Zhi-Sheng Ye

The Inverse Gaussian Process as a Degradation Model

This article systematically investigates the inverse Gaussian (IG) process as an effective degradation model. The IG process is shown to be a limiting compound Poisson process, which gives it a meaningful physical interpretation for modeling degradation of products deteriorating in random environments. Treated as the first passage process of a Wiener process, the IG process is flexible in incorporating random effects and explanatory variables that account for heterogeneities commonly observed in degradation problems. This flexibility makes the class of IG process models much more attractive compared with the Gamma process, which has been thoroughly investigated in the literature of degradation modeling. The article also discusses statistical inference for three random effects models and model selection. It concludes with a real world example to demonstrate the applicability of the IG process in degradation analysis. Supplementary materials for this article are available online.

Degradation-based burn-in with preventive maintenance

As many products are becoming increasingly more reliable, traditional lifetime-based burn-in approaches that try to fail defective units during the test require a long burn-in duration, and thus are not effective. Therefore, we promote the degradation-based burn-in approach that bases the screening decision on the degradation level of a burnt-in unit. Motivated by the infant mortality faced by many Micro-Electro-Mechanical Systems (MEMSs), this study develops two degradation-based joint burn-in and maintenance models under the age and the block based maintenances, respectively. We assume that the product population comprises a weak and a normal subpopulations. Degradation of the product follows Wiener processes with linear drift, while the weak and the normal subpopulations possess distinct drift parameters. The objective of joint burn-in and maintenance decisions is to minimize the long run average cost per unit time during field use by properly choosing the burn-in settings and the preventive replacement intervals. An example using the MEMS devices demonstrates effectiveness of these two models.

A new class of Wiener process models for degradation analysis

Abstract For many products, it is not uncommon to see that a unit with a higher degradation rate has a more volatile degradation path. Motivated by this observation, we propose a new class of random effects model for the Wiener process model. We express the Wiener process in a special form and allow one of the parameters to be random across the product population so that a unit with a high degradation rate would also possess high volatility. Statistical inference of the model is discussed. By the same token, we introduce a stress–acceleration relation for the Wiener process so that both the degradation rate and the volatility of the product are increasing in the stress level. The proposed models are demonstrated by analyzing a dataset of fatigue crack growth and a dataset of head wears of hard disk drives. The applications suggest that our models perform better than existing models that ignore the positive correlation between the drift rate and the volatility.

Condition-based maintenance using the inverse Gaussian degradation model

Condition-based maintenance has been proven effective in reducing unexpected failures with minimum operational costs. This study considers an optimal condition-based replacement policy with optimal inspection interval when the degradation conforms to an inverse Gaussian process with random effects. The random effects parameter is used to account for heterogeneities commonly observed among a product population. Its distribution is updated when more degradation observations are available. The observed degradation level together with the unit’s age are used for the replacement decision. The structure of the optimal replacement policy is investigated in depth. We prove that the monotone control limit policy is optimal. We also provide numerical studies to validate our results and conduct sensitivity analysis of the model parameters on the optimal policy.

Accelerated Degradation Test Planning Using the Inverse Gaussian Process

The IG process models have been shown to be an important family in degradation analysis. In this paper, we are interested in optimal constant-stress accelerated degradation tests (ADTs) planning when the underlying degradation follows the inverse Gaussian (IG) process. We first consider ADT planning for the IG process without random effects. Asymptotic variance of the estimate of a lower quantile is derived, and the objective of the planning is to minimize this variance by properly choosing the testing stresses, and the number of samples allocated to each stress. Next, ADT planning for a random-effects IG process model is considered. We then applied the IG process to fit the stress relaxation data of a component, and use the developed methods to help with the optimal ADT design.

