Author(s)

L. Lee Ho & A. Sá Peixoto Pinheiro

Abstract

: In a strength-stress interference model we are interested in estimating the reliability. Here we present two results: the first is a conservative lower bound of confidence interval of the reliability when stress and strength are independent normal random variables and the second is an empirical estimator of the reliability which inferential aspects were developed under a Bayesian perspective. Both results were illustrated by examples and simulations. 1 Introduction In many situations, we are interested in calculating the probability of the event X < Y, where X and Y are independent random variables with means and variances ux, ox2and uy, oy2 respectively. One of this situation is in a stress- strength interference model where X and Y are assumed respectively as strength and stress random variables. In engineering science, safety margin (SM) and safety factor (SF) are functions of stress and strength and they are respectively settled as SM=X-Y and SF=X/Y and the most interest concerns in obtaining the probability pr=P(SM>O)=P(X-Y>O) or P(SF>1)=P(X/Y>l). (See Ebeling [I]). There is a large number of studies on this subject. And results under distribution functions for strength and stress such as normal, log-normal, exponential, gamma or Weibull are known. It is not difficult to verify that when X and Y are independent normally distributed, the probability pr=P(SM>O) is given by pr=D((ux-uy)/(ox2+oy2)0.5) (1) where D (.) denotes the cumulative standard normal distribution. Similarly when X and Y are independent log-normally distributed, pr= P(SF>1) is given by

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