Reliability Estimation in Multicomponent Stress-strength Model based on Generalized Pareto Distribution

Parameshwar V Pandit^1, and Shubhashree Joshi¹

¹Department of Statistics, Bangalore University, Bangalore -560056

Cite this paper:
Parameshwar V Pandit and Shubhashree Joshi. Reliability Estimation in Multicomponent Stress-strength Model based on Generalized Pareto Distribution. American Journal of Applied Mathematics and Statistics. 2018; 6(5):210-217. doi: 10.12691/ajams-6-5-5

Abstract

The paper deals with the estimation of multicomponent system reliability where the system has k components with their strengths X₁, X₂, … X_k being independently and identically distributed random variables and each component is experiencing a random stress Y. The s-out-of-k system is said to function if atleast s out of k (1 ≤ s ≤ k) strength variables exceed the random stress. The reliability of such a system is derived when both strength and stress variables follow generalized Pareto distribution. The system reliability is estimated using maximum likelihood and Bayesian approaches. The maximum likelihood estimators are derived under both simple random sampling and ranked set sampling schemes. Lindley's approximation technique is used to get approximate Bayes estimators. The reliability estimators obtained from both the methods are compared by using mean squares error criteria and real data analysis is carried out to illustrate the procedure.

Keywords:
generalized Pareto distribution stress-strength reliability ranked set sampling simple random sampling maximum likelihood estimator Bayes estimator

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