Abstract
Accelerated life tests are often expensive and difficult to conduct. Failure time censoring is anticipated because some test units do not fail over the testing period even under the accelerated stress condition. Therefore, a test plan must be carefully designed to maximize its statistical efficiency. This chapter presents an approach to optimal test planning based on the proportional hazard model of accelerated life test data. It is shown that this approach can accommodate multiple stress factors and is applicable to any failure time distribution.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Aitkin, M., & Clayton, D. (1980). The fitting of exponential, Weibull and extreme value distributions to complex censored survival data using GLIM. Applied Statistics, 29(2), 156–163.
Balakrishnan, N. (2009). A synthesis of exact inferential results for exponential step-stress models and associated optimal accelerated life-tests. Metrika, 69–351.
Barbosa, E., Colosimo, E., & Louzada-Neto, F. (1996). Accelerated life tests analyzed by a piecewise exponential distribution via generalized linear models. IEEE Transactions on Reliability, 45(4), 619–623.
Cox, D. R. (1972). Regression models and life-tables. Journal of the Royal Statistical Society. Series B (Methodological) 34(2), 187–220.
Dahmen, K., Burkschat, M., & Cramer, E. (2012). A-and D-optimal progressive Type-II censoring designs based on Fisher information. Journal of Statistical Computation and Simulation, 82(6), 879–905.
Ding, C., & Tse, S. K. (2013). Design of accelerated life test plans under progressive Type II interval censoring with random removals. Journal of Statistical Computation and Simulation, 83(7), 1330–1343.
Escobar, L. A., & Meeker, W. Q. (1995). Planning accelerated life tests with two or more experimental factors. Technometrics, 37(4), 411–427.
Finkelstein, D. M. (1986). A proportional hazards model for interval-censored failure time data. Biometrics, 42(4), 845–854.
Finkelstein, D. M., & Wolfe, R. A. (1985). A semiparametric model for regression analysis of interval-censored failure time data. Biometrics, 41(4), 933–945.
Islam, A., & Ahmad, N. (1994). Optimal design of accelerated life tests for the Weibull distribution under periodic inspection and type I censoring. Microelectronics Reliability, 34(9), 1459–1468.
Kiefer, J. (1959). Optimum experimental designs. Journal of the Royal Statistical Society B, 21, 272–304.
Kiefer, J. (1961). Optimum designs in regression problems. Annals of Mathematical Statistics, 32, 298–325.
Meeker, W. Q., & Nelson, W. (1975). Optimum accelerated life-tests for the Weibull and extreme value distributions. IEEE Transactions on Reliability, R-24(5), 321–332.
Meeker, W. Q., & Escobar, L. A. (1998). Statistical methods for reliability data. New York: John Wiley and Sons Inc.
Monroe, E. M., & Pan, R. (2008). Experimental design considerations for accelerated life tests with nonlinear constraints and censoring. Journal of Quality Technology, 40(4), 355–367.
Monroe, E. M., Pan, R., Anderson-Cook, C., Montgomery, D. C., & Borror, C. M. (2010). Sensitivity analysis of optimal designs for accelerated life testing. Journal of Quality Technology, 42(2), 121–135.
Monroe, E. M., Pan, R., Anderson-Cook, C., Montgomery, D. C., & Borror, C. M. (2011). A generalized linear model approach to designing accelerated life test experiments. Quality and Reliability Engineering International, 27(4), 595–607.
Montgomery, D. C. (2012). Design and analysis of experiments (8th ed.). Hoboken: Wiley.
Myers, R. H., Montgomery, D. C., & Anderson-Cook, C. M. (2009). Response surface methodology: Process and product optimization using designed experiments (3rd ed.). Hoboken: Wiley.
Nelder, J. A., & Wedderburn, R. W. M. (1972). Generalized linear models. Journal of the Royal Statistical Society. Series A (General), 135(3), 370–384.
Nelson, W. (2005a). A bibliography of accelerated test plans. IEEE Transactions on Reliability, 54(2), 194–197.
Nelson, W. (2005b). A bibliography of accelerated test plans part II – references. IEEE Transactions on Reliability, 54(3), 370–373.
Nelson, W. (2009). Accelerated testing: statistical models, test plans, and data analysis (Vol. 344). Hoboken: John Wiley & Sons.
Nelson, W. (2015). An updated bibliography of accelerated test plans. In 2015 Annual Reliability and Maintainability Symposium (RAMS), 1–6.
Nelson, W., & Kielpinski, T. J. (1976). Theory for optimum censored accelerated life tests for normal and lognormal life distributions. Technometrics, 18(1), 105–114.
Nelson, W., & Meeker, W. Q. (1978). Theory for optimum accelerated censored life tests for Weibull and extreme value distributions. Technometrics, 20(2), 171–177.
Ng, H. K. T., Chan, P. S., & Balakrishnan, N. (2004). Optimal progressive censoring plans for the Weibull distribution. Technometrics, 46(4), 470–481.
Ng, H. K. T., Kundu, D., & Chan P. S. (2009). Statistical analysis of exponential lifetimes under an adaptive Type? II progressive censoring scheme. Naval Research Logistics, 56(8), 687–698.
Pan, R. & Yang, T. (2014). Design and evaluation of accelerated life testing plans with dual objectives. Journal of Quality Technology 46(2), 114.
Pan, R., Yang, T., & Seo, K. (2015). Planning constant-stress accelerated life tests for acceleration model selection. IEEE Transactions on Reliability 64(4), 1356–1366.
Park, J.-W., & Yum, B.-J. (1996). Optimal design of accelerated life tests with two stresses. Naval Research Logistics (NRL), 43(6), 863–884.
Pascual, F. (2007). Accelerated life test planning with independent Weibull competing risks with known shape parameter. IEEE Transactions on Reliability, 56(1), 85–93.
Pascual, F. (2008). Accelerated life test planning with independent Weibull competing risks. IEEE Transactions on Reliability, 57(3), 435–444.
Seo, K., & Pan, R. (2015). ALTopt: An R package for optimal experimental design of accelerated life testing. R Journal, 7, 2.
Seo, K., & Pan, R. (2018). Planning accelerated life tests with random effects of test chambers. Applied Stochastic Models in Business and Industry, 34, 224–243.
Seo, S.-K., & Yum, B.-J. (1991). Accelerated life test plans under intermittent inspection and type-I censoring: The case of Weibull failure distribution. Naval Research Logistics (NRL), 38(1), 1–22.
Sitter, R. R., & Torsney, B. (1995). Optimal designs for binary response experiments with two design variables. Statistica Sinica, 5, 495–419.
Tobias, P. A., & Trindade, D. (2011). Applied reliability. Boca Raton: CRC Press.
Yang, T. & Pan, R. (2013). A novel approach to optimal accelerated life test planning with interval censoring. IEEE Transactions on Reliability 62(2), 527–536.
Yum, B.-J., & Choi, S.-C. (1989). Optimal design of accelerated life tests under periodic inspection. Naval Research Logistics (NRL), 36(6), 779–795.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Pan, R., Seo, K. (2019). An Introduction of Generalized Linear Model Approach to Accelerated Life Test Planning with Type-I Censoring. In: Lio, Y., Ng, H., Tsai, TR., Chen, DG. (eds) Statistical Quality Technologies. ICSA Book Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-20709-0_14
Download citation
DOI: https://doi.org/10.1007/978-3-030-20709-0_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-20708-3
Online ISBN: 978-3-030-20709-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)