Modern complex engineering systems often present the analyst with a mix of data types that can be used for reliability prediction: system test results, lifetime data from unit tests of components, and subsystem data, all of which may have predictive value for the system lifetime. We present a hierarchical nonparametric framework, using Dirichlet processes, in which time-to-event distributions may be estimated from sample data or derived based on physical failure mechanisms. By applying a Bayesian methodology, the framework can incorporate prior information, including expert opinion.
HamadaMMartzHReeseC.
A fully Bayesian approach for combining multilevel failure information in fault tree quantification and optimal follow-on resource allocation.
Reliab Eng Syst Safe2004;
86:
297–305.
2.
CollinsDHuzurbazarA.
Prognostic models based on statistical flowgraphs.
Appl Stoch Model Bus2011;
28(2):
141–151.
3.
JohnsonVGravesTHamadaM.
A hierarchical model for estimating the reliability of complex systems.
Bayesian Stat2003;
7:
199–213.
4.
GravesTAnderson-CookCHamadaM.
Reliability models for almost-series and almost-parallel systems.
Technometrics2010;
52(2):
160–171.
5.
ReeseCWilsonAGuoJ.
A Bayesian model for integrating multiple sources of lifetime information.
J Qual Technol2011;
42(2):
127–141.
6.
WalkerSGDamienPLaudP.
Bayesian nonparametric inference for random distributions and related functions.
J Roy Stat Soc B1999;
61(3):
485–527.
7.
MüllerPQuintanaFA.
Nonparametric Bayesian data analysis.
Stat Sci2004;
19(1):
95–110.
8.
SingpurwallaND.
Reliability and risk: a Bayesian perspective.
Chichester:
John Wiley & Sons,
2006.
9.
GhoshKTiwariRC.
Nonparametric and semiparametric Bayesian reliability analysis. In:
RuggeriFKenettRFaltinFW (eds)
Encyclopedia of statistics in quality and reliability.
Chichester:
John Wiley & Sons,
2007, pp.1239–1248.
10.
SusarlaVVan RyzinJ.
Nonparametric Bayesian estimation of survival curves from incomplete observations.
J Am Stat Assoc1976;
71(356):
897–902.
11.
KalbfleischJD.
Non-parametric Bayesian analysis of survival time data.
J Roy Stat Soc B1978;
40(2):
214–221.
12.
KumarSTiwariRC.
Bayes estimation of reliability under a random environment governed by a Dirichlet prior.
IEEE T Reliab1989;
38(2):
218–223.
13.
DykstraRLLaudP.
A Bayesian nonparametric approach to reliability.
Ann Stat1981;
9(2):
356–367.
14.
SinhaDDeyDK.
Semiparametric Bayesian analysis of survival data.
J Am Stat Assoc1997;
92(439):
1195–1212.
15.
MerrickJRWSoyerRMazzuchiciTA.
A Bayesian semiparametric analysis of the reliability and maintenance of machine tools.
Technometrics2003;
45(1):
58–69.
16.
Nieto-BarajasLEWalkerSG.
A semi-parametric Bayesian analysis of survival data based on LÉvy-driven processes.
Lifetime Data Anal2005;
11:
529–543.
17.
CoxDROakesD.
Analysis of survival data.
London:
Chapman & Hall,
1984.
18.
ChristensenRJohnsonWBranscumA.
Bayesian ideas and data analysis: an introduction for scientists and statisticians.
Boca Raton, FL:
CRC Press,
2010.
19.
GhoshJRamamoorthiR.
Bayesian nonparametrics.
New York:
Springer Verlag,
2003.
20.
FergusonTS.
A Bayesian analysis of some nonparametric problems.
Ann Stat1973;
1(2):
209–230.
21.
HjortNHolmesCMüllerP.
Bayesian nonparametrics,
vol. 28.
Cambridge:
Cambridge University Press,
2010.
22.
AussererJK.
Integration, testing, and validation of a small hybrid-electric remotely-piloted aircraft. Master’s Thesis,
Air Force Institute of Technology,
Wright-Patterson AFB, OH,
2012.
23.
BlumJSusarlaV.
On the posterior distribution of a Dirichlet process given randomly right censored observations.
Stoch Proc Appl1977;
5(3):
207–211.
24.
WarrRLCollinsDH. Bayesian nonparametric models for combining heterogeneous reliability data. In: JSM proceedings, physical and engineering sciences section, 28 July - 02 August 2012, San Diego, CA: American Statistical Association, pp.2220–2232.