Some improvements on adaptive genetic algorithms for reliability-related applications

Adaptive genetic algorithms (GAs) have been shown to be able to improve GA performance in reliability-related optimization studies. However, there are different ways to implement adaptive GAs, some of which are even in conflict with each other. In this study, a simple parameter-adjusting method using mean and variance of each generation is introduced. This method is used to compare two of such conflicting adaptive GA methods: GAs with increasing mutation rate and decreasing crossover rate and GAs with decreasing mutation rate and increasing crossover rate. The illustrative examples indicate that adaptive GAs with decreasing mutation rate and increasing crossover rate finally yield better results. Furthermore, a population disturbance method is proposed to avoid local optimum solutions. This idea is similar to exotic migration to a tribal society. To solve the problem of large solution space, a variable roughening method is also embedded into GA. Two case studies are presented to demonstrate the effectiveness of the proposed method.

Degradation-Based Burn-In Planning Under Competing Risks

Motivated by two real-life examples, this article develops a burn-in planning framework with competing risks. Existing approaches to planning burn-in tests are confined to a single failure mode based on the assumption that this failure mode is subject to infant mortality. Considering the prevalence of competing risks and the high reliability of modern products, our framework differentiates between normal and infant mortality failure modes and recommends degradation-based burn-in approaches. This framework is employed to guide the burn-in planning for an electronic device subject to both a degradation-threshold failure, which is an infant mortality mode and can be modeled by a gamma process with random effect, and a catastrophic mode, which is normal and can be represented with a conventional reliability model. Three degradation-based burn-in models are built and the optimal cutoff degradation levels are derived. Their validity is demonstrated by an electronic device example. We also propose three approaches to deal with uncertainty due to parameter estimation. Algorithmic details and proofs are provided in supplementary material online.

Semiparametric Estimation of Gamma Processes for Deteriorating Products

This article investigates the semiparametric inference of the simple Gamma-process model and a random-effects variant. Maximum likelihood estimates of the parameters are obtained through the EM algorithm. The bootstrap is used to construct confidence intervals. A simulation study reveals that an estimation based on the full likelihood method is more efficient than the pseudo likelihood method. In addition, a score test is developed to examine the existence of random effects under the semiparametric scenario. A comparison study using a fatigue-crack growth dataset shows that performance of a semiparametric estimation is comparable to the parametric counterpart. This article has supplementary material online.

How do heterogeneities in operating environments affect field failure predictions and test planning

The main objective of accelerated life tests (ALTs) is to predict fraction failings of products in the field. However, there are often discrepancies between the predicted fraction failing from the lab testing data and that from the field failure data, due to the yet unobserved heterogeneities in usage and operating conditions. Most previous research on ALT planning and data analysis ignores the discrepancies, resulting in inferior test plans and biased predictions. In this paper we model the heterogeneous environments together with their effects on the product failures as a frailty term to link the lab failure time distribution and field failure time distribution of a product. We show that in the presence of the heterogeneous operating conditions, the hazard rate function of the field failure time distribution exhibits a range of shapes. Statistical inference procedure for the frailty models is developed when both the ALT data and the field failure data are available. Based on the frailty models, optimal ALT plans aimed at predicting the field failure time distribution are obtained. The developed methods are demonstrated through a real life example.

A Bayesian approach to condition monitoring with imperfect inspections

Degradation is a common phenomenon for many products. Because of a variety of reasons, the degradation rates of units from the same population are often heterogeneous. In addition, when the degradation process is monitored using dedicated sensors, the measurements are often inaccurate because of various noisy factors. To account for the heterogeneous degradation rate and the non-negligible measurement errors, we model the degradation observations using a random-effects Wiener process with measurement errors. Under the model, direct estimation of current degradation and prediction of future degradation are difficult. We thus develop a filtering algorithm that recursively estimates the joint distribution of the degradation rate and the current degradation levels. Based on the estimates, the distribution of the remaining useful life can be timely predicted. Our method is both computational efficient and storage efficient. Its effectiveness is demonstrated through simulation and real data. Copyright