Design of Accelerated Life Testing Plans for Products Exposed to Random Usage

Document Type : Original Manuscript

Authors

1 Department of Industrial Engineering, Urmia University of Technology, Urmia, Iran.

2 Industrial Engineering Department Iran University of Science and Technology, Tehran, Iran

10.22094/joie.2020.1907303.1783

Abstract

< p>Accelerated Life Testing (ALT) is very important in evaluating the reliability of highly reliable products. According to ALT procedure, products undergo higher stress levels than normal conditions to reduce the failure times. ALTs have been studied for various conditions and stresses. In addition to common stress such as temperature and humidity, random usage can also be considered as another stress that can cause failure. Design of ALT plan for products which are exposed to random usage process have not been studied in the literature. Therefore, a procedure for designing ALT plan for these products is studied in this paper. To do so, hazard rate of products is formulated based on the random usage process and other stresses. Then, the variance of the hazard rate is estimated over a predetermined time period. Optimum stress levels and the number of units at every stress level are obtained by numerically minimizing the variance of the hazard rate estimate. Numerical example and sensitivity analysis are performed to show the application and robustness of the model to parameter deviations. The results show that the proposed procedure is robust to parameter changes and can be used for ALT planning of products under random usage.

Graphical Abstract

Design of Accelerated Life Testing Plans for Products Exposed to Random Usage

Highlights

  • A new kind of Accelerated Life Test is proposed which takes into account random usage.
  • We design optimum ALT plans for products which are under a random usage process.
  • The optimum combinations of stresses and their levels are determined such that the variance of the hazard rate estimate of the product over a specified period of time is minimized.

