Studies on properties and estimation problems for modified extension of exponential distribution

The present paper considers modified extension of the exponential distribution with three parameters. We study the main properties of this new distribution, with special emphasis on its median, mode and moments function and some characteristics related to reliability studies. For Modified- extension exponential distribution (MEXED) we have obtained the Bayes Estimators of scale and shape parameters using Lindley's approximation (L-approximation) under squared error loss function. But, through this approximation technique it is not possible to compute the interval estimates of the parameters. Therefore, we also propose Gibbs sampling method to generate sample from the posterior distribution. On the basis of generated posterior sample we computed the Bayes estimates of the unknown parameters and constructed 95 % highest posterior density credible intervals. A Monte Carlo simulation study is carried out to compare the performance of Bayes estimators with the corresponding classical estimators in terms of their simulated risk. A real data set has been considered for illustrative purpose of the study.Comment: 22,

Study of Reliability with Mixed Standby Components

This paper deals with the reliability characteristics of two different series system configurations with mixed standby (include cold and warm standby) components. The failure rates of the primary and warm standby components are assumed to follow the Weibull distribution. The repair time distribution of each server is exponentially distributed. Moreover, we will derive the mean time-to-failure, and the steady-state availability for a special case of a serial system of two primary components, two warm standby components, and one cold standby component, when the failure and repair rate are constant

Semi-Markov Model of a Series-Parallel System Subject to Preventive Maintenance

The purpose of this paper is to analyze a series-parallel system by using semi-Markov process. There is a preventive maintenance action provided to the system in order to increase the life time of the system. We suppose that the failure, repair, and maintenance times are stochastically independent random variables each having an arbitrary distribution. The kernel matrix associated with this system is constructed. Expressions for mean sojourn times, steady-state availability, availability function, reliability function, mean time to failure, and mean time to repair are presented. Numerical solutions of the system are obtained