平均値と分散による破損確率および安全係数の上界評価 (連続・単峰性のみを仮定した場合)

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This paper is concerned with evaluation of the upper bound of probability of failure when the distribution forms of the strength R and the stress S are unknown and only their means μ_R and μ_S and variances σ^2_R and σ^2_S are known. In the previous paper, assuming (a) the distribution of Z≡R-S is continuous and unimodal and (b) the mode of Z is equal to the mean of Z, the present author derived the formula P_<fU>=(4/9)(f^2_cη^2_R+η^2_S)/(f_c-1)^2 using Camp-Meidell inequality, where f_c≡μ_R/μ_S is the central factor of safety, and η_R≡σ_R/μ_R and η_S≡σ_S/μ_S are the coefficients of variation of r and s, respectively. However, the assumption (b) can be satisfied only in limited cases. Thus, it was attenpted in the present paper to evaluate P_<fu> assuming only (a) without assuming (b). The problem was formulated as an optimization problem and solved using linear programming. It was found that the above formula can still be used under the assumption (a) alone. That is, the formula gives an almost exact value of P_<fu> under the assumption (a) alone when η_z is large. Hence, practical applicability was given to the above formula in the present study. The upper bound of the central factor of safety can also be obtained from this formula only by assuming the condition (a). Thus, by merely assuming that the distribution of Z≡R-S is continuous and unimodal, considerably lower upper bounds can be obtained for the probability of failure and for the factor of safety as compared with the case when no assumption is made.
社団法人日本材料学会の論文
1989-12-15

平均値と分散による破損確率および安全係数の上界評価 (連続・単峰性のみを仮定した場合)

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