Real-time reliability evaluation based on damaged measurement degradation data

Abstract

A method was proposed to evaluate the real-time reliability for a single product based on damaged measurement degradation data. Most researches on degradation analysis often assumed that the measurement process did not have any impact on the product’s performance. However, in some cases, the measurement process may exert extra stress on products being measured. To obtain trustful results in such a situation, a new degradation model was derived. Then, by fusing the prior information of product and its own on-line degradation data, the real-time reliability was evaluated on the basis of Bayesian formula. To make the proposed method more practical, a procedure based on expectation maximization (EM) algorithm was presented to estimate the unknown parameters. Finally, the performance of the proposed method was illustrated by a simulation study. The results show that ignoring the influence of the damaged measurement process can lead to biased evaluation results, if the damaged measurement process is involved.

Keywords

degradation analysis / damaged measurement / real-time reliability / expectation maximization algorithm

References

[1] ElwangA., GebraeelN. Z.. Real-time estimation of mean remaining life using sensor-based degradation models [J]. Journal of Manufacturing Science and Engineering, 2009, 131(5): 0510051-0510059

[2] LiaoC.-m., TsengS. T.. Optimal design for step-stress accelerated degradation tests [J]. IEEE Transactions on Reliability, 2006, 55(1): 59-66

[3] ZhaoJ.-y., LiuFang.. Reliability assessment of the metallized film capacitors from degradation data [J]. Microelectronics Reliability, 2007, 47(2): 434-436

[4] LuJ. C., JinhoP., QingY.. Statistical inference of a time-to-failure distribution derived from linear degradation data [J]. Technometrics, 1997, 39(4): 391-400

[5] GebraeelN. Z., LawleyM. A., LiR., RyanJ. K.. Residual-life distributions from component degradation signals: A Bayesian approach [J]. IIE Transactions, 2005, 37(6): 543-557

[6] GebraeelN. Z.. Sensory-updated residual life distributions for components with exponential degradation patterns [J]. IEEE Transactions on Automation Science and Engineering, 2006, 3(4): 382-393

[7] LuJ. C., MeekerW. Q.. Using degradation measures to estimate a time-to-failure distribution [J]. Technometrics, 1993, 35(2): 161-174

[8] WangW.-bin.. A model to determine the optimal critical level and the monitoring intervals in condition-based maintenance [J]. International Journal of Production Research, 2000, 38(6): 1425-1436

[9] BaeS. J., KvamP. H.. A nonlinear random-coefficients model for degradation [J]. Technometrics, 2004, 46(4): 460-469

[10] YuanX. X., PandeyM. D.. A nonlinear mixed-effects model for degradation data obtained from in-service inspections [J]. Reliability Engineering and System Safety, 2009, 94(2): 509-519

[11] SiX.-s., WangW.-b., HuC.-h., ZhouD.-hua.. Remaining useful life estimation-A review on the statistical data driven approaches [J]. European Journal of Operational Research, 2011, 213(1): 1-14

[12] PandeyM. D., YuanX. X., NoortwijkJ. M.. The influence of temporal uncertainty of deterioration on life-cycle management of structures [J]. Structure and Infrastructure Engineering, 2009, 5(2): 145-156

[13] YangK., XueJ.-an.. Continuous state reliability analysis [C]. Proceedings of the Annual Reliability & Maintainability Symposium, 1996Las VegasElsevier251-257

[14] ZuoM.-j., JiangR.-y., YamR.. Approaches for reliability modeling of continuous-state devices [J]. IEEE Transactions on Reliability, 1999, 48(1): 9-18

[15] HUANG Wei. Reliability analysis considering product performance degradation [D]. The University of Arizona, 2002.

[16] NoortwijkJ. M., FrangopolD. M.. Two probabilistic life-cycle maintenance models for deteriorating civil infrastructures [J]. Probabilistic Engineering Mechanics, 2004, 19(4): 345-359

[17] NoortwijkJ. M., WeideJ. A. M., KallenM. J., PandeyM. D.. Gamma processes and peaks-over-threshold distributions for time-dependent reliability [J]. Reliability Engineering and System Safety, 2007, 92(12): 1651-1658

[18] NoortwijkJ. M.. A survey of the application of Gamma processes in maintenance [J]. Reliability Engineering and System Safety, 2009, 94(1): 2-21

[19] TsengS. T., BalakrishnanN., TsaiC. C.. Optimal step-stress accelerated degradation test plan for gamma degradation processes [J]. IEEE Transactions on Reliability, 2009, 58(4): 611-618

[20] WhitmoreG. A.. Estimating degradation by a wiener diffusion process subject to measurement error [J]. Lifetime Data Analysis, 1995, 1(3): 307-319

[21] WangXiao.. Wiener processes with random effects for degradation data [J]. Journal of Multivariate Analysis, 2010, 101(2): 340-351

[22] RossS. M.Introduction to probability models [M], 2000New YorkAcademic Press625-662

[23] BaiJ. M., LiZ. H., KongX. B.. Generalized shock models based on a cluster point process [J]. IEEE Transaction on Reliability, 2006, 55(3): 542-550

[24] WangZ.-l., HuangH.-z., DuLi.. Reliability analysis on competitive failure processes under fuzzy degradation data [J]. Applied Soft Computing, 2011, 11(3): 2964-2973

[25] PandeyM. D., YuanX. X., NoortwijkJ. M.. The influence of temporal uncertainty of deterioration on life-cycle management of structures [J]. Structure and Infrastructure Engineering, 2009, 5(2): 145-156

[26] ChinnamR. B.. On-line reliability estimation for individual components using statistical degradation signal models [J]. Quality and Reliability Engineering International, 2002, 18(1): 53-73

[27] DempsterA. P., LairdN. M., RubinD. B.. Maximum likelihood from incomplete data via the EM algorithm [J]. Journal of the Royal Statistical Society, 1977, 39(1): 1-38

[28] XuA.-c., TangY.-cai.. EM algorithm for degradation data analysis [J]. Journal of East China Normal University, 2010, 5(5): 38-48