ARIMA-based investigation of resistance of member composed of elements with correlated strengths

Abstract

A method for computing the variance of the strength of a compound member consisting of identical mass-produced ductile elements is presented that accounts for correlation between the strengths of the individual elements. The individual element strengths are represented as a first-order, zero-mean, autoregressive time series and the associated variance, covariance and correlation are computed. The variance of the overall strength of the compound member is derived, and can be computed efficiently without requiring derivation of the element strength correlation matrix. The sensitivity of the variance of the overall strength of the compound member to the number of elements and the degree of correlation between their strengths is investigated. The common assumption of fully correlated strengths is increasingly conservative as the number of elements increases or the degree of correlation between their strengths reduces. Two practical examples illustrate the method. The first also quantifies approximately the impact of the degree of correlation on the resistance factor of the compound member. The second also indicates how readily available data, such as the within-batch strength variation of individual members, can be used to estimate the degree of correlation of their strengths.