Bayesian Analysis of P[Y<X] in its Limiting Form

 

K.K. Sharma, B. Singh, and S. Rathi (2006). Bayesian Analysis of P[Y<X] in its Limiting Form. Journal of Statistical Research, Vol. 40, No. 2, pp.  29-40.

 

Abstract

The present study deals with the Bayesian estimation of the remodeled stress-strength system reliability, $ P[Y < X]. $ Here, $ X $ and $ Y $ represent strength and stress variables respectively. The random variables $ X $ and $ Y $ have been respectively redefined as $ U = min(X_1,X_2,\ldots,X_m) $ and $ V = max(Y_1, Y_2,\ldots, Y_n) $ to conceptualize the concept of limiting stress-strength reliability, $ P[V < U], $ for meeting the requirements of the systems in defense. For such systems, the designer wishes to attach high probability to the event that the system remains operable at its minimum strength encountering with the maximum stress.

 

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