對於高可靠度的產品, 傳統的加速壽命測試往往在高應力測試下, 亦無法在合理的時間內, 獲得足夠的壽命資料, 導致壽命分配推估上的困難. 因此, 加速衰變測試採取測量退化即隨著時間而監控的實驗方式. 這些退化量提供產品失效有價值的訊息, 使得產品壽命分配的推估上較精準. 因此, 加速衰變模型目前已逐漸廣泛地被用來評估高可靠度產品的壽命資訊. 另外, 有些高可靠度之產品, 需利用破壞性試驗來量測產品之退化量, 例如, 利用拉斷的力量來量測黏著劑的強度, 而導致每個產品僅能量得一次的退化量. 對於如此的試驗便稱為加速破壞性衰變測試.
對數常態分配以及韋伯分配是常用於描述加速破壞性衰變測試中, 產品特性之分配. 在分配誤判的情況下, 壽命訊息之推估將會有偏差, 以及不準確的情形產生. 因此, 本研究中, 在考慮破壞性退化試驗下, 提供分配誤判時的壽命推估偏差及精準值之資訊. 並且提供具穩健性之實驗規劃, 使得在分配誤判情況產生時, 我們在實驗後估計產品壽命能較具不偏及精準度.
再者, 若透過先前之經驗得知兩個分配之尺度參數滿足某一特定之關係, 我們進一步利用校正後之概似函數來提供具穩健性之實驗規劃, 使得我們在實驗後取得之樣本, 透過校正後之概似函數來進行壽命訊息之推論時, 能有較精準之估計.

For highly reliable products, traditional accelerated life tests (ALTs) may be difficult to
estimate the life time of products since the products are not likely to fail in a reasonable
test time. For this reason, accelerated degradation tests (ADTs) take measurements of
degradation along experiment and monitor it over time. These measurements provide valuable
information for inferring distribution of life time more precisely. Hence, accelerated
degradation tests are increasingly used to assess the life time information of highly
reliable products today. In addition, for some products, destructive test is needed for
obtaining the degradation measurements. For example, the test of a adhesive bond needs
to break the product to obtain the strength of the bond. This kind of test which only
one meaningful measurement can be taken on each unit is called an accelerated destructive
degradation test (ADDT).
The lognormal and Weibull distribution are often used to describe the distribution of
product characteristics in life and degradation tests. When the distribution is
misspecified, the life time quantile, often of interest to the practitioner, may differ
significantly between these two distributions. In this study, under a specific ADDT, we
give the information of bias and inefficiency under distribution misspecification. And
we provide robust plans that will give more unbiased and efficient estimate of life time
quantile.
Furthermore, if the scale parameters of two distributions satisfy certain specific
relationship by previous experience, we use the adjusted profile likelihood of working
model to obtain robust test plans. After the implement of the robust plan, the estimate
of the life time quantile by using adjusted profile likelihood will be more precise under
distribution misspecification than those estimations without using adjusted profile
likelihood.

Birnbaum A. (1962),
“On The Foundations of Statistical Inference (With Discussion),”
Journal of the American Statistical Association, 53, 259–326.

Boulanger, M., and Escobar, L. A. (1994),
“Experimental Design for a Class of Accelerated Degradation Tests,”
Technometrics, 36(3), 260–272.

Chiao, C. H., and Hamada, M. (1996),
“Robust Reliability for Light Emitting Diodes Using Degradation Measurements,”
Quality and Reliability Engineering International, 12(2), 89–94.

Chao, M. T. (1999),
“Degradation Analysis and Related Topics: Some Thoughts and a Review,”
Proceedings of the National Science Council, 23, 555–566.

Condra, L. W. (2001),
Reliability Improvement with Design of Experiments,
New Tork: Marcel Dekker.

Escobar, L. A., and Meeker, W. Q. (1995),
“Planning Accelerated Life Tests With Two or More Experimental Factors,”
Technometrics, 37, 411–427.

Escobar, L. A., Meeker, W. Q., Kugler, D. L., and Kramer, L. L. (2003),
“Accelerated Destructive Degradation Tests: Data, Models, and Analysis,”
Chapter 21 in Mathematical and Statistical Methods in Reliavility,
B. H. Lindqvist and K. A. Doksum, Editors, River Edge, NJ: World
Scientific Publishing Company.

Jeffrey, D. B., Li Su, Remigio M. O., and Stephen T. M. (2007),
“Statistical evidence for GLM regression parameters: A robust likelihood approach,”
Statistics in Medicine, 26, 2919–2936.

Lu, C. J., and Meeker, W. Q. (1993),
“Using Degradation Measures to Estimate a Timeto-Failure Distribution,”
Technometrics, 35(2), 161–174.

Meeter, C. A., and Meeker, W. Q. (1994),
“Optimum Accelerated Life Tests with a Nonconstant Scale Parameter,”
Technometrics, 35(1), 71–83.

Meeker,W. Q., Escobar, L. A., and C. Joseph Lu (1998),
“Accelerated Degradation Tests: Modeling and Analysis,”
Technometrics, 40(2), 89–99.

Meeker, W. Q., and Escobar, L. A. (1998),
Statistical Methods for Reliability Data Analysis,
New York: Wiley & Sons.

Nelson, W. (1990),
Acceleratd Testing: Statistical Model, Test Plans, and Data Analyses,
New York: Wiley.

Pascual, F. G., and Montepiedra. G. (2005),
“Lognormal and Weibull Accelerated Life Test Plans Under Distribution Misspecification,”
IEEE Transactions on Reliability, 54(1), 43–52.

Pascual, F. G. (2006),
“Accelerated Life Test Plans Robust to Misspecification of the StressVLife Relationship,”
Technometrics, 48(1), 11–26.

Royall, R. M. (1997),
Statistical Evidence: A Likelihood Paradigm,
Chapman & Hall: London.

Royall, R. M. (2000),
“On The Probability of Observing Misleading Statistical Evidence(with discussion),”
Journal of the American Statistical Association, 95, 760–780.

Royall, R. M., and Tsou, T. S. (2003),
“Interpreting Statistical Evidence Using Imperfect Models:
Robust Adjusted Likelihood Functions,”
Journal of the Royal Statistical Society Series B, 65(2), 391–404.

Stafford, J. E. (1996),
“A Robust Adjustment of the profile likelihood,” Annals of Statistics,
24(11), 336–352.

Shi, Y., Meeker, W. Q., and Escobar, L. A. (2009),
“Accelerated Destructive Degradation Test Planning,”
Technometrics, 51(1), 1–13.

White, H. (1982),
“Maximum Likelihood Estimation of MisspecifiedModels,” Econometrica,
50(1), 1–26.

Yu, H. F. (2002),
“Designing an Accelerated Degradation Experiment by Optimizing the Interval
Estimation of the Mean-Time-to-Failure,”
Journal of the Chinese Institute of Industrial Engineers, 19(5), 23–33.

Yu, H. F. (2003),
“Designing an Accelerated Degradation Experiment by Optimizing
the Estimation of the Percentile,”
Quality and Reliability Engineering International, 19, 197–214.