Toward the Effect of Dependent Distribution Parameters on Reliability Prediction

Random variables are commonly encountered in engineering applications, and their distributions are required for analysis and design, especially for reliability prediction during the design process. Distribution parameters are usually estimated using samples. In many applications, samples are in the form of intervals, and the estimated distribution parameters will also be in intervals. Traditional reliability methodologies assume independent interval distribution parameters, but as shown in this study, the parameters are actually dependent since they are estimated from the same set of samples. This study investigates the effect of the dependence of distribution parameters on the accuracy of reliability analysis results. The major approach is numerical simulation and optimization. This study demonstrates that the independent distribution parameter assumption makes the estimated reliability bounds wider than the true bounds. The reason is that the actual combination of the distribution parameters may not include the entire box-type domain assumed by the independent interval parameter assumption. The results of this study not only reveal the cause of the imprecision of the independent distribution parameter assumption, but also demonstrate a need of developing new reliability methods to accommodate dependent distribution parameters.