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Statistical Inferences on Multicomponent Reliability for PRHR Family of Distributions Based on Records

  • Anupam Pathak,
  • Taruna Kumari

摘要

In this study, we have introduced and obtained the estimators for the multicomponent reliability function \(\rho_{k} \left( t \right)\) ρ k t using lower record values. The estimators of \(\rho_{k} \left( t \right)\) ρ k t are used to derive the well-known multicomponent stress-strength reliability function \(\rho_{s, \, k}\) ρ s , k . In order to develop multicomponent model, we have considered a system having k statistically independent and identically distributed strength components, and each of these strength components is receptive to a universal random stress. It is assumed that the strength and stress variables are independent and follow distinct proportional reversed hazard rate families of distributions. The estimators of \(\rho_{k} \left( t \right)\) ρ k t and \(\rho_{s, \, k}\) ρ s , k are obtained by using both the classical and Bayesian approaches. The maximum likelihood, uniformly minimum variance unbiased and Bayes estimators, all are obtained in explicit form. Monte Carlo simulation technique is employed for comparative analysis of the proposed estimators. The theoretical findings are illustrated through real-world data set.