Accelerated degradation test (ADT) has become an efficient approach to assess the reliability of
degradation products within limited time and budget. Some products have more than one degradation process
that is responsible for failure of product, which introduces some problems of modeling accelerated degradation data
and estimating unknown parameters. In order to solve the problems, a practical method of inferring reliability
with multivariate accelerated degradation data is proposed in this paper. Stochastic processes are used to fit
accelerated degradation data, and then margin reliability functions are derived from the degradation models.
Unlike the traditional assumption that the degradation increments of multivariate degradation processes at the
same observing time are mutually dependent, the margin reliabilities at the same time are considered to be
dependent, which is applicable to the situation that multivariate degradation data is not simultaneously observed.
Copula functions are used to describe the dependency between marginal reliabilities, and the two situations that
copula parameter is independent of accelerated stress or dependent on accelerated stress are both considered. In
the case study, the bivariate accelerated degradation data of O-ring rubber is used to demonstrate our proposed
method. The research results indicate that the proposed method provides a practical and feasible approach to
reliability inference with multivariate accelerated degradation data.
ZHOU Yuan (周源), WANG Haowei (王浩伟), Lü Weimin (吕卫民)
. Statistical Inference of Reliability with Multivariate Accelerated Degradation Data[J]. Journal of Shanghai Jiaotong University(Science), 2020
, 25(2)
: 237
-245
.
DOI: 10.1007/s12204-019-2124-0
[1] JIN G, MATTHEWS D. Reliability demonstration for long-life products based on degradation testing and a Wiener process model [J]. IEEE Transactions on Reliability,2014, 63(3): 781-797.
[2] TAN C M, SINGH P. Time evolution degradation physics in high power white LEDs under high temperature-humidity conditions [J]. IEEE Transactions on Device and Materials Reliability, 2014, 14(2):742-750.
[3] PENG C Y, TSENG S T. Statistical lifetime inference with skew-Wiener linear degradation models [J]. IEEE Transactions on Reliability, 2013, 62(2): 338-350.
[4] WANG H W, TENG K N, GAI B L. The method of analyzing accelerated degradation data based on acceleration factor constant principle [J]. Acta Electronica Sinica, 2018, 46(3): 739-747 (in Chinese).
[5] HAMADA M. Using degradation data to assess reliability [J]. Quality Engineering, 2015, 17(4): 615-620.
[6] WANG F K, CHU T P. Lifetime predictions of LEDbased light bars by accelerated degradation test [J].Microelectronics Reliability, 2012, 52(7): 1332-1336.
[7] SANTINI T, MORAND S, FOULADIRAD M, et al. Accelerated degradation data of Sic Mosfets for lifetime and remaining useful life assessment [J]. Microelectronics Reliability, 2014, 54(9/10): 1718-1723.
[8] PENG C Y, TSENG S T. Progressive-stress accelerated degradation test for highly-reliable products [J].IEEE Transactions on Reliability, 2010, 59(1): 30-37.
[9] YE Z S, CHEN L P, TANG L C, et al. Accelerated degradation test planning using the inverse Gaussian process [J]. IEEE Transactions on Reliability, 2014,63(3): 750-763.
[10] LING M H, TSUI K L, BALAKRISHNAN N. Accelerated degradation analysis for the quality of a system based on the Gamma process [J]. IEEE Transactions on Reliability, 2015, 64(1): 463-472.
[11] PARK J I, BAE S J. Direct prediction methods on lifetime distribution of organic light-emitting diods from accelerated degradation tests [J]. IEEE Transactions on Reliability, 2010, 59(1): 74-90.
[12] WANG H W, XU T X, MI Q L. Lifetime prediction based on Gamma processes from accelerated degradation data [J].Chinese Journal of Aeronautics, 2015,28(1): 172-179.
[13] ESCOBAR L A, MEEKER W Q. A review of accelerated test models [J]. Statistical Science, 2006, 21(4): 552-577.
[14] NELSON W B. Accelerated testing: Statistical models,test plans and data analysis [M]. New Jersey: John Wiley & Sons, 2004.
[15] ZHOU Y, WANG H W, GAI B L. Quantitative validation methods for accelerated degradation model and extrapolated results [J]. Acta Aeronautica et Astronautica Sinica, 2018, 39(9): 221950 (in Chinese).
[16] PAN J, WANG X Y, CHEN W H, et al. Research on optimal design of accelerated degradation test plan based on multiple performance parameters [J]. Journal of Mechanical Engineering, 2012, 48(2): 30-35 (in Chinese).
[17] PENGWW, LI Y F, MI J, et al. Reliability of complex systems under dynamic conditions: A Bayesian multivariate degradation perspective [J]. Reliability Engineering and System Safety, 2016, 153: 75-87.
[18] WANG Y P, PHAM H. Modeling the dependent competing risks with multiple degradation processes and random shock using time-varying copulas [J]. IEEE Transactions on Reliability, 2012, 61(1): 13-22.
[19] PAN Z Q, BALAKRISHNAN N, SUN Q, et al. Bivariate degradation analysis of products based on Wiener processes and copulas [J]. Journal of Statistical Computation and Simulation, 2013, 83(7): 1316-1329.
[20] PENG W W, LI Y F, YANG Y J, et al. Bivariate analysis of incomplete degradation obervations based on inverse Gaussian processes and copulas [J]. IEEE Transactions on Reliability, 2016, 65(2): 1-16.
[21] XIAO X, YE Z S. Optimal design for destructive degradation tests with random initial degradation values using the Wiener process [J]. IEEE Transactions on Reliability,2016, 65(3): 1327-1342.
[22] WANG H W, XI W J. Acceleration factor constantprinciple and the application under ADT [J].Quality and Reliability Engineering International, 2016, 32(7): 2591-2600.
[23] TSAI C C, TSENG S T, BALAKRISHNAN N. Optimal design for degradation tests based on Gamma processes with random effects [J]. IEEE Transactions on Reliability, 2012, 61(2): 604-613.
[24] VAN NOORTWIJK J M. A survey of the application of gamma processes in maintenance [J]. Reliability Engineering and System Safety, 2009, 94(1): 2-21.
[25] BALAKRISHNAN N, LING M H. Gamma lifetimes and one-shot device testing analysis [J]. Reliability Engineering and System Safety, 2014, 126: 54-64.
[26] PENG C Y. Inverse Gaussian processes with random effects and explanatory variables for degradation data[J]. Technometrics, 2015, 57(1): 100-111.
[27] WANG H W, TENG K N, ZHOU Y. Design an optimal accelerated-stress reliability acceptance test plan based on acceleration factor [J]. IEEE Transactions on Reliability, 2018, 67(3): 1008-1018.
[28] WANG X, XU D H. An inverse Gaussian process model for degradation data [J].Technometrics, 2010, 52(2):188-197.
[29] ZHANG X P, SHANG J Z, CHEN X, et al. Statistical inference of accelerated life testing with dependent competing failures based on copula theory [J]. IEEE Transactions on Reliability, 2014, 63(3): 764-780.
