Optimum Accelerated Degradation Tests for the Gamma Degradation Process Case under the Constraint of Total Cost
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, stat...
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| Format: | Article |
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MDPI AG
2015-04-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/17/5/2556 |
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| author | Heonsang Lim |
| author_facet | Heonsang Lim |
| author_sort | Heonsang Lim |
| collection | DOAJ |
| description | 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. |
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| format | Article |
| id | doaj.art-9c73da9718d741579e411c63086de7b2 |
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| language | English |
| last_indexed | 2024-04-11T22:42:44Z |
| publishDate | 2015-04-01 |
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| spelling | doaj.art-9c73da9718d741579e411c63086de7b22022-12-22T03:58:57ZengMDPI AGEntropy1099-43002015-04-011752556257210.3390/e17052556e17052556Optimum Accelerated Degradation Tests for the Gamma Degradation Process Case under the Constraint of Total CostHeonsang Lim0Memory Division, Samsung Electronics Co., Ltd., Gyeonggi, 445-701, KoreaAn 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.http://www.mdpi.com/1099-4300/17/5/2556accelerated degradation testgamma processoptimal plancompromise planmaximum likelihood estimation |
| spellingShingle | Heonsang Lim Optimum Accelerated Degradation Tests for the Gamma Degradation Process Case under the Constraint of Total Cost Entropy accelerated degradation test gamma process optimal plan compromise plan maximum likelihood estimation |
| title | Optimum Accelerated Degradation Tests for the Gamma Degradation Process Case under the Constraint of Total Cost |
| title_full | Optimum Accelerated Degradation Tests for the Gamma Degradation Process Case under the Constraint of Total Cost |
| title_fullStr | Optimum Accelerated Degradation Tests for the Gamma Degradation Process Case under the Constraint of Total Cost |
| title_full_unstemmed | Optimum Accelerated Degradation Tests for the Gamma Degradation Process Case under the Constraint of Total Cost |
| title_short | Optimum Accelerated Degradation Tests for the Gamma Degradation Process Case under the Constraint of Total Cost |
| title_sort | optimum accelerated degradation tests for the gamma degradation process case under the constraint of total cost |
| topic | accelerated degradation test gamma process optimal plan compromise plan maximum likelihood estimation |
| url | http://www.mdpi.com/1099-4300/17/5/2556 |
| work_keys_str_mv | AT heonsanglim optimumaccelerateddegradationtestsforthegammadegradationprocesscaseundertheconstraintoftotalcost |