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An Estimation of Reliability: Case of One-Parameter Burr Type X Distribution

Mohammed A. Shayib, Aliakbar Montazer Haghighi

Abstract


Estimation of the reliability , where X and Y stand for the strength and stress, respectively, assuming X and Y to be independent and identically distributed random variables, has been extensively studied in the literature. Probability distribution functions such as: normal, Burr type X (in this paper, referred to as Burr X), exponential, gamma, extreme-value, logistic, and Weibull have been considered. However, the effect of the sample size and the parameters’ values of the distribution on the estimation of R have not been addressed, but just recently. In this paper, the one-parameter Burr X distribution is considered as the underlying distribution for X and Y. The estimation of the unknown parameter of the distribution of R is obtained via simulation utilizing (i) the Maximum Likelihood Estimation (MLE), (ii) Uniformly Minimum Variance Unbiased Estimation (UMVUE), (iii) Shrinkage Estimation Procedures (SEP), and (iv) Method of Moments. The performances of the mentioned estimators are compared based on the mean squared error (MSE) and the relative efficiency of the estimators. Additionally, a comparison between the MLE estimators, found by two different methods, for computing R based on Burr X distribution will be performed to choose the best value for R.

Keywords


Reliability, Burr type X Distribution, MLE, Shrinkage, Method of Moments, Sample sizes, Simulation

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