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Abstract

The importance of degradation analysis as a method of reliability assessment has been increasing because the products become more and more reliable. Bayesian updating is important in the dynamic analysis of few degradation data collected in multiple stages. A problem of assessing the reliability of a degradation system, wherein calibration of a development program is carried out, within a multi-stage, by Bayesian inference, is proposed in this article. Two types of posterior distribution are obtained in each testing stage under an assumption that degradation performance follows a normal distribution for two cases. Then, two Bayesian models are presented to evaluate the system reliability. A conclusion is also derived, that is, the variance of a key random variable decreases as the number of testing stage grows. Finally, a numerical example illustrates the model, process and the analysis results.

Keywords

Multi-stage reliability assessment degradation Bayesian inference calibration variance

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References

Barlow

Scheuer

. Reliability growth during a development testing program. Technometrics 1966; 8(1): 53–60.

Smith

AFM

. A Bayesian note on reliability growth during a development testing program. IEEE T Reliab 1977; 26(5): 346–347.

Bae

Kuo

Kvam Paul

. Degradation models and implied lifetime distributions. Reliab Eng Syst Safe 2007; 92: 601–608.

Crk

. Reliability assessment from degradation data. In: Proceedings of annual reliability and maintainability symposium, Los Angeles, CA, 24–27 January 2000, pp.155–161. New York: IEEE.

Zhou

Lee

. Reliability-centered predictive maintenance scheduling for a continuously monitored system subject to degradation. Reliab Eng Syst Safe 2007; 92: 530–534.

Zhao

. On preventive maintenance policy of a critical reliability level for system subject to degradation. Reliab Eng Syst Safe 2003; 79: 301–308.

Wang

Huang

. An approach to reliability assessment under degradation and shock process. IEEE T Reliab 2011; 60(4): 852–863.

Pan

Balakrishnan

. Reliability modeling of degradation of products with multiple performance characteristics based on gamma processes. Reliab Eng Syst Safe 2011; 96: 949–957.

Peng

Huang

Xie

. A Bayesian approach for system reliability analysis with multilevel pass-fail, lifetime and degradation data sets. IEEE T Reliab 2013; 62(3): 689–699.

10.

Xie

. Stochastic modelling and analysis of degradation for highly reliable products. Appl Stoch Model Bus. Epub ahead of print 10 October 2014. DOI: 10.1002/asmb.2063.

11.

Box

GEP

Tiao

. Bayesian inference in statistics analysis. Reading, MA: Addison-Wesley, 1973.

12.

Bernardo

. Reference posterior distributions for Bayesian inference (with discussion). J Roy Stat Soc B 1979; 41: 113–147.

13.

Gelman

. Parameterization and Bayesian modeling. J Am Assoc 2004; 99: 537–545.

14.

Gelman

. Analysis of variance: why it is more important than ever (with discussion). Ann Stat 2005; 33: 1–53.

15.

Gelman

. Prior distribution for variance parameters in hierarchical models. Bayesian Anal 2006; 1(3): 515–533.

16.

Martz

Waller

Fickas

. Bayesian reliability analysis of series systems of binomial subsystems and components. Technometrics 1988; 30: 143–154.

17.

George

Makov

Smith

AFM

. Conjugate likelihood distribution. Scand J Stat 1993; 20(2): 147–156.

18.

Wang

Pan

. A Bayesian reliability evaluation method with integrated accelerated degradation testing and field information. Reliab Eng Syst Safe 2013; 116: 38–47.

19.

Dixit

Phal

. On estimating scale parameter of a truncated gamma distribution. Soochow J Math 2005; 31(4): 515–523.

20.

Robert

. Simulation of truncated normal variables. Stat Comput 1995; 5: 121–125.

21.

Brawn

Upton

. Closed-form parameter estimates for a truncated gamma distribution. Environmetrics 2007; 18: 633–645.

22.

Glanzel

Teles

Schubert

. Characterization by truncated moments and its application to Pearson-type distributions. Probab Theory Rel 1984; 66(2): 173–183.

23.

Calabria

Guaida

Pulcini

. A reliability-growth model in a Bayes-decision framework. IEEE T Reliab 1996; 45(3): 505–510.

24.

Shane

Wilson

Guo

. A Bayesian model for integrating multiple sources of lifetime information in system-reliability assessments. J Qual Technol 2011; 43: 127–141.

25.

Warr

Collins

. Bayesian nonparametric models for combining heterogeneous reliability data. Proc IMechE, Part O: J Risk and Reliability 2014; 228(2): 166–175.

Bayesian inference of multi-stage reliability for degradation systems with calibrations

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