Abstract
The problem of hypothesis testing and interval estimation of the reliability parameter in a stress–strength model involving two-parameter exponential distributions is considered. Test and interval estimation procedures based on the generalized variable approach are given. Statistical properties of the generalized variable approach and an asymptotic method are evaluated by Monte Carlo simulation. Simulation studies show that the proposed generalized variable approach is satisfactory for practical applications while the asymptotic approach is not satisfactory even for large samples. The results are illustrated using simulated data.
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References
Aminzadeh MS (1997) Estimation of reliability for exponential stress-strength models with explanatory variables. J Appl Math Comput 84:269–274
Baklizi A, El-Masri AE (2004) Shrinkage estimation of P(X < Y) in the exponential case with common location parameter. Metrika 59:163–171
Bhattacharyya GK, Johnson RA (1974) Estimation of a reliability in a multi-component stress-strength model. J Am Stat Assoc 69:966–970
Chao A (1982) On comparing estimators of P(Y <X) in the exponential case. IEEE Trans Reliability 31:389–392
Gamage J, Mathew T, Weerahandi S (2004) Generalized p-values and generalized confidence regions for the multivariate Behrens–Fisher problem. J Multivariate Anal 88:177–189
Guo H, Krishnamoorthy K (2004) New approximate inferential methods for the reliability parameter in a stress–strength model: The normal case. Commun Stat Theory Methods 33:1715–1731
Hall IJ (1984) Approximate one-sided tolerance limits for the difference or sum of two independent normal variates. J Qual Technol 16:15–19
Kotz S, Lumelskii Y, Pensky M (2003) The stress–strength model and its generalizations: theory and applications. World Scientific, Singapore
Krishnamoorthy K, Mathew T (2003) Inferences on the means of lognormal distributions using generalized p-values and generalized confidence intervals. J Stat Plan Inference 115:103-121
Krishnamoorthy K, Mathew T (2004) One-Sided tolerance limits in balanced and unbalanced one-way random models based on generalized confidence limits. Technometrics 46:44–52
Kunchur SH, Munoli SB (1993) Estimation of reliability for a multicomponent survival stress–strength model based on exponential distributions. Commun Stat Theory Methods 22:769–779
Lawless JF (1982) Statistical models and methods for lifetime data. Wiley, New York
Tsui KW, Weerahandi S (1989) Generalized p-values in significance testing of hypotheses in the presence of nuisance parameters. J Am Stat Assoc 84:602–607
Weerahandi S (1993) Generalized confidence intervals. J Am Stat Assoc 88:899–905
Weerahandi S (1995a) ANOVA under unequal error variances. Biometrics 51:589–599
Weerahandi S (1995b) Exact statistical methods for data analysis. Springer, Berlin Heidelbery New York
Weerahandi S, Johnson RA (1992) Testing reliability in a stress-strength model when X and Y are normally distributed. Technometrics 34:83–91
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Krishnamoorthy, K., Mukherjee, S. & Guo, H. Inference on Reliability in Two-parameter Exponential Stress–strength Model. Metrika 65, 261–273 (2007). https://doi.org/10.1007/s00184-006-0074-7
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DOI: https://doi.org/10.1007/s00184-006-0074-7