Abstract #300575

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JSM 2003 Abstract #300575
Activity Number: 206
Type: Contributed
Date/Time: Tuesday, August 5, 2003 : 8:30 AM to 10:20 AM
Sponsor: Section on Physical and Engineering Sciences
Abstract - #300575
Title: An Improved Method for Estimating and Testing the Reliability Parameter in the Normal Case
Author(s): Huizhen Guo*+ and Kalimuthu Krishnamoorthy
Companies: University of Louisiana, Lafayette and University of Louisiana, Lafayette
Address: PO Box 40003, Lafayette, LA, 70504-0001,
Keywords: Satterthwaite Approximation ; noncentral t distribution ; quantile ; generalized p value ; size ; tolerance limit
Abstract:

We consider the problem of testing and interval estimation of the reliability parameter P(X > Y), where X and Y are independent normal random variables with unknown means and variances. A new approximate method is proposed, and is compared with two existing approximate methods and a generalized variable method. Simulation studies indicate that the sizes of the existing approximate tests exceed the nominal level considerably in some situations while the new method controls the sizes satisfactorily in all situations considered. The studies also indicated that the generalized variable test is too conservative for small samples. A confidence limit for the reliability parameter based on the new approximate test is also given. The results are extended to the case where X and Y depend on some explanatory variables. The methods are illustrated using three examples.

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