A comparative inference on reliability estimation for a multi-component stress-strength model under power Lomax distribution with applications

Hanan Haj Ahmad; Ehab M. Almetwally; Dina A. Ramadan; Hanan Haj Ahmad; Ehab M. Almetwally; Dina A. Ramadan

doi:10.3934/math.2022994

AIMS Mathematics

2022, Volume 7, Issue 10: 18050-18079. doi: 10.3934/math.2022994

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Research article

A comparative inference on reliability estimation for a multi-component stress-strength model under power Lomax distribution with applications

1.
Department of Basic Science, Preparatory Year Deanship, King Faisal University, Hofuf, Al-Ahsa, 31982, Saudi Arabia
2.
Department of Statistics, Faculty of Business Administration, Delta university for Science and Technology, Gamasa 11152, Egypt
3.
The Scientific Association for Studies and Applied Research, Al Manzalah 35646, Egypt
4.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt

Received: 30 April 2022 Revised: 24 June 2022 Accepted: 03 July 2022 Published: 08 August 2022
MSC : 62N05, 62N02, 62N01, 62H12, 62F15, 62F10, 62F40

In this article, reliability estimation for a system of multi-component stress-strength model is considered. Working under progressively censored samples is of great advantage over complete and usual censoring samples, therefore Type-II right progressive censored sample is selected. The lifetime of the components and the stress and strength components are following the power Lomax distribution. Consequently, the problem of point and interval estimation has been studied from different points of view. The maximum likelihood estimate and the maximum product spacing of reliability are evaluated. Also approximate confidence intervals are constructed using the Fisher information matrix. For the traditional methods, bootstrap confidence intervals are calculated. Bayesian estimation is obtained under the squared error and linear-exponential loss functions, where the numerical techniques such as Newton-Raphson and the Markov Chain Monte Carlo algorithm are implemented. For dependability, the largest posterior density credible intervals are generated. Simulations are used to compare the results of the proposed estimation methods, where it shows that the Bayesian estimation method of the reliability function is significantly better than the other methods. Finally, a real data of the water capacity of the Shasta reservoir is examined for illustration.
- reliability analysis,
- power Lomax,
- multi-component stress-strength model,
- maximum likelihood,
- maximum product spacing,
- Bayes estimation,
- Markov Chain Monte Carlo,
- highest posterior density
Citation: Hanan Haj Ahmad, Ehab M. Almetwally, Dina A. Ramadan. A comparative inference on reliability estimation for a multi-component stress-strength model under power Lomax distribution with applications[J]. AIMS Mathematics, 2022, 7(10): 18050-18079. doi: 10.3934/math.2022994

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Abstract

In this article, reliability estimation for a system of multi-component stress-strength model is considered. Working under progressively censored samples is of great advantage over complete and usual censoring samples, therefore Type-II right progressive censored sample is selected. The lifetime of the components and the stress and strength components are following the power Lomax distribution. Consequently, the problem of point and interval estimation has been studied from different points of view. The maximum likelihood estimate and the maximum product spacing of reliability are evaluated. Also approximate confidence intervals are constructed using the Fisher information matrix. For the traditional methods, bootstrap confidence intervals are calculated. Bayesian estimation is obtained under the squared error and linear-exponential loss functions, where the numerical techniques such as Newton-Raphson and the Markov Chain Monte Carlo algorithm are implemented. For dependability, the largest posterior density credible intervals are generated. Simulations are used to compare the results of the proposed estimation methods, where it shows that the Bayesian estimation method of the reliability function is significantly better than the other methods. Finally, a real data of the water capacity of the Shasta reservoir is examined for illustration.

