Importance measures of basic variable under multiple failure modes and their solutions

For reliability model with multiple failure modes commonly used in engineering, an importance measure of the basic variable on the global joint probability distribution of multiple-dimensional response performance functions is proposed and it is named as the importance measure I. By taking the specialties of the reliability model into consideration, two importance measures are established to measure the effects of the basic variable on the local joint probability distribution respectively. The properties of three importance measures are analyzed and verified, and their similarities, dissimilarities and applicability are discussed, too. A standard computational method is given to solve three importance measures. Then more reference information can be provided to designer without adding computational cost by the given standard solutions. Finally, a numerical example and an engineering example are used to demonstrate the accuracy and feasibility of the proposed importance measures and their solutions.