Analytical approach for designing accelerated degradation tests under an exponential dispersion model

Tung, Hung-Ping; Lee, I‐Chen; Tseng, Sheng‐Tsaing

doi:10.1016/j.jspi.2021.10.002

Cited by 7 publications

(5 citation statements)

References 14 publications

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“…Therefore, for different settings

\left(\mathbf{n},\mathbf{m}\right)

and

\left({\mathbf{n}}^{\prime },{\mathbf{m}}^{\prime}\right)

, if

{n}_i{m}_i={n}_i^{\prime }{m}_i^{\prime }

, for all

i=1,\dots, I

, then the two designs carry the same information. Such phenomena has been mentioned in Tung et al (2022). To overcome this difficulty, let

N={\sum}_{i=1}^I{n}_i{m}_i

denote the total number of measurements.…”

Section: Optimal Criteriamentioning

confidence: 54%

See 1 more Smart Citation

Optimizing two‐variable gamma accelerated degradation tests with a semi‐analytical approach

Tung

2023

Naval Research Logistics

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In this paper, we provide a semi‐analytical approach to determine the optimal designs for two‐variable gamma accelerated degradation tests under three criteria: ‐optimality, ‐optimality, and ‐optimality. We first use general equivalence theorem to prove that the optimal approximate designs only allocate test units at the four vertices of a rectangular design region, and the corresponding optimal proportion of total number of measurements at each stress level is derived. Next, we apply the concept of prescribed accuracy level and total experimental cost to further determine optimal integer designs. More specifically, a numerical approach is used to resolve the number of test units and number of measurements at each stress level. Finally, an example is presented to illustrate the proposed procedure and compare the efficiency of optimal designs under three optimal criteria.

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“…Therefore, for different settings

\left(\mathbf{n},\mathbf{m}\right)

and

\left({\mathbf{n}}^{\prime },{\mathbf{m}}^{\prime}\right)

, if

{n}_i{m}_i={n}_i^{\prime }{m}_i^{\prime }

, for all

i=1,\dots, I

, then the two designs carry the same information. Such phenomena has been mentioned in Tung et al (2022). To overcome this difficulty, let

N={\sum}_{i=1}^I{n}_i{m}_i

denote the total number of measurements.…”

Section: Optimal Criteriamentioning

confidence: 54%

“…Therefore, for different settings (n, m) and (n ′ , m ′ ), if n i m i = n ′ i m ′ i , for all i = 1, … , I, then the two designs carry the same information. Such phenomena has been mentioned in Tung et al (2022). To overcome this difficulty, let N = ∑ I i=1 n i m i denote the total number of measurements.…”

Section: Optimal Criteriamentioning

confidence: 99%

Optimizing two‐variable gamma accelerated degradation tests with a semi‐analytical approach

Tung

2023

Naval Research Logistics

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“…For the TED process, the PDF (1) of ( ) has no closed expression except for some special values [32]. According to the previous research [33][34], the saddle-point approximation (SAM) method provides a highly accurate approximation expression of PDF of ( ). Therefore, we adopt SAM to obtain the approximated PDF of TED process, which is expressed as…”

Section: Ted Degradation Modelmentioning

confidence: 99%

Optimal design of step-stress accelerated degradation tests based on the Tweedie exponential dispersion process

Yan¹,

Xu²,

Bigaud³

et al. 2023

Reliability Engineering & System Safety

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Section: Introductionmentioning

confidence: 99%

“…Shat and Schwabe 17 considered repeated measures ADT assuming the degradation paths follow a linear mixed effects model and proposed optimal experimental designs. Tung et al 18 proposed an optimal design for a k-level ADT design problem assuming the degradation paths follow an exponential dispersion model. For other practical applications based on data from degradation tests, one can refer to those by Ye et al, 19 and Shi et al 20 Among these stochastic processes used for describing failure-mechanisms, the Wiener process has been studied extensively.…”

Section: Introductionmentioning

confidence: 99%

Optimum degradation test sampling plan for the Wiener process

Huang

2022

Quality & Reliability Eng

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In this paper, we propose degradation test sampling plans (DTSPs) used to determine the acceptability of a product in a Wiener process model. A test statistic and the acceptance criterion based on Wiener process parameter estimates are proposed. The design of a degradation test is investigated using a model incorporating test cost constraint to minimize the asymptotic variance of the proposed test statistic. Some important variables, including the sample size, measurement frequency, and the total test time, are chosen as decision variables in a degradation test plan. The asymptotic variance of the test statistic and the approximate functional forms of the optimal solutions are derived. A search algorithm is also represented in a flow chart for the purpose of finding the optimal DTSPs. In addition, we assess the minimum cost requirement for the result of the test procedure to satisfy the minimum requirements for the producer's risk and the consumer's risk. When the given test budget is not large enough, we suggest some methods to find appropriate solutions. Finally, a numerical example is used to illustrate the proposed methodology. Optimum DTSPs are obtained and tabulated for some combinations of commonly used producer and consumer risk requirements. A sensitivity analysis is also conducted to investigate the sensitivity of the obtained DTSPs to the cost parameters used.

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Analytical approach for designing accelerated degradation tests under an exponential dispersion model

Cited by 7 publications

References 14 publications

Optimizing two‐variable gamma accelerated degradation tests with a semi‐analytical approach

Optimizing two‐variable gamma accelerated degradation tests with a semi‐analytical approach

Optimal design of step-stress accelerated degradation tests based on the Tweedie exponential dispersion process

Optimum degradation test sampling plan for the Wiener process

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