Estimation Study of Multicomponent Stress-Strength Reliability Using Advanced Sampling Approach
Year 2024,
, 465 - 481, 01.03.2024
Amal Hassan
,
Rasha Elshaarawy
,
Heba Nagy
Abstract
In this study, we analyze a multicomponent system with v independent and identical strength components X1,…, Xv and each of these components is exposed to a common random stress Y. The system is considered to be operating only if at least u out of v (1 u v) strength variables exceed the random stress. The estimate of the system reliability is investigated, assuming the strength and stress random variables follow the exponentiated exponential distribution having different shape parameters. The maximum likelihood estimator for the system reliability is derived from ranked set sampling (RSS), neoteric RSS (NRSS), and median RSS (MRSS). Some accuracy measurements, such as mean squared errors and efficiencies, are used to examine the behaviour of various estimates. Simulation studies demonstrate that the NRSS scheme's reliability estimates are chosen above those of the others under the RSS and MRSS schemes in the majority of situations. Theoretical research is explained through real data analysis.
References
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- [12] Bantan, R., Elsehetry, M., Hassan, A.S., Elgarhy, M., Sharma, D., Chesneau, C., Jamal, F., “A two-parameter model: properties and estimation under ranked sampling”, Mathematics, 9(11): 1214, (2021). https://doi.org/10.3390/math9111214
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- [14] Nagy, H.F., Al-Omari, A.I., Hassan, A.S., Alomani, G.A., “Improved estimation of the inverted Kumaraswamy distribution parameters based on ranked set sampling with an application to real data”, Mathematics, 10(21): 4102, (2022). https://doi.org/10.3390/math10214102.
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- [18] Al-Omari, A.I., Hassan, A.S., Alotaibi, N., Shrahili, M., Nagy, H.F., “Reliability estimation of inverse Lomax distribution using extreme ranked set sampling”, Advances in Mathematical Physics: 4599872 (2021). https://doi.org/10.1155/2021/4599872
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- [24] Hassan, A.S., Basheikh, H.M., “Estimation of reliability in multi-component stress-strength model following exponentiated Pareto distribution”, The Egyptian Statistical Journal, 56(2): 82–95, (2012).
- [25] Rao, G.S., Aslam, M., Kundu, D., “Burr-XII distribution parametric estimation and estimation of reliability of multicomponent stress-strength”, Communications in Statistics-Theory and Methods, 44(23): 4953–4961, (2015).
- [26] Rao, G.S., Aslam, M., Arif, O.H., “Estimation of reliability in multicomponent stress–strength based on two parameter exponentiated Weibull distribution”, Communications in Statistics-Theory and Methods, 46(15): 7495–7502, (2017).
- [27] Dey, S., Mazucheli, J., Anis, M.Z., “Estimation of reliability of multicomponent stress–strength for a Kumaraswamy distribution”, Communications in Statistics-Theory and Methods, 46(4): 1560–1572, (2017).
- [28] Hassan, A.S., Nagy, H.F., Muhammed, H.Z., Saad, M.S., “Estimation of multicomponent stress-strength reliability following Weibull distribution based on upper record values”, Journal of Taibah University for Science, 14(1): 244–253, (2020).
- [29] Akgül, F.G., “Classical and Bayesian estimation of multicomponent stress–strength reliability for exponentiated Pareto distribution”, Soft Computing, 25(14): 9185–9197, (2021).
- [30] Hassan, A.S., Nagy, H.F., “Reliability estimation in multicomponent stress-strength for generalized inverted exponential distribution based on ranked set sampling”, Gazi University Journal of Science, 35(1): 314–331, (2022).
- [31] Yousef, M.M., Hassan, A.S., Al-Nefaie, A.H., Almetwally, E.M., Almongy, H.M., “Bayesian estimation using MCMC method of system reliability for inverted Topp-Leone distribution based on ranked set sampling”, Mathematics, 10(17): 3122, (2022). https://doi.org/10.3390/math10173122.
- [32] Gupta, R.D., Kundu, D., “Theory & methods: Generalized exponential distributions”, Australian & New Zealand Journal of Statistics, 41(2): 173–188, (1999).
