A DISCRETE STRESS STRENGTH INTERFERENCE MODEL FOR UNRELIABILITY BOUNDS

Abstract

This study presents a multiple-line-segment method of implementing the stress-strength interference model when only discrete interval probabilities of stress and strength inside an interference region are available. Based on the discrete interval probabilities, the probability density functions are represented by line segments, which are in turn expressed by piecewise linear polynomials. Thus, unlike in existing empirical methods, when both stress and strength fall into the same subinterval, one can calculate the probability of failure by directly integrating the joint probability of stress and strength over the subinterval. Quadratic programming optimization is implemented to determine the upper and lower bounds on the failure probability, and the average value of the bounds is treated as the point estimate of the failure probability. Finally, numerical examples are carried out to demonstrate the proposed method. Three quantities are used to evaluate the accuracy and effectiveness of the proposed method-the relative error of the point estimate of the unreliability, the width of the bounds on the unreliability, and the minimum number of subintervals needed to generate the bounds that contain the exact unreliability. These three quantities are compared with results in the literature.