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189 – Hybrid or Online Teaching and Quantitative Reasoning

Inference Procedures for Bivariate Exponential Model of Gumbel in Reliability Theory

Sponsor: International Indian Statistical Association
Keywords: Multivariate Central Limit Theorem, Slutsky Theorem, Standby System, Steady State Availability

Paul Savariappan

Luther College

S. Thobias

Loyola College

P. Chandrasekhar

Loyola College

M. Sulvai Anthony

Loyola College

Assuming that the joint distribution of lifetime and repair time of a failed unit in a two unit cold standby system is bivariate exponential (see Gumbel(1960)), measures of system performance such as system reliability, MTBF, point availability and steady state availability are obtained. Further, 100 (1-a) % asymptotic confidence limits for steady state availability of the system and an estimator of system reliability based on moments are obtained. Numerical work is carried out to illustrate the behaviour of steady state availability as well as the system reliability based on moments by simulating samples from bivariate exponential distribution due to Gumbel (1960).

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