References

[1]	M. E. Ghitany, D. K. Al-Mutairi, S. M. Aboukhamseen, Estimation of the reliability of a stress-strength system from power Lindley distributions, Commun. Stat.-Simul. Comput., 44 (2015), 118–136. https://doi.org/10.1080/03610918.2013.767910 doi: 10.1080/03610918.2013.767910
[2]	J. Chen, C. Cheng, Reliability of stress-strength model for exponentiated Pareto distributions, J. Stat. Comput. Simul., 87 (2017), 791–805. https://doi.org/10.1080/00949655.2016.1226309 doi: 10.1080/00949655.2016.1226309
[3]	A. Rezaei, M. Sharafi, J. Behboodian, A. Zamani, Inference on stress-streng the parameter based on GLD5 distribution, Commun. Stat.-Simul. Comput., 47 (2018), 1251–1263. https://doi.org/10.1080/03610918.2017.1309666 doi: 10.1080/03610918.2017.1309666
[4]	V. K. Sharma, Bayesian analysis of head and neck cancer data using generalized inverse Lindley stress-strength reliability model, Commun. Stat.-Theor. M., 47 (2018), 1155–1180. https://doi.org/10.1080/03610926.2017.1316858 doi: 10.1080/03610926.2017.1316858
[5]	A. I. Genç, Estimation of $P$ $(X>Y)$ with Topp-Leone distribution, J. Stat. Comput. Simul., 83 (2013), 326–339. https://doi.org/10.1080/00949655.2011.607821 doi: 10.1080/00949655.2011.607821
[6]	H. Krishna, M. Dube, R. Garg, Estimation of $P$ $(Y < X)$ for progressively first-failure-censored generalized inverted exponential distribution, J. Stat. Comput. Simul., 87 (2017), 2274–2289. https://doi.org/10.1080/00949655.2017.1326119 doi: 10.1080/00949655.2017.1326119
[7]	S. Babayi, E. Khorram, Inference of stress-strength for the Type-II generalized logistic distribution under progressively Type-II censored samples, Commun. Stat.-Simul. Comput., 47 (2018), 1975–1995. https://doi.org/10.1080/03610918.2017.1332214 doi: 10.1080/03610918.2017.1332214
[8]	M. Nadar, F. Kızılaslan, Classical and Bayesian estimation of $P$ $(X < Y)$ using upper record values from Kumaraswamy's distribution, Stat. Pap., 55 (2014), 751–783. https://doi.org/10.1007/s00362-013-0526-x doi: 10.1007/s00362-013-0526-x
[9]	A. Tripathi, U. Singh, S. K. Singh, Estimation of $P$ $(X < Y)$ for Gompertz distribution based on upper records, Int. J. Model. Simul., 42 (2022), 388–399. https://doi.org/10.1080/02286203.2021.1923979 doi: 10.1080/02286203.2021.1923979
[10]	A. Asgharzadeh, R. Valiollahi, M. Z. Raqab, Estimation of $P$ $(Y < X)$ for the two-parameter generalized exponential records, Commun. Stat.-Simul. Comput., 46 (2017), 379–394. https://doi.org/10.1080/03610918.2014.964046 doi: 10.1080/03610918.2014.964046
[11]	F. G. Akgül, B. Şenoğlu, Estimation of $P$ $(X < Y)$ using ranked set sampling for Weibull distribution, Qual. Technol. Quant. M., 14 (2017), 296–309. https://doi.org/10.1080/16843703.2016.1226590 doi: 10.1080/16843703.2016.1226590
[12]	F. G. Akgül, Ş. Acıtaş, B. Şenoğlu, Inference on stress-strength reliability based on ranked set sampling data in case of Lindley distribution, J. Stat. Comput. Simul., 88 (2018), 3018–3032. https://doi.org/10.1080/00949655.2018.1498095 doi: 10.1080/00949655.2018.1498095
[13]	F. G. Akgül, B. Şenoğlu, Ş. Acıtaş, Interval estimation of the system reliability for Weibull distribution based on ranked set sampling data, Hacet. J. Math. Stat., 47 (2018), 1404–1416. https://doi.org/10.15672/HJMS.2018.562 doi: 10.15672/HJMS.2018.562
[14]	A. Safariyan, M. Arashi, R. A. Belaghi, Improved point and interval estimation of the stress strength reliability based on ranked set sampling, Statistics, 53 (2019), 101–125. https://doi.org/10.1080/02331888.2018.1547906 doi: 10.1080/02331888.2018.1547906
