015. "Interval Estimation of the Stress-Strength Reliability with Independent Normal Random Variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(6), pages 1210-1221, March.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:6:p:1210-1221
    DOI: 10.1080/03610926.2012.762399
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