Analytic Evaluation of the Statistical Power of Accelerated Reliability Demonstration Tests
The planning of reliability demonstration tests is a typical task for reliability engineers. To find the optimum test plan, many different scenarios must be considered and compared. Comparing test plans by their estimation variance has several disadvantages, as it only considers the type I error. To...
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2025-01-01
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| author | Philipp Mell Martin Dazer |
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| description | The planning of reliability demonstration tests is a typical task for reliability engineers. To find the optimum test plan, many different scenarios must be considered and compared. Comparing test plans by their estimation variance has several disadvantages, as it only considers the type I error. To overcome these disadvantages, the probability of successfully demonstrating a lifetime target is used to implement a statistical power analysis for test plans from a practical perspective. Typically, this is done through simulation based on existing knowledge about the relevant failure mechanism. Such simulations are inadequate for real-world applications, mostly as their are computationally demanding. To enable wide applicability of optimal test planning methods based on the probability of test success, an analytic approach is presented in this paper. The simulation is replaced with an approximation of the stochastical distribution of the test results. The analytic method consists of two steps. First, the expected mean and covariance of the maximum likelihood estimates for a given Weibull distribution with an integrated lifetime model are derived by using pivotal quantities. Second, the delta method is applied to describe the lifetime demonstrated with a particular test plan. The method is compared against simulation results, showing an average error of 1.3–<inline-formula> <tex-math notation="LaTeX">$1.7~\%$ </tex-math></inline-formula>. |
| format | Article |
| id | doaj-art-a8aa633c745c4d19bbad21153af093a1 |
| institution | DOAJ |
| issn | 2169-3536 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IEEE |
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| spelling | doaj-art-a8aa633c745c4d19bbad21153af093a12025-08-20T03:20:29ZengIEEEIEEE Access2169-35362025-01-0113998929991010.1109/ACCESS.2025.357736611026920Analytic Evaluation of the Statistical Power of Accelerated Reliability Demonstration TestsPhilipp Mell0https://orcid.org/0009-0000-8474-6392Martin Dazer1https://orcid.org/0000-0002-5314-5874Institute of Machine Components, University of Stuttgart, Stuttgart, GermanyInstitute of Machine Components, University of Stuttgart, Stuttgart, GermanyThe planning of reliability demonstration tests is a typical task for reliability engineers. To find the optimum test plan, many different scenarios must be considered and compared. Comparing test plans by their estimation variance has several disadvantages, as it only considers the type I error. To overcome these disadvantages, the probability of successfully demonstrating a lifetime target is used to implement a statistical power analysis for test plans from a practical perspective. Typically, this is done through simulation based on existing knowledge about the relevant failure mechanism. Such simulations are inadequate for real-world applications, mostly as their are computationally demanding. To enable wide applicability of optimal test planning methods based on the probability of test success, an analytic approach is presented in this paper. The simulation is replaced with an approximation of the stochastical distribution of the test results. The analytic method consists of two steps. First, the expected mean and covariance of the maximum likelihood estimates for a given Weibull distribution with an integrated lifetime model are derived by using pivotal quantities. Second, the delta method is applied to describe the lifetime demonstrated with a particular test plan. The method is compared against simulation results, showing an average error of 1.3–<inline-formula> <tex-math notation="LaTeX">$1.7~\%$ </tex-math></inline-formula>.https://ieeexplore.ieee.org/document/11026920/Reliability demonstrationreliability test planningstatistical power analysisaccelerated life testingtest planoptimal design |
| spellingShingle | Philipp Mell Martin Dazer Analytic Evaluation of the Statistical Power of Accelerated Reliability Demonstration Tests IEEE Access Reliability demonstration reliability test planning statistical power analysis accelerated life testing test plan optimal design |
| title | Analytic Evaluation of the Statistical Power of Accelerated Reliability Demonstration Tests |
| title_full | Analytic Evaluation of the Statistical Power of Accelerated Reliability Demonstration Tests |
| title_fullStr | Analytic Evaluation of the Statistical Power of Accelerated Reliability Demonstration Tests |
| title_full_unstemmed | Analytic Evaluation of the Statistical Power of Accelerated Reliability Demonstration Tests |
| title_short | Analytic Evaluation of the Statistical Power of Accelerated Reliability Demonstration Tests |
| title_sort | analytic evaluation of the statistical power of accelerated reliability demonstration tests |
| topic | Reliability demonstration reliability test planning statistical power analysis accelerated life testing test plan optimal design |
| url | https://ieeexplore.ieee.org/document/11026920/ |
| work_keys_str_mv | AT philippmell analyticevaluationofthestatisticalpowerofacceleratedreliabilitydemonstrationtests AT martindazer analyticevaluationofthestatisticalpowerofacceleratedreliabilitydemonstrationtests |