Discrete Multicomponent Stress-Strength inference in Proportional Hazard Model

چکیده مقاله

‎In stress-strength models‎, ‎consider a system which has $k$ independent strength components and each component is constructed by a pair of dependent elements‎. ‎These elements $(X_1‎, ‎Y_1)‎, ‎(X_2‎, ‎Y_2)‎, ‎\ldots‎, ‎(X_k‎, ‎Y_k)$ follow a discrete bivariate proportional hazard rate family and‎ ‎each element is exposed to a common random stress $T$ which follows a discrete univariate proportional hazard rate family‎. ‎The system is regarded as operating only if at least $s$ out of $k$ ($1 \leq s \leq k$) strength variables exceed the random stress‎. ‎In this paper‎, ‎based on a general form of discrete lifetime distribution in proportional hazard rate models‎, ‎the estimation of multicomponent stress-strength reliability parameter is studied‎. Finally, as an example the model have studied in a new bivariate Gemometric distribution.