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Nonparametric optimal designs for degradation tests.

Narayanaswamy Balakrishnan1, Chengwei Qin1

  • 1Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada.

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|June 16, 2022
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Summary
This summary is machine-generated.

This study optimizes degradation test designs using empirical Lévy processes. It determines sample size, measurement frequency, and operation time to minimize estimation errors for first passage time (FPT) within a budget.

Keywords:
First passage timeLaplace inversionLévy processempirical saddlepoint approximationgamma bridgeoptimization

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Area of Science:

  • Reliability Engineering
  • Statistical Modeling
  • Nonparametric Statistics

Background:

  • Degradation testing is crucial for estimating product lifetime.
  • Existing methods often assume specific parametric distributions for degradation.
  • Nonparametric approaches offer flexibility but require careful experimental design.

Purpose of the Study:

  • To develop an optimal design strategy for nonparametric degradation tests.
  • To investigate the impact of design variables (sample size, measurement frequency, total operation time) on estimation accuracy.
  • To minimize the mean squared error of the first passage time (FPT) distribution percentile under budget constraints.

Main Methods:

  • Modeling the degradation process using an empirical Lévy process with heterogeneity.
  • Defining design variables: sample size, measurement frequency, and total operation time.
  • Employing bootstrap methods to estimate the mean squared error (MSE) of the FPT percentile.

Main Results:

  • The study identifies optimal values for design variables that minimize FPT estimation MSE.
  • It quantifies the trade-offs between experimental cost and estimation precision.
  • The nonparametric framework effectively handles heterogeneity in degradation processes.

Conclusions:

  • Optimal design of degradation tests can be achieved within a nonparametric framework.
  • Careful selection of sample size, measurement frequency, and operation time is critical for accurate FPT estimation.
  • The proposed methodology provides a cost-effective approach to designing reliable degradation experiments.