Open Access Open Access  Restricted Access Subscription Access

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

Mohammed A. Shayib, Aliakbar Montazer Haghighi


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.


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

Full Text:


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information.