Analysis And Experimental Design Of Degradation Data Based On The Inverse Gaussian Process

The step-stress accelerated degradation test (SSADT) is a useful tool for as-sessing the lifetime distribution of highly reliable product or very expensive product. Some efficient SSADT plans have been proposed when the underlying degradation follows the Wiener process or Gamma process. However, how to design an efficient SSADT plan for the inverse Gaussian (IG) process, which also plays an important role in degradation data analysis, is an essential problem to be solved. The aim of this paper is to provide an optimal SSADT test plan for the IG degradation process.Firstly, We assume that the degradation follows a stationary IG process. The SSADT degradation model of the product and its likelihood function are deduced based on a series of assumptions. Under the constraint that the total experimental cost does not exceed a pre-specified budget, the design variables, including sample size, measurement frequency, and the number of measurements for each stress level, are optimized by minimizing the asymptotic variance of the estimated p-quantile of the failure time distribution of the product. Finally, we illustrate the proposed procedure with a numerical example based on the data from the carbon-film-resistor problem. The sensitivity of the SSADT plan is also studied, and we find the optimal test plan is quite robust for a moderate departure from the values of the parameters. We also use Monte Carlo simulations to prove the stability of the optimal test plan.Furthermore, we investigate the planning of SSADT for the non-stationary IG process. A cumulative exposure (CE) model for the SSADT is adopted, in which the future degradation path depends only on the current stress level and the degradation accumulated, and has nothing to do with the way of accumulation. Next, under the constraint that the total experimental cost does not exceed a pre-specified budget, the optimal design variables are obtained by minimizing the asymptotic variance of the estimated the p-quantile of the failure time distribution. Finally, we use the proposed method to deal with the optimal SSADT design for a type of electrical connector. The sensitivity and stability of the optimal test plan are studied.We also use the random volatility model to discuss SSADT planning for a random-effects IG process model. We still use the CE model to establish the S-SADT. Next, under the constraint that the total experimental cost does not exceed a pre-specified budget, the optimal design variables are obtained by minimizing the asymptotic variance of the estimated the p-quantile of the failure time distribution of the product. We then use the proposed methods to deal with the optimal SSADT design for a type of electrical connector based on a set of stress relaxation data.