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

Abstract

The paper deals with the estimation of multicomponent system reliability where the system has k components with their strengths X 1 , X 2 , … 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.

Bayesian Estimation of Exponentiated Exponential Strength and Exponentiated Weibull Stress Reliability Model for Real Data

“…The estimation and testing methods for the reliability functions of exponentiated distributions under censoring were studied by Chaturvedi and Vyas [1]. Li and Hao [6] estimated the reliability of a stress-strength model for the inverse Weibull distribution, Chaturvedi and Kumari [4] concentrated on the robust Bayesian analysis of the generalized half logistic distribution, Pandit and Joshi [16] investigated the estimation of multicomponent system stress-strength reliability for the generalized Pareto distribution. The stress-strength parameter was studied by Eissa [8] using Bayesian and non-Bayesian conclusions when random variables X and Y had the exponentiated Weibull distribution.…”

Estimation of Reliability under Conditional Stress - Strength Setup based on Weibull Distribution

“…Erylmaz S [8] investigated stress-strength reliability within the framework of multi-state system modeling. Recently, Pandit and Joshi [9] studied stress -strength reliability for generalized Pareto distribution.…”

Employ Shrinkage Estimation Technique for the Reliability System in Stress-Strength Models: special case of Exponentiated Family Distribution

“…A multicomponent system consuming k th strength independently and non-identically random variables and everyone subjected to random stress was presented by Bhattacharyya and Johnson (1974) [1].The system reliability model, (s out of k ) was denoted by R(s,k) when at least s ( 1≤ s≤ k) of components survive. In (2012), Pandit and Kantu studied the reliability estimation in multicomponent stress-strength(s-s) with the assumption that strengths and stresses followed the Pareto distribution [2] . Rao & Naidu in (2013) studied the multicomponent system reliability in (s-s) model for Exponentiated half Logistic distribution [3].…”