[15]	A. A. Al-Babtain, I. Elbatal, E. M. Almetwally, Bayesian and non-Bayesian reliability estimation of stress-strength model for power-modified Lindley distribution, Comput. Intell. Neurosci., 2022 (2022). https://doi.org/10.1155/2022/1154705
[16]	M. A. Sabry, E. M. Almetwally, H. M. Almongy, Monte Carlo simulation of stress-strength model and reliability estimation for extension of the exponential distribution, Thail. Statist., 20 (2022), 124–143.
[17]	M. M. Yousef, E. M. Almetwally, Multi stress-strength reliability based on progressive first failure for Kumaraswamy model: Bayesian and non-Bayesian estimation, Symmetry, 13 (2021), 2120. https://doi.org/10.3390/sym13112120 doi: 10.3390/sym13112120
[18]	S. Rezaei, R. Tahmasbi, M. Mahmoodi, Estimation of $P$ $[Y < X]$ for generalized Pareto distribution, J. Stat. Plan. Infer., 140 (2010), 480–494. https://doi.org/10.1016/j.jspi.2009.07.024 doi: 10.1016/j.jspi.2009.07.024
[19]	D. Kundu, R. D. Gupta, Estimation of $P$ $[Y < X]$ for Weibull distributions, IEEE Trans. Reliab., 55 (2006), 270–280.
[20]	J. K. Jose, Estimation of stress-strength reliability using discrete phase type distribution, Commun. Stat.-Theor. M., 51 (2022), 368–386. https://doi.org/10.1080/03610926.2020.1749663 doi: 10.1080/03610926.2020.1749663
[21]	E. M. Almetwally, R. Alotaibi, A. A. Mutairi, C. Park, H. Rezk, Optimal plan of multi-stress-strength reliability Bayesian and non-Bayesian methods for the alpha power exponential model using progressive first failure, Symmetry, 14 (2022), 1306. https://doi.org/10.3390/sym14071306 doi: 10.3390/sym14071306
[22]	S. Kotz, Y. Lumelskii, M. Pensky, The stress-strength model and its generalizations: Theory and applications, Singapore, World Scientific, 2003.
[23]	G. K. Bhattacharyya, R. A. Johnson, Estimation of reliability in a multicomponent stress-strength model, J. Am. Stat. Assoc., 69 (1974), 966–970. https://doi.org/10.1080/01621459.1974.10480238 doi: 10.1080/01621459.1974.10480238
[24]	A. Kohansal, On estimation of reliability in a multicomponent stress-strength model for a Kumaraswamy distribution based on progressively censored sample, Stat. Pap., 60 (2017), 2185–2224. https://doi.org/10.1007/s00362-017-0916-6 doi: 10.1007/s00362-017-0916-6
[25]	F. Kızılaslan, Classical and Bayesian estimation of reliability in a multicomponent stress strength model based on the proportional reversed hazard rate mode, Math. Comput. Simul., 136 (2017), 36–62. https://doi.org/10.1016/j.matcom.2016.10.011 doi: 10.1016/j.matcom.2016.10.011
[26]	S. Gunasekera, Classical, Bayesian, and generalized inferences of the reliability of a multicomponent system with censored data, J. Stat. Comput. Simul., 88 (2018), 3455–3501. https://doi.org/10.1080/00949655.2018.1523410 doi: 10.1080/00949655.2018.1523410
[27]	N. Balakrishnan, R. Aggarwala, Progressive censoring: Theory, methods, and applications, Springer, Berlin, 2000.
[28]	N. Balakrishnan, E. Cramer, The art of progressive censoring, Springer, New York, 2014.
[29]	M. Z. Raqab, M. T. Madi, Inference for the generalized Rayleigh distribution based on progressively censored data, J. Stat. Plan. Infer., 141 (2011), 3313–3322. https://doi.org/10.1016/j.jspi.2011.04.016 doi: 10.1016/j.jspi.2011.04.016
[30]	S. F. Wu, C. C. Wu, C. H. Chou, H. M. Lin, Statistical inferences of a two-parameter distribution with the bathtub shape based on progressive censored sample, J. Stat. Comput. Simul., 81 (2011), 315–329. https://doi.org/10.1080/00949650903334221 doi: 10.1080/00949650903334221
