Abstract
The present study deals with the method of estimation of the parameters of k-components load-sharing parallel system model in which each component’s failure time distribution is assumed to be geometric. The maximum likelihood estimates of the load-share parameters with their standard errors are obtained. (1 − γ) 100% joint, Bonferroni simultaneous and two bootstrap confidence intervals for the parameters have been constructed. Further, recognizing the fact that life testing experiments are time consuming, it seems realistic to consider the load-share parameters to be random variable. Therefore, Bayes estimates along with their standard errors of the parameters are obtained by assuming Jeffrey’s invariant and gamma priors for the unknown parameters. Since, Bayes estimators can not be found in closed form expressions, Tierney and Kadane’s approximation method have been used to compute Bayes estimates and standard errors of the parameters. Markov Chain Monte Carlo technique such as Gibbs sampler is also used to obtain Bayes estimates and highest posterior density credible intervals of the load-share parameters. Metropolis–Hastings algorithm is used to generate samples from the posterior distributions of the unknown parameters.
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Singh, B., Sharma, K.K. & Kumar, A. Analyzing the dynamic system model with discrete failure time distribution. Stat Methods Appl 18, 521–542 (2009). https://doi.org/10.1007/s10260-008-0111-y
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DOI: https://doi.org/10.1007/s10260-008-0111-y