Nonparametric optimal designs for degradation tests

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.