A novel pseudo‐maximum likelihood estimation method for accelerated degradation tests under Wiener process

Abstract

For reliability assessment based on accelerated degradation tests (ADTs), an appropriate parameter estimation method is very important because it affects the extrapolation and prediction accuracy. The well‐adopted maximum likelihood estimation (MLE) method focuses on interpolation fitting and obtains results via maximizing the likelihood of the observations. However, a best interpolation fitting does not necessarily yield a best extrapolation. In this paper, therefore, a pseudo‐MLE (P‐MLE) method is proposed to improve the prediction accuracy of constant‐stress ADTs by considering the degradation mechanism equivalence under Wiener process. In particular, the degradation mechanism equivalence is characterized by a mechanism equivalence factor which presents the proportional relationship between degradation rate and variation. Then, the mechanism equivalence factor is determined via a two‐step method. The other model parameters can be estimated by the general MLE method. The asymptotic variances of acceleration factors and the p‐quantile of product failure time under normal condition are adopted to compare the statistical properties of the proposed method and the general MLE approach. Numerical examples show that the novel P‐MLE method may not achieve a maximum likelihood but can provide more benefits regarding prediction accuracy enhancement especially when the sample size is limited.

Degradation analysis on trend gamma process

“…where Φ GA (⋅|𝑎𝑡 𝑏 , 𝛽) represents the CDF of gamma distribution Γ(𝑎𝑡 𝑏 , 𝛽), Φ 𝐹 (⋅|2𝑎𝑡 𝑏 , 2𝛿) represents the CDF of F distribution associated with the degree of freedom 2𝑎𝑡 𝑏 and 2𝛿, and Φ IG (⋅|𝜇𝑡 𝑏 , 𝜂𝑡 2𝑏 ) represents the CDF of inverse Gaussian distribution IG(𝜇𝑡 𝑏 , 𝜂𝑡 2𝑏 ). Similarly, the CDF of TGP model can be found in Equation (7), denoted by 𝐹 TGP (𝑡). Figure 3 displays four estimated CDFs, where black dots represent the empirical CDF 𝐹 * (𝑡), and the red, violet, blue, and black curves represent FGP (𝑡) FREGP (𝑡), FIGP (𝑡), and FTGP (𝑡) with their corresponding 95% CIs (Algorithm 2), respectively.…”

“…In addition, the Wiener process is usually implemented to analyze the non-monotonic degradation data (Doksum and Hóyland 4 ). More descriptions for Wiener process model can be referred to Wang, 5 Chhikara and Folks, 6 Wang et al, 7 Whitmore, 8 and Whitmore and Schenkelberg. 9 The GP is an applicative method to fit the monotonically increasing degradation path.…”

Optimal design of step stress accelerated degradation test with multistress considering stress weight

“…The results show that using the proposed method under Bayes D-optimality not only improves the accuracy of model parameters but also eliminates the impact of model uncertainty. Wang et al 32 proposed a pseudo-Maximum Likelihood Estimate (p-MLE) method to improve the prediction accuracy of model parameters to address the problem of failing to obtain the best extrapolation results using the best interpolation fitting model parameters. Example verification revealed that the proposed method may not achieve the maximum likelihood under the condition of limited sample size but can improve the prediction accuracy of the reliability of tested products.…”