Estimation of multicomponent stress-strength reliability following Weibull distribution based on upper record values

Abstract

Stress-strength models are of special importance in reliability literature and engineering applications. This paper deals with the estimation problem of a stress-strength model incorporating multi-component system. The system is regarded as alive only if at least S out of k (S < k) strength components exceed the stress. The reliability of such system is obtained when strength and stress variables have Weibull distributions. Maximum likelihood estimator of R S,k and asymptotic confidence intervals are obtained based on upper record values. Bayesian estimator under squared error and linear exponential loss functions using gamma prior distributions and the corresponding credible intervals are obtained. Due to the lack of explicit forms for the Bayes estimates, the Markov Chain Monte Carlo (MCMC) method is employed. A simulation study is implemented to assess the performance of estimates. A real-life example is presented to show how the proposed model may be utilized in breaking strength of jute fibre data.

On suitability of modified Weibull extension distribution in modeling product lifetimes and reliability

“…El-Morshedy et al 4 introduced three parametric exponentiated inverse flexible Weibull extension distribution and compared its performance with various modification of WD. The other recently introduced modifications of WD and their estimation can be seen from the contributions of Tahir et al, 5 Cordeiro et al, 6 Basheer, 7 Hassan et al, 8 and Afify et al 9…”

“…El-Morshedy et al 4 introduced three parametric exponentiated inverse flexible Weibull extension distribution and compared its performance with various modification of WD. The other recently introduced modifications of WD and their estimation can be seen from the contributions of Tahir et al, 5 Cordeiro et al, 6 Basheer, 7 Hassan et al, 8 and Afify et al 9 The Bayesian estimation of modifications of the WD has also attracted the attention of many researchers. Kaur et al 10 implemented the Bayesian and semi Bayesian estimation of generalized inverse WD parameters using LA.…”

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

“…[28] discussed the estimation of the MSS reliability when X and Y are independent Burr XII distribution under selective RSS. [29] discussed s-out-of-k reliability estimator for Weibull distribution from record values.…”

Stress‐Strength Reliability for Exponentiated Inverted Weibull Distribution with Application on Breaking of Jute Fiber and Carbon Fibers

“…Let X and Y be independent exponentiated inverted Weibull random variables and follow EIW ( θ 1 , β ) and EIW ( θ 2 , β ), respectively; then R = P ( Y < X ) can be written as follows (see Hassan et al [ 24 ]): …”