Imprecise Probability Method with the Power-Normal Model for Accelerated Life Testing

doi:10.1007/s12204-019-2126-y

Abstract

Abstract: We present a new nonparametric predictive inference (NPI) method using a power-normal model for accelerated life testing (ALT). Combined with the accelerating link function and imprecise probability theory, the proposed method is a feasible way to predict the life of the product using ALT failure data. To validate the method, we run a series of simulations and conduct accelerated life tests with real products. The NPI lower and upper survival functions show the robustness of our method for life prediction. This is a continuous research, and some progresses have been made by updating the link function between different stress levels. We also explain how to renew and apply our model. Moreover, discussions have been made about the performance.

Key words: accelerated life testing (ALT)| power-normal model| lower and upper survival functions| nonparametric predictive inference (NPI)| imprecise probability

摘要： We present a new nonparametric predictive inference (NPI) method using a power-normal model for accelerated life testing (ALT). Combined with the accelerating link function and imprecise probability theory, the proposed method is a feasible way to predict the life of the product using ALT failure data. To validate the method, we run a series of simulations and conduct accelerated life tests with real products. The NPI lower and upper survival functions show the robustness of our method for life prediction. This is a continuous research, and some progresses have been made by updating the link function between different stress levels. We also explain how to renew and apply our model. Moreover, discussions have been made about the performance.

关键词: accelerated life testing (ALT)| power-normal model| lower and upper survival functions| nonparametric predictive inference (NPI)| imprecise probability

CLC Number:

TB 114.3

YIN Yichao(殷毅超), HUANG Hongzhong (黄洪钟), LIU Zheng (刘征). Imprecise Probability Method with the Power-Normal Model for Accelerated Life Testing[J]. J Shanghai Jiaotong Univ Sci, 2019, 24(6): 805-810.

References 17

[12]	DE FINETTI B. Theory of probability: A critical introductorytreatment [J]. Journal of the Royal StatisticalSociety, 1975, 138(1): 953-959.
[1]	NELSON W B. Accelerated testing: Statistical models,test plans, and data analysis [M]. Hoboken, USA:John Wiley & Sons, 2004.
[13]	AUGUSTIN T, COOLEN F P A, DE COOMAN G,et al. Introduction to imprecise probabilities [M]. Hoboken,USA: John Wiley & Sons, 2014.
[2]	WU S J, HUANG S R. Planning two or more levelconstant-stress accelerated life tests with competingrisks [J]. Reliability Engineering and System Safety,2017, 158: 1-8.
[14]	COOLEN F P A, YAN K J. Nonparametric predictiveinference with right-censored data [J]. Journal of StatisticalPlanning and Inference, 2004, 126(1): 25-54.
[3]	ZAHARIA S M, MARTINESCU I, MORARIU C O.Life time prediction using accelerated test data of thespecimens from mechanical element [J]. Maintenanceand Reliability, 2012, 14(2): 99-106.
[15]	MATURI T A. Nonparametric predictive inference formultiple comparisons [D]. Durham, UK: Durham University,2010.
[4]	PAN R, YANG T, SEO K. Planning constant-stress acceleratedlife tests for acceleration model selection [J].IEEE Transactions on Reliability, 2015, 64(4): 1356-1366.
[16]	MATURI T A, COOLEN-SCHRIJNER P, COOLENF P A. Nonparametric predictive inference for competingrisks [J]. Journal of Risk and Reliability, 2010,224(1): 11-26.
[5]	HU Z, MAHADEVAN S. Accelerated life testing(ALT) design based on computational reliability analysis[J]. Quality and Reliability Engineering International,2016, 32(7): 2217-2232.
[17]	WEI J. Research on the life quickly evaluate methodfor the LED lighting products [D]. Xi’an, China:Northwest University, 2014 (in Chinese).
[6]	MI J H, LI Y F, YANG Y J, et al. Reliability assessmentof complex electromechanical systems underepistemic uncertainty [J]. Reliability Engineering andSystem Safety, 2016, 152: 1-15.
[7]	FAN T H, WANG W L. Accelerated life test forWeibull series systems with masked data [J]. IEEETransactions on Reliability, 2011, 60(3): 557-569.
[8]	YIN Y C, COOLEN F P A, COOLEN-MATURI T. Animprecise statistical method for accelerated life testingusing the power-Weibull model [J]. Reliability Engineeringand System Safety, 2017, 167: 158-167.
[9]	HILL B M. Posterior distribution of percentiles: Bayes’theorem for sampling from a population [J]. Journal ofthe American Statistical Association, 1968, 63(322):677-691.
[10]	AUGUSTIN T, COOLEN F P A. Nonparametric predictiveinference and interval probability [J]. Journal ofStatistical Planning and Inference, 2004, 124(2): 251-272.
[11]	COOLEN F P A. On nonparametric predictive inferenceand objective Bayesianism [J]. Journal of Logic,Language and Information, 2006, 15(1/2): 21-47.
[12]	DE FINETTI B. Theory of probability: A critical introductorytreatment [J]. Journal of the Royal StatisticalSociety, 1975, 138(1): 953-959.
[13]	AUGUSTIN T, COOLEN F P A, DE COOMAN G,et al. Introduction to imprecise probabilities [M]. Hoboken,USA: John Wiley & Sons, 2014.
[14]	COOLEN F P A, YAN K J. Nonparametric predictiveinference with right-censored data [J]. Journal of StatisticalPlanning and Inference, 2004, 126(1): 25-54.
[15]	MATURI T A. Nonparametric predictive inference formultiple comparisons [D]. Durham, UK: Durham University,2010.
[16]	MATURI T A, COOLEN-SCHRIJNER P, COOLENF P A. Nonparametric predictive inference for competingrisks [J]. Journal of Risk and Reliability, 2010,224(1): 11-26.
[17]	WEI J. Research on the life quickly evaluate methodfor the LED lighting products [D]. Xi’an, China:Northwest University, 2014 (in Chinese).