- [33] Gupta, R.D., Kundu, D., “Generalized exponential distribution: different method of estimations”, Journal of Statistical Computation and Simulation, 69(4): 315–337, (2001).
- [34] Gupta, R.D., Kundu, D., “Exponentiated exponential family: an alternative to gamma and Weibull distributions”, Biometrical Journal: Journal of Mathematical Methods in Biosciences, 43(1): 117–130, (2001).
- [35] Raqab, M.Z., “Inferences for generalized exponential distribution based on record statistics”, Journal of Statistical Planning and Inference, 104(2): 339–350, (2002).
- [36] Kundu, D., Gupta, R.D., “Estimation of P [Y< X] for generalized exponential distribution”, Metrika, 61(3): 291–308, (2005).
- [37] Baklizi, A., “Likelihood and Bayesian estimation of Pr (X< Y) using lower record values from the generalized exponential distribution”, Computational Statistics & Data Analysis, 52(7): 3468–3473, (2008).
- [38] Subburaj, R., Gopal, G., Kapur, P.K., “A software reliability growth model for vital quality metrics”, South African Journal of Industrial Engineering, 18(2): 93–108, (2007).
- [39] Biondi, F., Kozubowski, T.J., Panorska, A.K., Saito, L., “A new stochastic model of episode peak and duration for eco-hydro-climatic applications”, Ecological Modelling, 211(3-4): 383–395, (2008).
- [40] Rao, G.S., “Estimation of reliability in multicomponent stress-strength based on generalized exponential distribution”, Revista Colombiana de Estadística, 35(1): 67–76, (2012).
- [41] Guo, L., Gui, W., “Statistical inference of the reliability for generalized exponential distribution under progressive type-II censoring schemes”, IEEE Transactions on Reliability, 67(2): 470–480, (2018).
- [42] Sadeghpour, A., Salehi, M., Nezakati, A., “Estimation of the stress–strength reliability using lower record ranked set sampling scheme under the generalized exponential distribution”, Journal of Statistical Computation and Simulation, 90(1): 51–74, (2020).
- [43] Esemen, M., Gurler, S., Sevinc, B., “Estimation of stress–strength reliability based on ranked set sampling for generalized exponential distribution”, International Journal of Reliability, Quality and Safety Engineering, 28(2): 2150011, (2021). https://doi.org/10.1142/S021853932150011X.
- [44] Xia, Z.P., Yu, J.Y., Cheng, L.D., Liu, L.F., Wang, W.M., “Study on the breaking strength of jute fibres using modified Weibull distribution”, Composites Part A: Applied Science and Manufacturing, 40(1): 54–59, (2009).
Year 2024,
, 465 - 481, 01.03.2024
Amal Hassan
,
Rasha Elshaarawy
,
Heba Nagy
References
- [1] McIntyre, G.A., “A method for unbiased selective sampling, using ranked sets”, Australian Journal of Agricultural Research, 3(4): 385–390, (1952).
- [2] Takahasi, K., Wakimoto, K., “On unbiased estimates of the population mean based on the sample stratified by means of ordering”, Annals of the Institute of Statistical Mathematics, 20(1): 1–31, (1968).
- [3] Dell, T.R., Clutter, J.L., “Ranked set sampling theory with order statistics background”, Biometrics: 545–555, (1972).
- [4] Bhushan, S., Kumar, A., “Novel log type class of estimators under ranked set sampling”, Sankhya B, 84(1): 421–447, (2022).
- [5] Bhushan, S., Kumar, A., “On optimal classes of estimators under ranked set sampling”, Communications in Statistics-Theory and Methods, 51(8): 2610–2639, (2022).
- [6] Bhushan, S., Kumar, A., Lone, S.A., “On some novel classes of estimators using ranked set sampling”, Alexandria Engineering Journal, 61(7): 5465–5474, (2022).
- [7] Muttlak, H.A., “Median ranked set sampling”, Journal of Applied Statistical Sciences, 6: 557–586, (1997).
- [8] Zamanzade, E., Al-Omari, A.I., “New ranked set sampling for estimating the population mean and variance”, Hacettepe Journal of Mathematics and Statistics, 45(6): 1891–1905, (2016).
- [9] Hassan, A.S., “Modified goodness of fit tests for exponentiated Pareto distribution under selective ranked set sampling”, Australian Journal of Basic and Applied Sciences, 6(1): 173–189, (2012).
