Qingyu Yang

Reliability of two-stage weighted-k-out-of-n systems with components in common

This paper extends the existing one-stage weighted-k-out-of-n model to two-stage weighted-k-out-of-n models with components in common. Algorithms are developed to calculate the system reliability, and generate the minimal cuts & minimal paths of two-stage weighted-k-out-of-n systems. Reliability bounds for systems with s-dependent component failures are investigated based on the generated minimal cuts & minimal paths. Two types of two-stage weighted-k-out-of-n models, the SW-k-out-of-n model, and the PW-k-out-of-n model, can be applied to investigate reliability issues in network applications, such as the project management, and the shortest path problems. Examples are provided to demonstrate the developed models & algorithms.

Reliability Analysis of Repairable Systems With Dependent Component Failures Under Partially Perfect Repair

Existing reliability models for repairable systems with a single component can be well applied for a range of repair actions from perfect repair to minimal repair. Establishing reliability models for multi-component repairable systems, however, is still a challenge problem when considering the dependency of component failures. This paper focuses on a special repair assumption, called partially perfect repair, for repairable systems with dependent component failures, where only the failed component is repaired to as good as new condition. A parametric reliability model is proposed to capture the statistical dependency among different component failures, in which the joint distribution of the latent component failure time is established using copula functions. The model parameters are estimated by using the maximum likelihood method, and the maximum likelihood function is calculated based on the conditional probability. Based on the proposed reliability model, statistical hypothesis testing procedures are developed to determine the dependency of component failures. The developed methods are illustrated with an application in a cylinder head assembling cell that consists of multiple stations.

Monte Carlo Methods for Reliability Evaluation of Linear Sensor Systems

A linear sensor system is defined as a sensor system in which the sensor measurements have a linear relationship to source variables that cannot be directly measured. Evaluation of the reliability of a general linear sensor system is a #P problem whose computational time increases exponentially with the increment of the number of sensors. To overcome the computational complexity, Monte Carlo methods are developed in this paper to approximate the sensor systems reliability. The crude Monte Carlo method is not efficient when the sensor system is highly reliable. A Monte Carlo method that has been improved for network reliability, known as the Recursive Variance Reduction (RVR) method, is further adapted for the reliability problem of linear sensor systems. To apply the RVR method, new methods are proposed to obtain minimal cut sets of the linear sensor system, particularly under the conditions where the states of some sensors are fixed as failed or functional. A case study in a multistage automotive assembly process is conducted to demonstrate the efficiency of the proposed methods.

Failure Profile Analysis of Complex Repairable Systems With Multiple Failure Modes

The relative failure frequency among different failure modes of a production system is referred to as failure profile in this paper. Identification of failure profile based on failure-time data collected in the production phase of a system can help pinpoint the bottleneck problems, and provide valuable information for system design evaluation and maintenance management. Major challenges of effective failure profile identification come from time-varying and limited failure-time data. In this paper, the failure profile is estimated by using the maximum likelihood method. In addition, statistical hypothesis testing procedures are proposed to inspect the existence of a dominating failure mode, and possible changes of failure profiles during a production period. The developed methods are illustrated with an automation system of a high throughput screening (HTS) process, and a production process for cylinder heads.

Optimal maintenance planning for repairable multi-component systems subject to dependent competing risks

Many complex multi-component systems suffer from dependent competing risks. The reliability modeling and maintenance planning of repairable dependent competing risks systems are challenging tasks because the repair of the failed component can change the lifetime of the other components when multiple components fail dependently. This article first proposes a generally dependent latent age model to capture the dependence of competing risks under general component repairs. Based on the proposed reliability model, both system- and component-level periodic inspection-based maintenance polices are considered for repairable multi-component systems that are subject to dependent competing risks. Under the system-level maintenance policy, the entire system is restored to the as-good-as-new state once a failure is detected. While under the component-level maintenance policy, only the failed component is repaired imperfectly. The optimal solution of the system-level policy is obtained by using renewal theory. The optimal solution of the component-level policy, however, cannot be obtained analytically, due to its complex failure and repair characteristics. A simulation-based optimization approach with stochastic approximation is developed to solve the optimization problem for the component-level policy. The developed methods are illustrated by using a cylinder head assembly cell that consists of multiple stations.

