Abstract
This study deals with the classical and Bayesian estimation of reliability in a multicomponent stress–strength model by assuming that both stress and strength variables follow exponentiated Pareto distribution. First, the maximum likelihood method is used to estimate reliability. The asymptotic confidence interval is constructed. We also propose two bootstrap confidence intervals. Next, the Bayesian estimates of reliability are obtained using Lindley’s approximation, Tierney–Kadane approximation and the Markov chain Monte Carlo (MCMC) method since there are no explicit forms. The MCMC method is used to construct the Bayesian credible interval. A Monte Carlo simulation study is performed to compare the performance of the corresponding methods. Finally, the hydrological data set is analyzed in the application part.
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References
Abbas K, Arshad IA, Hussain Z, Khan KS (2016) Bayesian estimation of exponentiated Pareto distribution. Pak J Statist 32(5):349–370
Afify WM (2010) On estimation of the exponentiated Pareto distribution under different sample schemes. Stat Method 7:77–83
Akgül FG (2019) Reliability estimation in multicomponent stress-strength model for Topp–Leone distribution. J Stat Comput Simul 89(15):2914–2929
Akgül FG, Şenoğlu B (2020) Inferences for stress-strength reliability of Burr Type X distributions based on ranked set sampling. Commun Stat Simul Comput. https://doi.org/10.1080/03610918.2020.1711949
Al-Omari AI, Almanjahie IM, Hassan AS, Nagy HF (2020) Estimation of the stress-strength reliability for exponentiated pareto distribution using median and ranked set sampling methods. Comput Mater Contin 64(2):835–857
Babayi S, Khorram E (2018) Inference of stress-strength for the Type-II generalized logistic distribution under progressively Type-II censored samples. Commun Stat Simul Comput 47(7):1975–1995
Bhattacharyya GK, Johnson RA (1974) Estimation of reliability in a multicomponent stress-strength model. J Am Stat Assoc 69:966–970
Birnbaum ZM (1956) On a use of Mann-Whitney statistics. In: Proceeding of 3rd Berkeley symposium on mathematical statistics and probability vol 1, pp 13–17
Chen J, Cheng C (2017) Reliability of stress-strength model for exponentiated Pareto distributions. J Stat Comput Simul 87(4):791–805
Efron B (1982) The Jacknife, the Bootstrap and Other Re-Sampling Plans. Philadelphia, PA:SIAM, 38, CBMS-NSF Regional Conference Series in Applied Mathematics.
Gupta R, Gupta RD, Gupta PL (1998) Modeling failure time data by Lehman alternatives. Commun Stat Theory Meth 27(4):887–904
Hall P (1988) Theoretical comparison of bootstrap confidence intervals. Annals Stat 16:927–953
Hassan AS, Abd-Alla M, Nagy HF (2018) Estimation of P(Y<X) using record values from the generalized inverted exponential distribution. Pak J Stat Oper Res 14(3):645–660
Hassan AS, Nagy HF, Muhammed HZ, Saad MS (2020) Estimation of multicomponent stress-strength reliability following Weibull distribution based on upper record values. J Taibah Univ Sci 14(1):244–253
Kızılaslan F, Nadar M (2018) Estimation of reliability in a multicomponent stress-strength model based on a bivariate Kumaraswamy distribution. Stat Papers 59:307–340
Kohansal A (2019) On estimation of reliability in a multicomponent stress-strength model of Kumaraswamy distribution based on progressively censored sample. Stat Papers 60:2185–2224
Lindley DV (1980) Approximate Bayesian Methods. Trab De Estad 31:281–288
Maurya RK, Tripathi YM (2020) Reliability estimation in a multicomponent stress-strength model for Burr XII distribution under progressive censoring. Brazil J Prob Stat 34(2):345–369
Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equations of state calculations by fast computing machines. J Chem Phys 21:1087–1091
Nadar M, Kızılaslan F (2016) Estimation of reliability in a multicomponent stress-strength model based on a Marshall-Olkin bivariate Weibull distribution. IEEE Trans Reliab 65(1):370–380
Rao GS, Kantam RRL, Rosaiah K, Reddy JP (2013) Estimation of reliability in multicomponent stress-strength based on inverse Rayleigh Distribution. J Stat Appl pro 2(3):261–267
Tarvirdizade B, Ahmadpour M (2016) Estimation of the stress-strength reliability for the two-parameter bathtub-shaped lifetime distribution based on upper record values. Stat Method 31:58–72
Tierney T, Kadane B (1986) Accurate approximations for posterior moments marginal densities. J Am Stat Assoc 81:82–86
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Akgül, F. Classical and Bayesian estimation of multicomponent stress–strength reliability for exponentiated Pareto distribution. Soft Comput 25, 9185–9197 (2021). https://doi.org/10.1007/s00500-021-05902-2
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DOI: https://doi.org/10.1007/s00500-021-05902-2