- [10] Bantan, R., Hassan, A.S., Elsehetry, M., “Zubair Lomax distribution: properties and estimation based on ranked set sampling”, CMC-Computers, Materials and Continua, 65: 2169–2187, (2020).
- [11] Sabry, M., Shaaban, M., “Dependent ranked set sampling designs for parametric estimation with applications”, Annals of Data Science, 7(2): 357–371, (2020).
- [12] Bantan, R., Elsehetry, M., Hassan, A.S., Elgarhy, M., Sharma, D., Chesneau, C., Jamal, F., “A two-parameter model: properties and estimation under ranked sampling”, Mathematics, 9(11): 1214, (2021). https://doi.org/10.3390/math9111214
- [13] Eftekharian, A., Razmkhah, M., Ahmadi, J., “A flexible ranked set sampling schemes: Statistical analysis on scale parameter”, Statistics, Optimization & Information Computing, 9(1): 189–203, (2021).
- [14] Nagy, H.F., Al-Omari, A.I., Hassan, A.S., Alomani, G.A., “Improved estimation of the inverted Kumaraswamy distribution parameters based on ranked set sampling with an application to real data”, Mathematics, 10(21): 4102, (2022). https://doi.org/10.3390/math10214102.
- [15] Birnbaum, Z.W., “On a use of the Mann-Whitney statistic”, Proceedings of the Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability. University of California Press Berkeley, Calif., (1956).
- [16] Akgül, F.G., Şenoğlu, B., “Estimation of P (X< Y) using ranked set sampling for the Weibull distribution”, Quality Technology & Quantitative Management, 14(3): 296–309, (2017).
- [17] Al-Omari, A.I., Almanjahie, I.M., Hassan, A.S., Nagy, H.F., “Estimation of the stress-strength reliability for exponentiated Pareto distribution using median and ranked set sampling methods”, CMC-Computers, Materials and Continua, 64(2): 835–857, (2020).
- [18] Al-Omari, A.I., Hassan, A.S., Alotaibi, N., Shrahili, M., Nagy, H.F., “Reliability estimation of inverse Lomax distribution using extreme ranked set sampling”, Advances in Mathematical Physics: 4599872 (2021). https://doi.org/10.1155/2021/4599872
- [19] Hassan, A.S., Al-Omari, A., Nagy, H.F., “Stress–strength reliability for the generalized inverted exponential distribution using MRSS”, Iranian Journal of Science and Technology, Transactions A: Science, 45(2): 641–659, (2021).
- [20] Hassan, A.S., Elshaarawy, R.S., Onyango, R., Nagy, H.F., “Estimating system reliability using neoteric and median RSS data for generalized exponential distribution”, International Journal of Mathematics and Mathematical Sciences: 2608656 (2022). https://doi.org/10.1155/2022/2608656
- [21] Hassan, A.S., Ismail, D.M., Nagy, H.F., “Reliability bayesian analysis in multicomponent stress–strength for generalized inverted exponential using upper record data”, IAENG International Journal of Applied Mathematics, 52(3): 1–13, (2022).
- [22] Hassan, A.S., Almanjahie, I.M., Al-Omari, A.I., Alzoubi, L., Nagy, H.F., “Stress-strength modeling using median-ranked set sampling: estimation, simulation, and application”, Mathematics, 11(2): 318, (2023). https://doi.org/10.3390/math11020318
- [23] Bhattacharyya, G.K., Johnson, R.A., “Estimation of reliability in a multicomponent stress-strength model”, Journal of the American Statistical Association, 69(348): 966–970, (1974).
- [24] Hassan, A.S., Basheikh, H.M., “Estimation of reliability in multi-component stress-strength model following exponentiated Pareto distribution”, The Egyptian Statistical Journal, 56(2): 82–95, (2012).
- [25] Rao, G.S., Aslam, M., Kundu, D., “Burr-XII distribution parametric estimation and estimation of reliability of multicomponent stress-strength”, Communications in Statistics-Theory and Methods, 44(23): 4953–4961, (2015).
