System signatures provide a powerful framework for reliability assessment for systems consisting of exchangeable components. The use of signatures in nonparametric predictive inference has been presented and leads to lower and upper survival functions for the system failure time, given failure times of tested components. However, deriving the system signature is computationally complex. This article presents how limited information about the signature can be used to derive bounds on such lower and upper survival functions and related inferences. If such bounds are sufficiently decisive they also indicate that more detailed computation of the system signature is not required.
SamaniegoFJ. System signatures and their applications in engineering reliability. Springer, New York2007.
2.
CoolenFPAAl-nefaieeAN. Nonparametric predictive inference for failure times of systems with exchangeable components. Proc IMechE, Part O: J Risk and Reliability2012; 226: 262–273.
3.
CoolenFPA. Nonparametric predictive inference. In: LovricM (ed.) International encyclopedia of statistical science. Springer, Berlin2011, pp.968–970.
4.
CoolenFPA. On nonparametric predictive inference and objective Bayesianism. J Logic, Language and Info2001; 15: 21–47.
5.
WilliamsonJ. Philosophies of probability. In: IrvineA (ed.) Handbook of the philosophy of mathematics, Volume 4 of Handbook of the philosophy of science. North-Holland, Amsterdam2009, pp.493–533.
6.
LawlessJFFredetteM. Frequentist prediction intervals and predictive distributions. Biometrika2005; 92: 529–542.
7.
AugustinTCoolenFPA. Nonparametric predictive inference and interval probability. J Statistical Planning and Inference2004; 124: 251–272.
8.
HillBM. Posterior distribution of percentiles: Bayes’ theorem for sampling from a population. J Am Stat Ass1968; 63: 677–691.
9.
DempsterAP. On direct probabilities. J Royal Stat Soc B1963; 25: 100–110.
10.
CoolenFPATroffaesMCAugustinT. Imprecise probability. In: LovricM (ed.) International encyclopedia of statistical science. Springer, Berlin2011, pp.645–648.
11.
CoolenFPAUtkinLV. Imprecise reliability. In: LovricM (ed.) International encyclopedia of statistical science. Springer, Berlin2011, pp.649–650.
12.
CoolenFPAMaturiTA. Nonparametric predictive inference for order statistics of future observations. In: BorgeltCGonzalez-RodriguezGTrutschnigW. Combining soft computing and statistical methods in data analysis. Springer, Berlin2010, pp.97–104.
EryilmazS. Review of recent advances in reliability of consecutive k-out-of-n and related systems. Proc IMechE, Part 0: J Risk and Reliability2010; 224: 225–237.
15.
GaofengDZhengBTaizhongH. On computing signatures of coherent systems. J Multivariate Analysis2012; 103: 142–150.
16.
AslettLJM. MCMC for inference on phase-type and masked system lifetime models. PhD Thesis, Trinity College Dublin, 2012. Available from www.louisaslett.com/PhD_Thesis.pdf
17.
CoolenFPACoolen-MaturiT. On generalizing the signature to systems with multiple types of components. In: ZamojskiWMazurkiewiczJSugierJ. (eds) Complex systems and dependability. Springer, Berlin2012, pp.115–130.
