Equivalent Representations of Set Functions
Mathematics of Operations Research
Reliability and expectation bounds for coherent systems with exchangeable components
Journal of Multivariate Analysis
Applications of average and projected systems to the study of coherent systems
Journal of Multivariate Analysis
On signature-based expressions of system reliability
Journal of Multivariate Analysis
On the extensions of Barlow-Proschan importance index and system signature to dependent lifetimes
Journal of Multivariate Analysis
Journal of Multivariate Analysis
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The concept of system signature was introduced by Samaniego for systems whose components have i.i.d. lifetimes. We consider its extension to the continuous dependent case and give an explicit expression for this extension as a difference of weighted means of the structure function values. We then derive a formula for the computation of the coefficients of these weighted means in the special case of independent continuous lifetimes. Finally, we interpret this extended concept of signature through a natural least squares approximation problem.