A Generalized Confidence Region for Stress-Strength Reliability

Consider a system which consists of primary and secondary members having strength X and Z respectively. For this system subject to a stress Y the reliability function is: Pr{X + Z > Y|Z = z}. A distribution-free simultaneous lower confidence region for this reliability based on the generalized Kolmogorov-Smirnov distance using empirical reliability is constructed. To avoid tedious computations a conservative confidence region is presented. The proposed method provides more precise information about the reliability of the system than is afforded by the existing methods. Numerical results for implementation are given along with an example.