Keywords


Ahmadini, A.A. and F.P. 2020. "Coolen, Statistical inference for the Arrhenius-Weibull accelerated life testing model with imprecision based on the likelihood ratio test. " Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 234(2): 275-289.
 Asadi, Amin, Mohammad Saidi-Mehrabad, and Faranak Fathi Aghdam. 2019. "A Two-Dimensional Warranty Model With Consideration Of Customer And Manufacturer Objectives Solved With Non-Dominated Sorting Genetic Algorithm."  Journal Of Optimization In Industrial Engineering 12 (1):15-22.
 Bai, D. S., and S. W. Chung. 1991. "An optimal design of accelerated life test for exponential distribution."  Reliability Engineering & System Safety 31 (1):57-64. doi: http://dx.doi.org/10.1016/0951-8320(91)90036-7.
 Bai, D. S., S. W. Chung, and Y. R. Chun. 1993. "Optimal design of partially accelerated life tests for the lognormal distribution under type I censoring."  Reliability Engineering & System Safety 40 (1):85-92. doi: http://dx.doi.org/10.1016/0951-8320(93)90122-F.
 Duchesne, Thierry, and Jerry Lawless. 2000. "Alternative time scales and failure time models."  Lifetime data analysis 6 (2):157-179.
 Elsayed, Elsayed A, and Hao Zhang. 2007. "Design of PH-based accelerated life testing plans under multiple-stress-type."  Reliability Engineering & System Safety 92 (3):286-292.
 Escobar, Luis A, and William Q Meeker. 2006. "A review of accelerated test models."  Statistical Science:552-577.
 Farewell, VT, and DR Cox. 1979. "A note on multiple time scales in life testing."  Applied Statistics:73-75.
 Finkelstein, Maxim S. 2004. "Alternative time scales for systems with random usage."  Reliability, IEEE Transactions on 53 (2):261-264.
 Frickenstein, Scott G., and Lyn R. Whitaker. 2003. "Age replacement policies in two time scales."  Naval Research Logistics 50 (6):592-613. doi: 10.1002/nav.10078.
 Gertsbakh, Ilya B, and Khaim B Kordonsky. 1998. "Parallel time scales and two-dimensional manufacturer and individual customer warranties."  IIE Transactions 30 (12):1181-1189.
 Hakamipour, Nooshin. 2020. "Approximated optimal design for a bivariate step-stress accelerated life test with generalized exponential distribution under type-I progressive censoring."  International Journal of Quality & Reliability Management.
 Han, David. 2017. "Optimal accelerated life tests under a cost constraint with non-uniform stress durations."  Quality Engineering:1-22.
 Han, David. 2020. "Time and cost constrained design of a simple step-stress accelerated life test under progressive Type-I censoring."  Quality Engineering:1-16.
 Kordonsky, Kh B, and I Gertsbakh. 1997. "Multiple time scales and the lifetime coefficient of variation: engineering applications."  Lifetime data analysis 3 (2):139-156.
 Lawless, Jerald F, and Martin J Crowder. 2010. "Models and estimation for systems with recurrent events and usage processes."  Lifetime data analysis 16 (4):547-570.
 Lawless, JF, MJ Crowder, and K-A Lee. 2009. "Analysis of reliability and warranty claims in products with age and usage scales."  Technometrics 51 (1):14-24.
 Lee, I. Chen, Yili Hong, Sheng-Tsaing Tseng, and Tirthankar Dasgupta. 2018. "Sequential Bayesian Design for Accelerated Life Tests."  Technometrics:0-0. doi: 10.1080/00401706.2018.1437475.
 Meeker, William Q, and Luis A Escobar. 2003. "Reliability: the other dimension of quality."  Quality Technology & Qualitative Management 1 (1):1.
 Meeker, William Q, and Luis A Escobar. 2014. Statistical methods for reliability data: John Wiley & Sons.
 Meeker, William Q, and Michael Hamada. 1995. "Statistical tools for the rapid development and evaluation of high-reliability products."  Reliability, IEEE Transactions on 44 (2):187-198.
 Mostafaeipour, Ali. 2016. "A novel innovative design improvement using value engineering technique: a case study."  Journal of Optimization in Industrial Engineering 9 (19):25-36.
 Nelson, Wayne B. 2005a. "A bibliography of accelerated test plans."  IEEE Transactions on Reliability 54 (2):194-197.
 Nelson, Wayne B. 2005b. "A bibliography of accelerated test plans part II-references."  Reliability, IEEE Transactions on 54 (3):370-373.
 Nelson, Wayne B. 2009. Accelerated testing: statistical models, test plans, and data analysis. Vol. 344: John Wiley & Sons.
 Noorossana, Rassoul, and Kamyar Sabri‐Laghaie. 2016. "System reliability with multiple failure modes and time scales."  Quality and Reliability Engineering International 32 (3):1109-1126.
 Oakes, David. 1995. "Multiple time scales in survival analysis."  Lifetime data analysis 1 (1):7-18.
 Polson, Nicholas G, and Refik Soyer. 2017. "Augmented probability simulation for accelerated life test design."  Applied Stochastic Models in Business and Industry.
 Roy, Soumya, and Chiranjit Mukhopadhyay. 2016. "Bayesian D-optimal Accelerated Life Test plans for series systems with competing exponential causes of failure."  Journal of Applied Statistics 43 (8):1477-1493.
 Sabri-Laghaie, Kamyar, and Rassoul Noorossana. 2016. "Reliability and Maintenance Models for a Competing-Risk System Subjected to Random Usage."  IEEE Transactions on Reliability 65 (3):1271-1283.
 Singpurwalla, Nozer D, and Simon P Wilson. 1998. "Failure models indexed by two scales."  Advances in Applied Probability 30 (4):1058-1072.
 Wu, Shuo-Jye, and Syuan-Rong Huang. 2019. "Optimal progressive interval censoring plan under accelerated life test with limited budget."  Journal of Statistical Computation and Simulation 89 (17):3241-3257.
 Yang, Tao, and Rong Pan. 2013. "A novel approach to optimal accelerated life test planning with interval censoring."  Reliability, IEEE Transactions on 62 (2):527-536.
 Zhu, Yada, and Elsayed A Elsayed. 2013a. "Design of accelerated life testing plans under multiple stresses."  Naval Research Logistics (NRL) 60 (6):468-478.
 Zhu, Yada, and Elsayed A Elsayed. 2013b. "Optimal design of accelerated life testing plans under progressive censoring."  IIE Transactions 45 (11):1176-1187.