INFERENTIAL ANALYSIS OF THE RE-MODELED STRESS-STRENGTH SYSTEM RELIABILITYWITH APPLICATION TO THE REAL DATA

Bhupendra  Singh; Shubhi  Rathi; Gajraj  Singh

Bhupendra Singh Department of Statistics, C.C.S. University, Meerut-250004, India
Shubhi Rathi Department of Statistics, C.C.S. University, Meerut-250004, India
Gajraj Singh Department of Statistics, C.C.S. University, Meerut-250004, India

Keywords: Stress-Strength model, maximum likelihood estimate, Bayes estimate, empirical distribution function, Gibbs sampler, Metropolis-Hastings algorithm, highest posterior density credible interval

Abstract

The present study deals with the classical and Bayesian analysis of re-modeled stress-strength system reliability by considering Weibull distribution as the distribution of both the stress and strength variables. The proposed re-modeled stress-strength system reliability is defined as the probability that the system is capable to withstand the maximum operated stress at its minimum strength i.e., P[U>V], where U=Min(X1, X2…Xm) and V=Max(Y1,Y2,……Yn). The observations X1, X2…Xm and Y1,Y2,……Yn are the measurements on the strength and stress variables at different time epochs. The goodness-of-fit of the two real data sets for the proposed model is also demonstrated.

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