{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T18:27:57Z","timestamp":1781720877823,"version":"3.54.5"},"reference-count":24,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2015,4,23]],"date-time":"2015-04-23T00:00:00Z","timestamp":1429747200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>An accelerated degradation test (ADT) is regarded as an effective alternative to an accelerated life test in the sense that an ADT can provide more accurate information on product reliability, even when few or no failures may be expected before the end of a practical test period. In this paper, statistical methods for optimal designing ADT plans are developed assuming that the degradation characteristic follows a gamma process (GP). The GP-based approach has an advantage that it can deal with more frequently encountered situations in which the degradation should always be nonnegative and strictly increasing over time. The optimal ADT plan is developed under the total experimental cost constraint by determining the optimal settings of variables such as the number of measurements, the measurement times, the test stress levels and the number of units allocated to each stress level such that the asymptotic variance of the maximum likelihood estimator of the q-th quantile of the lifetime distribution at the use condition is minimized. In addition, compromise plans are developed to provide means to check the adequacy of the assumed acceleration model. Finally, sensitivity analysis procedures for assessing the effects of the uncertainties in the pre-estimates of unknown parameters are illustrated with an example.<\/jats:p>","DOI":"10.3390\/e17052556","type":"journal-article","created":{"date-parts":[[2015,4,23]],"date-time":"2015-04-23T11:40:29Z","timestamp":1429789229000},"page":"2556-2572","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Optimum Accelerated Degradation Tests for the Gamma Degradation Process Case under the Constraint of Total Cost"],"prefix":"10.3390","volume":"17","author":[{"given":"Heonsang","family":"Lim","sequence":"first","affiliation":[{"name":"Memory Division, Samsung Electronics Co., Ltd., Gyeonggi, 445-701, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2015,4,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Nelson, W. (1990). Accelerating Test: Statistical Models, Test Plans and Data Analysis, Wiley.","DOI":"10.1002\/9780470316795"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1575","DOI":"10.1016\/j.jspi.2008.05.019","article-title":"Special Issue on Degradation, Damage, Fatigue and Accelerated Life Models in Reliability Testing","volume":"139","author":"Escobar","year":"2009","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_3","first-page":"372","article-title":"Planning performance degradation tests\u2014a review","volume":"14","author":"Yum","year":"2007","journal-title":"Int. J. Ind. Eng"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1080\/00401706.1994.10485803","article-title":"Experimental design for a class of accelerated degradation tests","volume":"36","author":"Boulanger","year":"1994","journal-title":"Technometrics"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1080\/03052159708941132","article-title":"Optimal design of accelerated degradation tests for estimating mean lifetime at the use condition","volume":"28","author":"Park","year":"1997","journal-title":"Eng. Optim"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1002\/qre.518","article-title":"Designing an accelerated degradation experiment by optimizing the estimation of the percentile","volume":"19","author":"Yu","year":"2003","journal-title":"Qual. Reliab. Eng. Int"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1016\/j.jspi.2004.06.030","article-title":"Designing an accelerated degradation experiment with a reciprocal Weibull degradation rate","volume":"136","author":"Yu","year":"2006","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1080\/16843703.2004.11673067","article-title":"Optimal design of step-stress degradation tests in the case of destructive measurement","volume":"1","author":"Park","year":"2004","journal-title":"Qual. Technol. Quant. Manag"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1198\/TECH.2009.0001","article-title":"Accelerated destructive degradation test planning","volume":"51","author":"Shi","year":"2009","journal-title":"Technometrics"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"315","DOI":"10.6339\/JDS.2007.05(3).351","article-title":"Stochastic diffusion modeling of degradation data","volume":"5","author":"Tseng","year":"2007","journal-title":"J. Data Sci"},{"key":"ref_11","unstructured":"Tang, L.C., Yang, G.Y., and Xie, M. (2004, January 26\u201329). Planning of step-stress accelerated degradation test. Los Angeles, CA, USA."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1109\/TR.2005.863811","article-title":"Optimal design for step-stress accelerated degradation tests","volume":"55","author":"Liao","year":"2006","journal-title":"IEEE Trans. Reliab"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1080\/02664760903406488","article-title":"Optimal design of accelerated degradation tests based on Wiener process models","volume":"38","author":"Lim","year":"2011","journal-title":"J. Appl. Stat"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"402","DOI":"10.1504\/IJMPT.2004.004998","article-title":"Reliability prediction and testing plan on an accelerated degradation rate model","volume":"21","author":"Liao","year":"2004","journal-title":"Int. J. Mater. Prod. Technol"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1023\/A:1009629311100","article-title":"Estimation in degradation models with explanatory variables","volume":"7","author":"Bagdonavicius","year":"2001","journal-title":"Lifetime Data Anal"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1023\/B:LIDA.0000036389.14073.dd","article-title":"Covariates and random effects in a gamma process model with application to degradation and failure","volume":"10","author":"Lawless","year":"2004","journal-title":"Lifetime Data Anal"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1007\/s10985-005-5237-8","article-title":"Accelerated degradation models for failure based on geometric Brownian motion and gamma processes","volume":"11","author":"Park","year":"2005","journal-title":"Lifetime Data Anal"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1109\/TR.2006.874937","article-title":"Stochastic degradation models with several accelerating variables","volume":"55","author":"Park","year":"2006","journal-title":"IEEE Trans. Reliab"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1109\/TR.2009.2033734","article-title":"Optimal design step-stress accelerated degradation test plan for gamma degradation processes","volume":"58","author":"Tseng","year":"2009","journal-title":"IEEE Trans. Reliab"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1080\/03610918.2012.700749","article-title":"Optimal Design for Step-Stress Accelerated Degradation Test with Multiple Performance Characteristics Based on Gamma Processes","volume":"43","author":"Pan","year":"2014","journal-title":"Comm. Stat. Simul. Comp"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Tsai, T.R., Sung, W.Y., Lio, Y.L., Chang, S.I., and Lu, J.C. (2015). Optimal Two-Variable Accelerated Degradation Test Plan for Gamma Degradation Processes. IEEE Trans. Reliab, in press.","DOI":"10.1109\/TR.2015.2435774"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1504\/IJMPT.2004.003913","article-title":"Optimal design of accelerated degradation tests","volume":"20","author":"Li","year":"2004","journal-title":"Int. J. Mater. Prod. Technol"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1108\/02656710610657611","article-title":"Design of an optimal plan for an accelerated degradation test: A case study","volume":"23","author":"Li","year":"2006","journal-title":"Int. J. Qual. Reliab. Manag"},{"key":"ref_24","unstructured":"Lawless, J.F. (1982). Statistical Models and Methods for Life Data, Wiley. [1st]."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/5\/2556\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:45:12Z","timestamp":1760215512000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/5\/2556"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4,23]]},"references-count":24,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2015,5]]}},"alternative-id":["e17052556"],"URL":"https:\/\/doi.org\/10.3390\/e17052556","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,4,23]]}}}