Reliability Estimation in Multicomponent Stress-Strength for Generalized Inverted Exponential Distribution Based on Ranked Set Sampling

Year 2022, Volume: 35 Issue: 1, 314 - 331, 01.03.2022

Heba Nagy , Amal Hassan

https://doi.org/10.35378/gujs.760469

Cited By: 8

Abstract

Stress-strength models are considered of great significance due to their applicability in varied fields. We address the estimation of the system reliability of a multicomponent stress-strength model, say Rs,k, of an s out of k system when the pair stress and strengths are drawn from a generalized inverted exponential distribution. The system is deemed as working if at least s out of k strengths be more than its stress. We obtain the reliability estimators when the data of strength and stress distributions are collected from three sampling schemes, specifically; simple random sampling, ranked set sampling, and median ranked set sampling. We obtain four estimators of Rs,k out from median ranked set sampling. The behavior of different estimates is examined via a simulation study based on mean squared errors and efficiencies. The simulation studies point out that the reliability estimates of Rs,k, from the ranked set sampling scheme are preferred than other estimates picked from the simple random sample and median ranked set sampling in a majority of the situations. The theoretical studies are explained with the aid of real data analysis. 

Keywords

Generalized inverted exponential, Multicomponent model, Ranked set sampling, Reliability estimation

