任何產品在製造過程中，必然會生產出少部分的瑕疵品，如何在出貨前能夠有效地篩選出潛在的不良品，將是生產者或廠商相當關注的一部份。執行一預燒試驗 (burn-in procedure) 將可達到篩選不良品之目的，但高可靠度產品，其壽命動輒上千小時，使用傳統預燒試驗，很難在有限的測試時間內篩選出潛在的不良品。若產品存在一具代表性之品質特徵值 (quality characteristic, QC) ，利用衰變試驗 (degradation test) 進行篩選分類將會是一實際可行的方法。近年來預燒試驗之相關文獻大多以衰變試驗為研究主軸，其中Tseng and Tang (2001) 與Tseng, Tang, and Ku (2003) 分別在window size為1及 (s + 1) 下，引入混合型Wiener過程，來描述高可靠度產品的品質特徵值之衰變模型，並皆以成本觀點建構一套篩選試驗執行程序。唯上述兩種篩選方法之績效表現，在文獻上並未深入分析，因此本研究將針對上述兩篩選方法進行優劣比較，且限定後者之window size為2。本研究發現衰變模型之結構在某些條件限制下，兩篩選方法之績效表現是相同的。更進一步利用數值方法探討一般化衰變模型之參數設定，其績效表現之差異則利用圖形呈現之，發現使用Tseng, Tang, and Ku (2003) 之準則比Tseng and Tang (2001) 更能有效篩選出早夭產品。然而因為前者沒有完整的理論架構且需要繁雜之數值計算，所以當兩篩選方法之績效表現差異不顯著時，其定義為兩分類準則造成之錯誤分類機率差異少於0.005，建議使用後者進行篩選試驗。在本研究的搜尋範圍當中，約10% 之參數設定適合使用window size為2之分類準則進行篩選試驗。而這些成果，對工程師規劃欲燒篩選試驗將有實質助益。

Today’s free market is very competitive. In order to compete with others, it is a great challenge for the manufactures to design an optimal burn-in policy to eliminate failure or weak components before their products are shipped to the market. Without removing these defective products, the warranty and replacement costs will increase substantially. The burn-in policy is conventionally based on the formulation of a mixture of two lifetime distributions. For highly-reliable products, it is not easy to obtain their lifetime distributions within a short time of life-testing. Instead, if there exists a quality characteristic whose degradation over time can be closely related with the product’s lifetime, then we can construct optimal burn-in policy based on suitable degradation models. Recently, Tseng and Tang (2001) and Tseng, Tang, and Ku (2003) proposed two optimal burn-in policies (which are essentially based on the choices of the different window size) to screen out the defective products. However, there is no suitable literature to compare the performance of these two burn-in policies. Focusing on the setting of window size 2, this study demonstrates that these two approaches are essentially the same under some specific conditions. Furthermore, under more general parameter settings, we use numerical computations and graphical approach to compare the performance of these approaches. The results demonstrate that the policy proposed by Tseng, Tang, and Ku (2003) is always better than that of Tseng and Tang (2001). More specifically, among all the parameter settings in this study, the ability of reducing total misclassification probabilities up to 0.5% is around 10%. Note that the former one, however, requires a complex computational effort to obtain its screening procedure. Therefore, we recommend to using the later one if these two policies did not have significant differences in their screening performance.

[1] Birnbaum, Z. W., and Saunders, S. C. (1969). A new family of life distributions. Journal of applied probability, 6(2), 319-327.
[2] Chhikara, R. S., and Folks, J. L. (1989). The inverse Gaussian distribution. New York: Dekker
[3] Dennis Jr, J. E., and Schnabel, R. B. (1996). Numerical methods for unconstrained optimization and nonlinear equations. Philadelphia: Siam.
[4] Doksum, K. A., and Hóyland, A. (1992). Models for Variable-Stress Accelerated Life Testing Experiments Based on Wiener Processes and the Inverse Gaussian Distribution. Technometrics, 34(1), 74-82.
[5] Genz, A. (1992). Numerical computation of multivariate normal probabilities. Journal of computational and graphical statistics, 1(2), 141-149.
[6] Jensen, F., and Petersen, N. E. (1982). Burn-in: an engineering approach to the design and analysis of burn-in procedures, New York: John Wiley & Sons.
[7] Johnson, R. A. and Wichern, D. W. (2007). Applied multivariate statistical analysis, 6th ed. New Jersey: Pearson Prentice Hall.
[8] Leemis, L. M., and Beneke, M. (1990). Burn-in models and methods: a review. IIE transactions, 22(2), 172-180.
[9] McLachlan, G. J. and Krishnan, T. (2008). The EM algorithm and extensions, 2nd ed, New York: John Wiley and Sons.
[10] Meeker, W. Q., and Escobar, L. A. (1998). Statistical methods for reliability data, New York: John Wiley and Sons.
[11] Nelson, W. (1990). Accelerated life testing: statistical models, data analysis and test plans, New York: John Wiley and Sons.
[12] Rice, J., Reich, T., Cloninger, C. R., and Wette, R. (1979). An approximation to the multivariate normal integral: its application to multifactorial qualitative traits. Biometrics, 35(2), 451-459.
[13] Titterington, D. M., Smith, A. F., and Makov, U. E. (1985). Statistical analysis of finite mixture distributions, New York: John Wiley and Sons.
[14] Tsai, C. C., Tseng, S. T., and Balakrishnan, N. (2011). Optimal burn-in policy for highly reliable products using gamma degradation process. IEEE Transactions on Reliability, 60(1), 234-245.
[15] Tseng, S. T., and Peng, C. Y. (2004). Optimal burn-in policy by using an integrated Wiener process. IIE Transactions, 36(12), 1161-1170.
[16] Tseng, S. T. and Tang, J. (2001). Optimal burn-in time for highly reliable products. International Journal of Industrial Engineering, 8(4), 329-338.
[17] Tseng, S. T., Tang, J., and Ku, I. H. (2003). Determination of burn‐in parameters and residual life for highly reliable products. Naval Research Logistics, 50(1), 1-14.
[18] Tseng, S. T., and Yu, H. F. (1997). A termination rule for degradation experiments. IEEE Transactions on Reliability, 46(1), 130-133.
[19] Wu, S. and Xie, M. (2007). Classifying weak, and strong components using ROC analysis with application to burn-in, IEEE Transactions on Reliability, 56(3), 552-561.
[20] Yu, H. F., and Tseng, S. T. (1999). Designing a degradation experiment. Naval Research Logistics, 46(6), 689-706.