Reliability Analysis for Two Components Connected in Parallel with Lindley Probability Model - Hussain, Ehtesham; Haq, Masood ul (International Journal of Statistics in Medical Research, 2015)
Reliability of structures has been discussed by several authors using probability models. Some of the early researches have been discussed by Birnbaum (1956) [1] in which two independent variables X and Y are defined as “Strength” and “Stress” respectively. This research is an extension of Mann- Whitney paper (1947) [2] on P(Y<X). Beg (1979c, 1980b, 1980c) [3-5] estimated reliability i.e R = P(Y<X), by taking two parameter Pareto and Power function distributions. Gupta and Gupta (1990) [6] have found point estimates of R=P(aX> bY) by Maximum likelihood and MVUE of R. In the present paper we have considered R=P(Y<X) where X and Y independently follow Lindley distribution. The MLE and Moment estimators of the distribution and then that of R have been found. A simulation study has been done to estimate biasedness and Confidence interval of R.