E- Bayesian Estimation of System Reliability (Series, Parallel) and Failure Rate Functions with Kumaraswamy Distribution based on Type II Censoring Data

Abstract

In this paper, the failure rate function and the shape parameter for the kumaraswamy distribution and reliability function of a system with a number (m) of independent compounds associated with a system (serial, parallel) were estimated, by relying on observational data of the second type, knowing that the survival time of the compounds are independent. Based on the findings the graphical predictor of the failure rate and parameter-and the reliability function of the serial and parallel system is smaller than the Standard Bayesian estimator (MLE) in simulation and real data. Thus, a decreasing in AMPE with an increase in the sample size n and an increase in the size of the failure sample r as the physical prediction capabilities have a high efficiency. The using of the Bayesian prediction method to estimate the reliability of different production systems for other failure distributions such as the Burr family distributions and various other failure distributions. Based on the output he results are reasonably consistent with simulation and real data. The E-Bayesian method was used for estimating with three primary distribution functions for the above parameters and comparing them with the standard Bayesian method with a squared loss function and the maximum likelihood method where simulation experiments were employed to compare the estimation results and the results showed the advantage of the E-Bayesian method in estimating through comparison statistics (MAPE).