Statistical Inference for Reliability from Stress Strength Relationships: The Normal Case.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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This paper examines statistical inference for PY X, where X and Y are independent normal variates with unknown means and variances. The case of unequal variances is stressed. X can be interpreted as the strength of a component subjected to a stress Y, and PY X is the components reliability. For point estimation, a predictive estimator which can be calculated from the Behrens-Fisher distribution is derived and compared with the maximum likelihood and uniformly minimum variance unbiased estimators through a simulation study. Two approximate methods for obtaining confidence intervals and an approximate Bayesian probability interval is obtained. The actual coverage probabilities of these intervals is examined by simulation. Author
- Statistics and Probability