[31]	M. K. Rastogi, Y. M. Tripathi, Estimating the parameters of a Burr distribution under progressive type II censoring, Stat. Methodol., 9 (2012), 381–391. https://doi.org/10.1016/j.stamet.2011.10.002 doi: 10.1016/j.stamet.2011.10.002
[32]	E. H. A. Rady, W. A. Hassanein, T. A. Elhaddad, The power Lomax distribution with an application to bladder cancer data, SpringerPlus, 5 (2016), 1838. https://doi.org/10.1186/s40064-016-3464-y doi: 10.1186/s40064-016-3464-y
[33]	C. R. Rao, Linear statistical inference and its applications, Wiley Eastern Limited, India, 1973.
[34]	H. K. T. Ng, L. Luo, Y. Hu, F. Duan, Parameter estimation of three parameter Weibull distribution based on progressively Type II censored samples, J. Stat. Comput. Simul., 82 (2012), 1661–1678. https://doi.org/10.1080/00949655.2011.591797 doi: 10.1080/00949655.2011.591797
[35]	R. C. H. Cheng, N. A. K. Amin, Estimating parameters in continuous univariate distributions with a shifted origin, J. Roy. Stat. Soc. B, 45 (1983), 394–403. https://doi.org/10.1111/j.2517-6161.1983.tb01268.x doi: 10.1111/j.2517-6161.1983.tb01268.x
[36]	R. C. H. Cheng, N. A. K. Amin, Maximum product of spacings estimation with applications to the lognormal distribution, Math. Report, University of Wales IST, 1979.
[37]	H. K. T. Ng, P. S. Chan, N. Balakrishnan, Optimal progressive censoring plans for the Weibull distribution, Technometrics, 46 (2004), 470–481. https://doi.org/10.1198/004017004000000482 doi: 10.1198/004017004000000482
[38]	W. S. Abu El Azm, E. M. Almetwally, A. S. Alghamdi, H. M. Aljohani, A. H. Muse, O. E. Abo-Kasem, Stress-strength reliability for exponentiated inverted Weibull distribution with application on breaking of Jute fiber and Carbon fibers, Comput. Intel. Neurosc., 2021 (2021). https://doi.org/10.1155/2021/4227346
[39]	M. A. Sabry, E. M. Almetwally, O. A. Alamri, M. Yusuf, H. M. Almongy, A. S. Eldeeb, Inference of fuzzy reliability model for inverse Rayleigh distribution, AIMS Math., 6 (2021), 9770–9785. https://doi.org/10.3934/math.2021568 doi: 10.3934/math.2021568
[40]	U. Singh, S. K. Singh, R. K. Singh, A comparative study of traditional estimation methods and maximum product spacings method in generalized inverted exponential distribution, J. Stat. Appl. Prob., 3 (2014), 153. https://doi.org/10.12785/jsap/030206 doi: 10.12785/jsap/030206
[41]	B. Efron, The jacknife, the bootstrap and other resampling plans, SIAM, Philadelphia, 1982.
[42]	R. E. Hall, Intertemporal substitution in consumption, J. Polit. Econ., 96 (1988), 339–357.
[43]	H. R. Varian, A Bayesian approach to real estate assessment, North Holland, Amsterdam, 1975,195–208.
[44]	A. Zellner, Bayesian estimation and prediction using asymmetric loss functions, J. Am. Stat. Assoc., 81 (1986), 446–451. https://doi.org/10.1080/01621459.1986.10478289 doi: 10.1080/01621459.1986.10478289
[45]	N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, Equations of state calculations by fast computing machines, J. Chem. Phys., 21 (1953), 1087–1092. https://doi.org/10.1063/1.1699114 doi: 10.1063/1.1699114
[46]	M. Nadar, F. Kızılaslan, Estimation of reliability in a multicomponent stress-strength model based on a Marshall-Olkin bivariate Weibull distribution, IEEE T. Reliab., 65 (2015), 370–380. https://doi.org/10.1109/TR.2015.2433258 doi: 10.1109/TR.2015.2433258
[47]	F. Kızılaslan, M. Nadar, Estimation of reliability in a multicomponent stress-strength model based on a bivariate Kumaraswamy distribution, Stat. Pap., 59 (2018), 307–340. https://doi.org/10.1007/s00362-016-0765-8 doi: 10.1007/s00362-016-0765-8

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