臺灣博碩士論文加值系統

隨著科技的進步和產品品質的提昇，對於高可靠度產品的研發勢在必行。
因此，針對現今之高可靠度產品，特別是電子產品而言，在產品送交顧客手中之前給予測試與評估其壽命，已成為生產者與製造商所面臨之重要問題。如果存在一產品之品質特性質與其壽命具有高度相關，則可使用品質特性質之衰變路徑來估計產品的壽命。如果品質特性質的衰變路徑通過某一臨界質，則稱此產品失效。若此產品特性質可以被某些性質所構建，則不需要觀測到失效資料則可估計此產品之壽命。

1 Introduction.................................................1
2 The Degradation Model and Its Related Estimation Problems....6
2.1 The Wiener Process.......................................6
2.2 The Inverse Gaussian Distribution........................6
2.3 Relationships............................................8
2.4 The Degradation Model....................................9
2.5 Parameter Estimations Based on Complete Time-to-Failure
Data....................................................12
2.6 The UMVUE for F(t) of T.................................14
3 Lifetime Assessment for the Products........................16
3.1 Estimation of the Lifetime Distribution of Products
Based on Initial Data...................................17
3.1.1 The UMVUEs Based on Initial Data..................17
3.1.2 The UMVUE of F(t) Based on Initial Burn-in Data...18
3.1.3 Approximate Percentiles of Lifetime Distribution
Based on Initial Data.............................21
4 LED Example.................................................25
5 Conclusions.................................................27
References....................................................29
Table 1. The Estimates of the Median Lifetime.................32

Alexanian, I. T. and Brodie, D. E., (1977), “A Method for Estimating the Reliability of ICS,” IEEE Transactions on Reliability, R-26(5), 359-361.
Bai, D. S., Kwon, H. M., and Lee M. K., (1995), “An Economic 2-Stage Screening-Procedure With A Prescribed Outgoing Quality In Logistic And Normal-Models,” Naval Research Logistics, 42, 1081-1097.
Carey, M. B., and Koenig, R. H., (1991), “Reliability Assessment Based on Accelerated Degradation: A Case Study,” IEEE Transactions on Reliability, R-40, 499-506.
Chang, D. S., (2000), “Optimal Burn-in Decision For Products With an Unimodel Failure Rate Function,” European Journal of Operational Research, 126, 534-540.
Chihkara, R. S. and Folks, L. (1977), “The Inverse Gaussian Distribution as a Lifetime Model,” Technometrics, 461-468.
Chhikara, R. S. and Folks, L. (1989), The Inverse Gaussian Distribution: Theory and Methodology, and Applications, Marcel Dekker, inc.
Chhikara, R. S. and Folks, L. (1974), “Estimation of the Inverse Gaussian Distribution Function,” Journal of the American Statistical association Journal, 69, 250-254.
Doksum, K. A., and Hoyland, A., (1992), “Models for Variable-Stress Accelerated Life Testing experiments Based on Wiener Processes and the Inverse Gaussian Distribution,” Technometrics, 34(1), 74-82.
Jensen, F., and Petersen, N. E., (1982), Burn-in: An Engineering Approach to the Design and Analysis of Burn-in Procedures, John Wiley & Sons: New York.
Kolarik, W. J., (1999), Creating Quality: Process Design for Results, McGraw-Hill Companies.
Kuo, W., (1984), “Reliability Enhancement through Optimal Burn-in,” IEEE Transactions on reliability, R-33(2), 145-156.
Kuo, W. and Kuo, Y., (1983), "Facing the Headaches of Early Failures: A State-of-the-Art Review of Burn-in Decisions," Proceedings of the IEEE, 71, 11, 1257-1266.
Korwar, R. M., (1980), “On the Uniformly Minimum Variance Unbiased Estimators of the Variance and its Reciprocal of an Inverse Gaussian Distribution,” Journal of the American Statistical association Journal 75, 734-735.
Kosei, I. and Noriaki, S., (1983), “Uniformly Minimum Variance Unbiased Estimation for the Inverse Gaussian Distribution,” Journal of the American Statistical association Journal, 660-663.
Lawrence, M. J., (1966), “An Investigation of the Burn-in Problem,” Technometrics, 8(1), 61-71.
Leemis, L. M., and Beneke, M., (1990), “Burn-in Models and Methods: A Review,” IIE Transactions, 22(2), 172-180.
Luke, Y. L., (1969), The Special Functions and Their Approximations, Vol. 1, Academic process, New York.
Meeker, W. Q., and Escobar, L. A., (1993), “A Review of Recent Research and Current Issues in Accelerated Testing,” International Statistical Review, 61(1), 147-168.
Nelson, W., (1990), Accelerated Testing: Statistical Models, Test Plans, and Data Analysis, John Wiley & Sons : New York.
Nguyen, D. G., and Nurthy, D. N. P., (1982), “Optimal Burn-in Time to Minimize Cost for Products Sold under Warranty,” IIE Transactions, 14(3), 167-174.
Oksendal, B., (1999), Stochastic Differential Equations: An Introduction with Applications, 5th ed., Springer-Verlag: Berlin.
Plesser, K. T., and Field, T. O., (1977), “Cost-optimized Burn-in Duration for Repairable Electronic Systems,” IEEE Transactions on reliability, R-26(3), 195-197.
Tweedie, M. C. K., (1957), “Statistical Properties of Inverse Gaussian Distributution I, II,” Annals of Mathematical Statistics, (June) 362-377, (September) 696-705.
Tseng, S.T., Tang, J., and Ku, I. H., (2002), “Determination of Optimal Burn-in Parameter and Residual Life For Highly Reliable Products,” Naval Research Logistics.
Tseng, S. T., and Yu, H. F., (1997), “A Termination rule for Degradation Experiment,” IEEE Transactions on reliability, R-46(1), 130-133.
Washburn, L., (1970), “Determination of Optimal Burn-in Time: A Composite Criterion,” IEEE Transactions on Reliability, R-19(4), 134-140.
Watson, G. S., and Wells, W. T., (1961), “On the Probability of Improving the Mean Useful Life of Items by Eliminating Those with Short Lives,” Technometrics, 3(2), 281-298.
Whitmore, G. A. and Yalovsky, M., (1978), “A Normalizing Logarithmic Transformation for Inverse Gaussian Random Variables,” Technometrics, 207-208.
Yu, H. F., and Tseng, S. T., (1999), “Designing A Degradation Test,” Naval Research Logistics, 46, 699-706.