Reliability Estimation for Multicomponent Stress-Strength Model Using Median Ranked Set Sampling in Case of Topp-Leone Distribution
Keywords:
Topp-Leone distribution, multicomponent stress strength model, ranked set sampling, median ranked set sampling, modified maximum likelihoodAbstract
This paper seeks to focus on estimation the reliability of multicomponent stress-strength model when component stresses and strengths are assumed to have Topp-Loene (TL) distribution, our study is concentrated on the probability exceed
where the
components having strengths following
-independently and identically distributed random variables
and each component experiencing a random stress
.
is estimated based on median ranked set sampling (MRSS) and ranked set sampling (RSS) schemes and compare the results with simple random sampling (SRS). Maximum likelihood method (ML) of estimation is obtained to make inference about
based on different sampling techniques. Modified maximum likelihood (MML) methodology is used to give explicit estimator of
as an alternative procedure to maximum likelihood method in case of ranked set sampling and median ranked set sampling. An extensive numerical study is investigated to compare the performance of the different sampling techniques. Finally, an illustrative example of a real data is used to show the application of the methods in practice.
References
Akgül FG, Şenoğlu B. Estimation of P(X < Y) using ranked set sampling for the Weibull distribution. Qual Technol Quant Manag. 2017; 14(3): 296-309.
Akgül FG. Reliability estimation in multicomponent stress-strength model for Topp-Leone distribution. J Stat Comput Simul. 2019; 89(5): 2914-2929.
Al-Omari AI, Almanjahie IM, Hassan AS, Nagy HF. Estimation of the stress-strength reliability for exponentiated Pareto distribution using median and ranked set sampling methods. Comput Mater Contin. 2020; 64(2): 835-857.
Bhattacharyya GK, Johnson RA. Estimation of reliability in a multicomponent stress-strength model. J Am Stat Assoc. 1974; 69(348): 966-970.
Caramanis M, Stremel JV, Fleck W, Daniel S. Probabilistic production costing: an investigation of alternative algorithms. Int J Electr Power Energy Syst. 1983; 5(2): 75-86.
Church JD, Harris B. The estimation of reliability from stress-strength relationship. Technometrics. 1970; 12(1): 49-54.
Dell TR, Clutter JL. Ranked set sampling theory with order statistics background. Biometrics. 1972; 28(2): 545-555.
Draper NR, Gattman I. Bayesian analysis of reliability in multi component stress-strength models. Commun Stat - Theory Methods. 1978; 7(5): 441-451.
Esemen M, Gurler S, Sevinc B. Estimation of stress-strength reliability based on ranked set sampling for generalized exponential distribution. Int J Reliab Qual Saf Eng. 2020; 28(3): 1-24.
Genç AI. Estimation of P(X > Y) with Topp-Leone distribution. J Stat Comput Simul. 2013; 83(2): 326-339.
Hassan AS. Maximum likelihood and Bayes estimators of the unknown parameters for exponentiated exponential distribution using ranked set sampling. Int J Eng Res Appl. 2013; 3(1): 720-725.
Hassan MK, Alohli MI, Alojail FA. A new application of R = P(Y < X) for the inverse Lindely distribution using ranked set sampling. J Stat Manag Syst. 2021; 24(8): 1713-1731.
Hassan AS, Assar SM, Yahya M. Estimation of R = P(Y < X) for Burr type XII distribution based on ranked set sampling. Int J Basic Appl Sci. 2014; 3(3): 274-280.
Hassan AS, Assar SM, Yahya M. Estimation of P(Y < X) for Burr distribution under several modifications for ranked set sampling. Aust J Basic Appl Sci. 2015; 9(1): 124-140.
Hussian MA. Estimation of stress-strength model for generalized inverted exponential distribution using ranked set sampling. Int J Adv Eng Technol. 2014; 6(6): 2354-2362.
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