References

• [1] McIntyre, G., “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., Clutter, J., “Ranked set sampling theory with order statistics background”, Biometrics, 28(2): 545-555, (1972).
• [4] 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).
• [5] Hassan, A. S., “Maximum likelihood and Bayes estimators of the unknown parameters for exponentiated exponential distribution using ranked set sampling”, International Journal of Engineering Research and Applications, 3(1): 720-725, (2013).
• [6] Hassan, A. S., Abd-Elfattah, A. M., Nagy, H. F., “Modified goodness of fit tests for the Weibull distribution based on moving extreme ranked set sampling”, In The 48th Annual Conference on Statistics, Computer Science and Operations Research, Faculty of Graduate Studies for Statistical Research, Cairo University, (2013).
• [7] Özdemir, Y. A., Ebegil, M., Gökpinar, F., “A test statistic based on ranked set sampling for two normal means”, Communications in Statistics-Simulation and Computation, 46(10): 8077-8085, (2017).
• [8] Özdemir, Y. A., Ebegil, M., Gökpinar, F., “A test statistic for two normal means with median ranked set sampling”, Iranian Journal of Science and Technology, Transactions A: Science, 43(3): 1109-1126, (2019).
• [9] Bantan, R., Hassan, A. S., Elsehetry, M., “Zubair Lomax distribution: properties and estimation based on ranked set sampling”, CMC-Comuters, Materials & Continua, 65(3): 2169-2187, (2020).
• [10] Muttlak, H., “Median ranked set sampling”, Journal of Applied Statistical Science, 6: 245-255, (1997).
• [11] Birnbaum, Z., “On a use of the Mann-Whitney statistic”, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability: Contributions to the Theory of Statistics, Berkeley, California: University of California Press, 1: 13-17, (1956).
• [12] Birnbaum, Z., McCarty, R., “A distribution-free upper confidence bound for Pr{Y<X} based on independent samples of X and Y”, The Annals of Mathematical Statistics, 29(2): 558-562, (1958).
• [13] Sengupta, S., Mukhuti, S., “Unbiased estimation of P(X>Y) for exponential populations using order statistics with application in ranked set sampling”, Communications in Statistics-Theory and Methods, 37(6): 898-916, (2008).
• [14] Muttlak, H. A., Abu-Dayyeh, W., Saleh, M., Al-Sawi, E., “Estimating P (Y< X) using ranked set sampling in case of the exponential distribution”, Communications in Statistics-Theory and Methods, 39(10): 1855-1868, (2010).
• [15] Hussian, M. A., “Estimation of stress-strength model for generalized inverted exponential distribution using ranked set sampling”, International Journal of Advances in Engineering & Technology, 6(6): 2354-2362, (2014).
• [16] Hassan, A. S., Assar, S., Yahya, M., “Estimation of R= P [Y< X] for Burr type XII distribution based on ranked set sampling”, International Journal of Basic and Applied Sciences, 3(3): 274-280, (2014).
• [17] Hassan, A. S., Assar, S., Yahya, M., “Estimation of P (Y< X) for Burr distribution under several modifications for ranked set sampling”, Australian Journal of Basic and Applied Sciences, 9(1): 124-140, (2015).
• [18] Akgül, F. G., Şenoğlu, B., “Estimation of P (X< Y) using ranked set sampling for the Weibull distribution”, Quality Technology and Quantitative Management, 14(3): 296-309, (2017).
• [19] Akgül, F. G., Acıtaş, Ş., Şenoğlu, B., “Inferences on stress–strength reliability based on ranked set sampling data in case of Lindley distribution”, Journal of Statistical Computation and Simulation, 88(15): 3018-3032, (2018).
• [20] Al-Omari, A. I., 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 & Continua, 64(2): 835-857, (2020).
• [21] Bhattacharyya, G., Johnson, R. A., “Estimation of reliability in a multicomponent stress-strength model”, Journal of the American Statistical Association, 69(348): 966-970, (1974).
• [22] Kuo, W., Zuo, M. J., “Optimal Reliability Modeling: Principles and Applications”, John Wiley & Sons, (2003).
• [23] Rezaei, S., Tahmasbi, R., Mahmoodi, M., “Estimation of P[Y< X] for generalized Pareto distribution”, Journal of Statistical Planning and Inference, 140(2): 480-494, (2010).
• [24] Hassan, A. S., Basheikh, H. M., “Estimation of reliability in multi-component stress-strength model following exponentiated Pareto distribution”, The Egyptian Statistical Journal, Faculty of Graduate Studies for Statistical Research, Cairo University, 56(2): 82-95, (2012).
• [25] Hassan, A. S., Basheikh, H. M., “Reliability estimation of stress-strength model with non-identical component strengths: the exponentiated Pareto case”, International Journal of Engineering Research and Applications, 2(3): 2774-2781, (2012).
• [26] Rao, G. S., “Estimation of reliability in multicomponent stress-strength based on generalized exponential distribution”, Revista Colombiana de Estadística, 35(1): 67-76, (2012).
• [27] 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).
• [28] Hassan, A. S., Assar, M. S., Yahya, M., “Estimation of reliability in multicomponent stress- strength model following Burr Type XII distribution under selective ranked set sampling”, International Journal of Engineering Research and Applications, 5(2): 62-78, (2015).
• [29] 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).
• [30] Abouammoh, A., Alshingiti, A. M., “Reliability estimation of generalized inverted exponential distribution”, Journal of Statistical Computation and Simulation, 79(11): 1301-1315, (2009).
• [31] Dey, S., Dey, T., “Generalized inverted exponential distribution: Different methods of estimation”, American Journal of Mathematical and Management Sciences, 33(3): 194-215, (2014).
• [32] Hassan, A. S., Abd-Allah, M., Nagy, H. F., “Bayesian analysis of record statistics based on generalized inverted exponential model”, International Journal on Advanced Science, Engineering and Information Technology, 8(2): 323-335, (2018).
• [33] Hassan, A. S., Abd-Allah, M., Nagy, H. F., “Estimation of P (Y<X) using record values from the generalized inverted exponential distribution”, Pakistan Journal of Statistics and Operation Research, 14(3): 645-660, (2018).
• [34] Hassan, A. S., Al-Omari, A. I., 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).
• [35] Krishna, H., Kumar, K., “Reliability estimation in generalized inverted exponential distribution with progressively type II censored sample”, Journal of Statistical Computation and Simulation, 83(6): 1007-1019, (2013).
• [36] Bader, M., Priest, A., “Statistical aspects of fibre and bundle strength in hybrid composites”, Progress in Science and Engineering of Composites: 1129-1136, (1982).