Bhupendra Singh

Parameter estimation of Lindley distribution with hybrid censored data

This study deals with the classical and Bayesian analysis of the hybrid censored lifetime data under the assumption that the lifetime follow Lindley distribution. In classical set up, the maximum likelihood estimate of the parameter with its standard error are computed. Further, by assuming Jeffrey’s invariant and gamma priors of the unknown parameter, Bayes estimate along with its posterior standard error and highest posterior density credible intervals of the parameter are obtained. Markov Chain Monte Carlo technique such as Metropolis–Hastings algorithm has been utilized to generate draws from the posterior density of the parameter. A real data set representing the waiting time of the bank customers has been analyzed for illustration purpose. A comparison study is conducted to judge the performance of the classical and Bayesian estimation procedure.

A classical and Bayesian estimation of a k-components load-sharing parallel system

The present study proposes the classical and Bayesian treatment to the estimation problem of parameters of a k-components load-sharing parallel system in which some of the components follow a constant failure-rate and the remaining follow a linearly increasing failure-rate. In the classical setup, the maximum likelihood estimates of the load-share parameters with their variances are obtained. (1-@c)100% individual, simultaneous, Bonferroni simultaneous and two bootstrap confidence intervals for the parameters have been constructed. Further, on recognizing the fact that life testing experiments are very time consuming, the parameters involved in the failure time distributions of the system are expected to follow some random variations. Therefore, Bayes estimates along with their posterior variances of the parameters are obtained by assuming gamma and Jeffreys invariant priors. Markov Chain Monte Carlo techniques such as a Gibbs sampler have also been used to obtain the Bayes estimates and highest posterior density credible intervals when all the parameters follow gamma priors.

Inferential statistics on the dynamic system model with time-dependent failure-rate

This study focuses on the classical and Bayesian analysis of a k-components load-sharing parallel system in which components have time-dependent failure rates. In the classical set up, the maximum likelihood estimates of the load-share parameters with their standard errors (SEs) are obtained. (1−γ) 100% simultaneous and two bootstrap confidence intervals for the parameters and system reliability and hazard functions have been constructed. Further, on recognizing the fact that life-testing experiments are very time consuming, the parameters involved in the failure time distribution of the system are expected to follow some random variations. Therefore, Bayes estimates along with their posterior SEs of the parameters and system reliability and hazard functions are obtained by assuming gamma and Jeffreys priors of the unknown parameters. Markov chain Monte Carlo technique such as Gibbs sampler has been used to obtain Bayes estimates and highest posterior density credible intervals.

Bayesian reliability estimation of a 1-out-of-k load-sharing system model

The study deals with the reliability analysis of a 1-out-of-k load-sharing system model under the assumption that each component’s failure time follows generalized exponential distribution. With the assumption of load-sharing inclination among the system’s components, the system reliability and hazard rate functions have been derived. In classical set up, we derive maximum likelihood estimates of the load-sharing parameters with their standard errors. Classical confidence intervals and two bootstrap confidence intervals for the parameters, system reliability and hazard rate functions have also been proposed. For Bayesian estimation, we adopt sampling-based posterior inference procedure based on Markov Chain Monte Carlo techniques such as Gibbs and Metropolis–Hastings sampling algorithms. We assume both non-informative and informative priors representing the variations in the model parameters. A simulation study is carried out for highlighting the theoretical developments.

The exponentiated Perks distribution

The study proposes the exponentiated Perks distribution as a generalization of Perks distribution. This generalized distribution provides monotone nondecreasing and bathtub shaped hazard rate function. We study its mathematical properties including mode, median, quantile function and order statistics. The estimation of the model parameters is discussed both in classical and Bayesian setups. The maximum likelihood estimates along with their standard errors and confidence intervals have been obtained. For Bayesian estimation, we use independent gamma priors for the model parameters. The posterior densities of the parameters are simulated using Metropolis–Hastings algorithm to obtain sample-based estimates and highest posterior density intervals. Applications of the proposed distribution to three real data sets have been demonstrated.

Distribution‐free inferences on system reliability

Describes how sampling distribution of the estimates of the reliability functions for various failure time distributions is either hard to obtain or is quite complicated and, as such, it becomes difficult to draw inferences about the reliability of a system. To overcome this situation, presents some distribution‐free inference techniques on system reliability and gives Bayesian reliability analysis using conjugate priors.