Designing Degradation Experiments Using a Log-Logistic Distribution
Assessing the reliability of a product is very important to improve the product’s quality and to get the trust of customers. Degradation experiments are usually used to assess the reliability of highly reliable products,
which are not expected to fail under the traditional life tests. Several decision variables, such as the sample size, the inspection frequency, and the termination time, have a direct influence on the experimental cost and the estimation precision of lifetime information. This paper deals with the optimal design of a degradation experiment where the degradation rate follows a log-logistic distribution. Under the constraint that the total experimental cost does not exceed a predetermined budget, the optimal decision variables are obtained by minimizing the mean squared error of the estimated 100pth percentile of the
lifetime distribution of the product. A simulation study and a real example of drug potency data are provided to illustrate the proposed method.
Al-Haj Ebrahem, M., Eidous, O., and Kamil, G. (2009b). Estimating percentiles of time-to-failure distribution obtained from a linear degradation model using kernel density method. Communications in Statistics – Simulation and Computation, 38, 1811-1822.
Chao, M. T. (1999). Degradation analysis and related topics: some thoughts and review. Proceedings of the National Science Council, 23, 555-566.
Chiodo, E., and Mazzanti, G. (2004). The log-logistic model for reliability characterization of power system components subjected to random stress. Speedam, Capri/Italy, 239-244.
Chow, S. C., and Shao, J. (1991). Estimating drug shelf-life with random effects. Biometrics, 47, 1071-1079.
Lu, C. J., and Meeker, W. Q. (1993). Using degradation measures to estimate a time-tofailure distribution. Technometrics, 35, 161-174.
Meeker, W. Q., and Escobar, L. A. (1998). Statistical methods for reliability data. New York: John Wiley.
Wu, S. J., and Chang, C. T. (2002). Optimal design of degradation tests in presence of cost constraint. Reliability Engineering & System Safety, 76, 109-115.
Yu, H. F. (2002a). Designing an accelerated degradation experiment by optimizing the interval estimation of the mean-time-to-failure. Journal of Chinese Institute of Industrial Engineers, 19, 23-33.
Yu, H. F. (2002b). Designing an accelerated degradation experiment with reciprocal Weibull degradation rate, journal=Journal of Statistical Planning and Inference, volume=136, pages=282-297.
Yu, H. F. (2003). Designing an accelerated degradation experiment by optimizing the estimation of the percentile. Quality and Reliability Engineering International, 19, 197-214.
Yu, H. F., and Tseng, S. T. (1999). Designing a degradation experiment. Naval Research Logistics, 46, 689-706.
Yu, H. F., and Tseng, S. T. (2004). Designing a degradation experiment with a reciprocal Weibull degradation rate. Quality Technology & Quantitative Management, 1, 47-63.
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