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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractThe survival signature has recently been presented as an attractive concept to aid quantification of system reliability. It has similar characteristics as the system signature, which is well established, but contrary to the latter it is easily applicable to systems with multiple types of components. We present an introductory overview of the survival signature together with new results to aid computation. We develop nonparametric predictive inference for system reliability using the survival signature. The focus is on the failure time of a system, given failure times of tested components of the same types as used in the system.

In reliability, failure data often correspond to competing risks, where several failure modes can cause a unit to fail. This paper presents nonparametric predictive inference (NPI) for competing risks data, assuming that the different failure modes are independent. NPI is a statistical approach based on few assumptions, with inferences strongly based on data and with uncertainty quantified via lower and upper probabilities. The focus is on the lower and upper probabilities for the event that a future unit will fail due to a specific failure mode. The paper illustrates the effect of grouping different failure modes together, and some special cases and features are discussed. It is also shown that NPI can easily deal with competing risks data resulting from experiments with progressive censoring. Furthermore, new formulae are presented for the NPI lower and upper survival functions.

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Recently, the survival signature has been presented as a summary of the structure function which is su cient for computation of common reliability metrics and has the crucial advantage that it can be applied to systems with components whose failure times are not exchangeable. The survival signature provides a huge reduction in required information, e.g. for its storage, compared to the full structure function, its implementation to larger systems is still di cult in a purely analytical manner and simulations may be required to derive the reliability metrics of interest. Hence, the main question addressed in this paper is whether or not the survival signature provides su cient information for e cient simulation to derive the system's failure time distribution. We answer this question in the a rmative by presenting two algorithms for survival signature-based simulation. In addition, we present a third simulation algorithm that can be used in case of repairable components. It turns out that these algorithms are very e cient, beyond the initial advantage of requiring only the survival signature to be available, instead of the full structure function.

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