- [26] Rao, G.S., Aslam, M., Arif, O.H., “Estimation of reliability in multicomponent stress–strength based on two parameter exponentiated Weibull distribution”, Communications in Statistics-Theory and Methods, 46(15): 7495–7502, (2017).
- [27] Dey, S., Mazucheli, J., Anis, M.Z., “Estimation of reliability of multicomponent stress–strength for a Kumaraswamy distribution”, Communications in Statistics-Theory and Methods, 46(4): 1560–1572, (2017).
- [28] Hassan, A.S., Nagy, H.F., Muhammed, H.Z., Saad, M.S., “Estimation of multicomponent stress-strength reliability following Weibull distribution based on upper record values”, Journal of Taibah University for Science, 14(1): 244–253, (2020).
- [29] Akgül, F.G., “Classical and Bayesian estimation of multicomponent stress–strength reliability for exponentiated Pareto distribution”, Soft Computing, 25(14): 9185–9197, (2021).
- [30] Hassan, A.S., Nagy, H.F., “Reliability estimation in multicomponent stress-strength for generalized inverted exponential distribution based on ranked set sampling”, Gazi University Journal of Science, 35(1): 314–331, (2022).
- [31] Yousef, M.M., Hassan, A.S., Al-Nefaie, A.H., Almetwally, E.M., Almongy, H.M., “Bayesian estimation using MCMC method of system reliability for inverted Topp-Leone distribution based on ranked set sampling”, Mathematics, 10(17): 3122, (2022). https://doi.org/10.3390/math10173122.
- [32] Gupta, R.D., Kundu, D., “Theory & methods: Generalized exponential distributions”, Australian & New Zealand Journal of Statistics, 41(2): 173–188, (1999).
- [33] Gupta, R.D., Kundu, D., “Generalized exponential distribution: different method of estimations”, Journal of Statistical Computation and Simulation, 69(4): 315–337, (2001).
- [34] Gupta, R.D., Kundu, D., “Exponentiated exponential family: an alternative to gamma and Weibull distributions”, Biometrical Journal: Journal of Mathematical Methods in Biosciences, 43(1): 117–130, (2001).
- [35] Raqab, M.Z., “Inferences for generalized exponential distribution based on record statistics”, Journal of Statistical Planning and Inference, 104(2): 339–350, (2002).
- [36] Kundu, D., Gupta, R.D., “Estimation of P [Y< X] for generalized exponential distribution”, Metrika, 61(3): 291–308, (2005).
- [37] Baklizi, A., “Likelihood and Bayesian estimation of Pr (X< Y) using lower record values from the generalized exponential distribution”, Computational Statistics & Data Analysis, 52(7): 3468–3473, (2008).
- [38] Subburaj, R., Gopal, G., Kapur, P.K., “A software reliability growth model for vital quality metrics”, South African Journal of Industrial Engineering, 18(2): 93–108, (2007).
- [39] Biondi, F., Kozubowski, T.J., Panorska, A.K., Saito, L., “A new stochastic model of episode peak and duration for eco-hydro-climatic applications”, Ecological Modelling, 211(3-4): 383–395, (2008).
- [40] Rao, G.S., “Estimation of reliability in multicomponent stress-strength based on generalized exponential distribution”, Revista Colombiana de Estadística, 35(1): 67–76, (2012).
- [41] Guo, L., Gui, W., “Statistical inference of the reliability for generalized exponential distribution under progressive type-II censoring schemes”, IEEE Transactions on Reliability, 67(2): 470–480, (2018).
- [42] Sadeghpour, A., Salehi, M., Nezakati, A., “Estimation of the stress–strength reliability using lower record ranked set sampling scheme under the generalized exponential distribution”, Journal of Statistical Computation and Simulation, 90(1): 51–74, (2020).
- [43] Esemen, M., Gurler, S., Sevinc, B., “Estimation of stress–strength reliability based on ranked set sampling for generalized exponential distribution”, International Journal of Reliability, Quality and Safety Engineering, 28(2): 2150011, (2021). https://doi.org/10.1142/S021853932150011X.
- [44] Xia, Z.P., Yu, J.Y., Cheng, L.D., Liu, L.F., Wang, W.M., “Study on the breaking strength of jute fibres using modified Weibull distribution”, Composites Part A: Applied Science and Manufacturing, 40(1): 54–59, (2009).