The 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.
SamaniegoFJ. System signatures and their applications in engineering reliability. New York: Springer, 2007.
2.
De FinettiB. Theory of probability. Hoboken, NJ: John Wiley & Sons, 1974.
3.
NavarroJRychlikT. Comparisons and bounds for expected lifetimes of reliability systems. Eur J Oper Res2010; 207: 309–317.
4.
EryilmazS. Review of recent advances in reliability of consecutive k-out-of-n and related systems. Proc IMechE, Part O: J Risk and Reliability2010; 224: 225–237.
5.
CoolenFPACoolen-MaturiT. On generalizing the signature to systems with multiple types of components. In: ZamojskiWMazurkiewiczJSugierJ. (eds) Complex systems and dependability. BerlinSpringer, 2012, pp.115–130.
6.
NavarroJSamaniegoFJBalakrishnanN. Signature-based representations for the reliability of systems with heterogeneous components. J Appl Probab2011; 48: 856–867.
7.
Al-nefaieeAHCoolenFPA. Nonparametric prediction inference for system failure time based on bounds for the signature. Proc IMechE, Part O: J Risk and Reliability2013; 227: 513–522.
8.
Al-nefaieeAH. Nonparametric predictive inference for system failure times. PhD Thesis, Durham University, 2014 (to appear) www.npi-statistics.com
9.
GaofengDZhengBTaizhongH. On computing signatures of coherent systems. J Multivariate Anal2012; 103: 142–150.
10.
AugustinTCoolenFPA. Nonparametric predictive inference and interval probability. J Stat Plan Infer2004; 124: 251–272.
11.
CoolenFPA. On nonparametric predictive inference and objective Bayesianism. J Logic Lang Inform2006; 15: 21–47.
12.
CoolenFPA. Nonparametric predictive inference. In: LovricM (ed.) International encyclopedia of statistical science. Berlin, Heidelberg: Springer, 2011, pp.968–970.
13.
AugustinTCoolenFPAde CoomanGTroffaesMCM (Eds). Introduction to imprecise probabilities. Hoboken, NJ: John Wiley & Sons, in press.
14.
CoolenFPATroffaesMCMAugustinT. Imprecise probability. In: LovricM (ed.) International encyclopedia of statistical science. Berlin, Heidelberg: Springer, 2011, pp.645–648.
WeichselbergerK. Elementare Grundbegriffe einer Allgemeineren Wahrscheinlichkeitsrechnung I. Intervallwahrscheinlichkeit als Umfassendes Konzept [Elementary Foundations of a Generalized Probability Calculus. I. Interval Probability as a Comprehensive Framework]. Heidelberg: Physika, 2001.
17.
CoolenFPAUtkinLV. Imprecise reliability. In: LovricM (ed.) International encyclopedia of statistical science. Berlin, Heidelberg: Springer, 2011, pp.649–650.
18.
UtkinLV. Interval reliability of typical systems with partially known probabilities. Eur J Oper Res2004; 153: 790–802.
19.
UtkinLVCoolenFPA. Imprecise reliability: an introductory overview. In: LovricM (ed.) Computational intelligence in reliability engineering: new metaheuristics, neural and fuzzy techniques in reliability, vol. 2. Berlin, Heidelberg: Springer, 2007, pp.261–306.
20.
AboalkhairAMCoolenFPAMacPheeIM. Nonparametric predictive reliability of series of voting systems. Eur J Oper Res2013; 226: 77–84.
21.
CoolenFPAAboalkhairAMMacPheeIM. Diversity in system reliability following component testing. J Saf Reliab Soc2010; 30: 78–93.
22.
Coolen-SchrijnerPCoolenFPAMacPheeIM. Nonparametric predictive inference for system reliability with redundancy allocation. Proc IMechE, Part O: J Risk and Reliability2008; 222: 463–476.
23.
MacPheeIMCoolenFPAAboalkhairAM. Nonparametric predictive system reliability with redundancy allocation following component testing. Proc IMechE, Part O: J Risk and Reliability2009; 223: 181–188.
24.
CoolenFPAAl-nefaieeAH. Nonparametric predictive inference for failure times of systems with exchangeable components. Proc IMechE, Part O: J Risk and Reliability2012; 226: 262–273.
25.
CoolenFPACoolen-SchrijnerP. A nonparametric predictive method for queues. Eur J Oper Res2003; 145: 425–442.
26.
Coolen-SchrijnerPShawSCCoolenFPA. Opportunity-based age replacement with a one-cycle criterion. J Oper Res Soc2009; 60: 1428–1438.
AbellánJBakerRMCoolenFPA. Maximising entropy on the nonparametric predictive inference model for multinomial data. Eur J Oper Res2011; 212: 112–122.
29.
AbellánJBakerRMCoolenFPACrossmanRJMasegosaAR. Classification with decision trees from a nonparametric predictive inference perspective. Comput Stat Data An2014; 71: 789–802.
30.
CoolenFPA. Low structure imprecise predictive inference for Bayes’ problem. Stat Probabil Lett1998; 36: 349–357.
31.
CoolenFPAMaturiTA. Nonparametric predictive inference for order statistics of future observations. In: BorgeltCGonzález-RodríguezGTrutschnigW. (eds) Combining soft computing and statistical methods in data analysis. Berlin, Heidelberg: Springer, 2010, pp.97–104.
32.
EryilmazS. Circular consecutive k-out-of-n systems with exchangeable dependent components. J Stat Plan Infer2011; 141: 725–733.
33.
EryilmazS. On the mean residual life of a k-out-of-n: G system with a single cold standby component. Eur J Oper Res2012; 222: 273–277.
CoolenFPAYanKJ. Nonparametric predictive inference with right-censored data. J Stat Plan Infer2004; 126: 25–54.
36.
Ruiz-CastroJELiQ. Algorithm for a general discrete k-out-of-n: G system subject to several types of failure with an indefinite number of repairpersons. Eur J Oper Res2011; 211: 97–111.
37.
Coolen-MaturiTCoolenFPA. Unobserved, re-defined, unknown or removed failure modes in competing risks. Proc IMechE, Part O: J Risk and Reliability2011; 225: 461–474.
38.
MaturiTACoolen-SchrijnerPCoolenFPA. Nonparametric predictive inference for competing risks. Proc IMechE, Part O: J Risk and Reliability2010; 224: 11–26.
39.
BuenoVCCarmoIM. Active redundancy allocation for a k-out-of-n: F system of dependent components. Eur J Oper Res2007; 176: 1041–1051.
40.
AslettLJM. MCMC for inference on phase-type and masked system lifetime models. PhD Thesis, Trinity College Dublin, 2012, www.louisaslett.com
