Inference on stress-strength reliability of power distribution
Keywords:Generalized confidence limit, Power distribution, Reliability, Stress – strength model
This paper deals with inference for the stress-strength reliability when X and Y are two independent power distribution. The problem of hypothesis testing and interval estimation of the reliability parameter in a stress-strength model 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.
Asgharzadeh. A, Valiollahi. R, Raqab. M. Z(2011), Stress-strength reliability of Weibull distribution based on progressively censored samples, SORT 35, 103-124.
Adimari. G and Chiogna. M (2006), Partially parametric interval estimation of Pr(Y X), Computational Statistics and Data Analysis 51, 1875-1891.
Ahmad. K. E, Fakhry. M. E. and Jaheen. Z. F (1997), Empirical Bayes estimation of P(Y X) and characterizations of the Burr-type X model, Journal of Statistical Planning and Inference 64, 297-308.
Awad, A. M., Azzam, M. M. and Hamdan, M. A(1981), Some inference results in P(Y X) in the bivariate exponential model, Communications in Statistics-Theory and Methods 10, 2515-2524.
Baklizi. A(2008), Likelihood and Bayesian estimation of P(Y X) using lower record values from the generalized exponential distribution, Computational Statistics and Data Analysis 52, 3468-3473.
Baklizi. A, El-Masri. AE(2004), Shrinkage estimation of P(X Y) in the exponential case with common location parameter. Metrika 59, 163-171.
Kotz. S, Lumelskii. Y and Pensky. M(2003), The stress–strength model and its generalizations: theory and applications. World Scientific, Singapore.
Kundu. D and Gupta. R. D(2005), Estimation of P(Y X) for the generalized exponential distribution, Metrika 61, 291-308.
Kundu. D and Gupta. R. D(2006), Estimation of P(Y X) for Weibull distributions, IEEE Transcations on Reliability 55(2), 270-280.
Krishnamoorthy. K, Mukherjee. S and Guo. H(2006), Inference on reliability in two-parameter exponential stress-strength model, Metrika 65 , 261-273.
Lawless. JF, Statistical models and methods for lifetime data, Wiley, New York, 1982.
Raqab. M. Z and Kundu. D(2005), Comparison of different estimators of P(Y X) for a scaled Burr type X distribution, Communications in Statistics-Simulation and Computation 34(2), 465-483.
Vladimirescu. I and Iasinschi. A(2003), Estimating Pr(X/Y C) for two power distributions, Annals of University of Craiova, Math. Comp. Sci 31, 102-108.
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 NewYork.
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Copyright (c) 2020 Mohammad Kazemi, Mehryar Fallahnejad
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