Estimation of reliability in multicomponent stress-strength based on generalized Rayleigh distribution
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Wayne State University Library System in Detroit
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Abstract. Full text available at https://digitalcommons.wayne.edu/jmasm/vol13/iss1/24/
A multicomponent system of k components having strengths following k- independently and identically distributed random variables x1, x2,…, xk and each component experiencing a random stress Y is considered. The system is regarded as alive only if at least s out of k (s < k) strengths exceed the stress. The reliability of such a system is obtained when strength and stress variates are given by a generalized Rayleigh distribution with different shape parameters. Reliability is estimated using the maximum likelihood (ML) method of estimation in samples drawn from strength and stress distributions; the reliability estimators are compared asymptotically. Monte-Carlo simulation is used to compare reliability estimates for the small samples and real data sets illustrate the procedure.
A multicomponent system of k components having strengths following k- independently and identically distributed random variables x1, x2,…, xk and each component experiencing a random stress Y is considered. The system is regarded as alive only if at least s out of k (s < k) strengths exceed the stress. The reliability of such a system is obtained when strength and stress variates are given by a generalized Rayleigh distribution with different shape parameters. Reliability is estimated using the maximum likelihood (ML) method of estimation in samples drawn from strength and stress distributions; the reliability estimators are compared asymptotically. Monte-Carlo simulation is used to compare reliability estimates for the small samples and real data sets illustrate the procedure.
Keywords
ML estimation, Confidence intervals, Stress-strength, Reliability estimation, Rayleigh distribution, Maximum likelihood, ML, Generalized rayleigh distribution