A physical–statistical model of overload retardation for crack propagation and application in reliability estimation

ABSTRACT Crack propagation subjected to fatigue loading has been widely studied under the assumption that loads are ideally cyclic with a constant amplitude. In the real world, loads are not exactly cyclic, due to either environmental randomness or artificial designs. Loads with amplitudes higher than a threshold limit are referred to as overloads. Researchers have revealed that for some materials, overloads decelerate rather than accelerate the crack propagation process. This effect is called overload retardation. Ignoring overload retardation in reliability analysis can result in a biased estimation of product life. In the literature, however, research on overload retardation mainly focuses on studying its mechanical properties without modeling the effect quantitatively and, therefore, it cannot be incorporated into the reliability analysis of fatigue failures. In this article, we propose a physical–statistical model to quantitatively describe overload retardation considering random errors. A maximum likelihood estimation approach is developed to estimate the model parameters. In addition, a likelihood ratio test is developed to determine whether the tested material has either an overload retardation effect or an overload acceleration effect. The proposed model is further applied to reliability estimation of crack failures when a material has the overload retardation effect. Specifically, two algorithms are developed to calculate the failure time cumulative distribution function and the corresponding pointwise confidence intervals. Finally, designed experiments are conducted to verify and illustrate the developed methods along with simulation studies.

A random effect autologistic regression model with application to the characterization of multiple microstructure samples

ABSTRACT The microstructure of a material can strongly influence its properties such as strength, hardness, wear resistance, etc., which in turn play an important role in the quality of products produced from these materials. Existing studies on a materials microstructure have mainly focused on the characteristics of a single microstructure sample and the variation between different microstructure samples is ignored. In this article, we propose a novel random effect autologistic regression model that can be used to characterize the variation in microstructures between different samples for two-phase materials that consist of two distinct parts with different chemical structures. The proposed model differs from the classic autologistic regression model in that we consider the unit-to-unit variability among the microstructure samples, which is characterized by the random effect parameters. To estimate the model parameters given a set of microstructure samples, we first derive a likelihood function, based on which a maximum likelihood estimation method is developed. However, maximizing the likelihood function of the proposed model is generally difficult as it has a complex form. To overcome this challenge, we further develop a stochastic approximation expectation maximization algorithm to estimate the model parameters. A simulation study is conducted to verify the proposed methodology. A real-world example of a dual-phase high strength steel is used to illustrate the developed methods.

Sensor system reliability modeling and analysis for fault diagnosis in multistage manufacturing processes

This paper investigates the reliability of coordinate sensor systems used for process fault diagnosis in multistage manufacturing processes. When considering catastrophic sensor failure, the reliability of a coordinate sensor system is defined based on its diagnosability performance. A mathematical tool called matroid theory is applied to study the reliability of the coordinate sensor system; properties of the minimal paths and minimal cuts are derived; efficient methods are developed to evaluate the exact system reliability for two special types of systems; and an efficient algorithm to evaluate the min–max lower bound of system reliability is provided that does not require assuming that all minimal paths must be known in advance. The proposed models and the developed methods are illustrated and applied in two case studies for fault diagnosis of a multistage panel assembly process.

Semiparametric Models for Accelerated Destructive Degradation Test Data Analysis

ABSTRACT Accelerated destructive degradation tests (ADDT) are widely used in industry to evaluate materials’ long-term properties. Even though there has been tremendous statistical research in nonparametric methods, the current industrial practice is still to use application-specific parametric models to describe ADDT data. The challenge of using a nonparametric approach comes from the need to retain the physical meaning of degradation mechanisms and also perform extrapolation for predictions at the use condition. Motivated by this challenge, we propose a semiparametric model to describe ADDT data. We use monotonic B-splines to model the degradation path, which not only provides flexible models with few assumptions, but also retains the physical meaning of degradation mechanisms (e.g., the degradation path is monotonic). Parametric models, such as the Arrhenius model, are used for modeling the relationship between the degradation and the accelerating variable, allowing for extrapolation to the use condition. We develop an efficient procedure to estimate model parameters. We also use simulations to validate the developed procedures and demonstrate the robustness of the semiparametric model under model misspecification. Finally, the proposed method is illustrated by multiple industrial applications. This article has online supplementary materials.

A distribution-based functional linear model for reliability analysis of advanced high-strength dual-phase steels by utilizing material microstructure images

ABSTRACT The microstructure of a material is known to strongly influence its macroscopic properties, such as strength, hardness, toughness, and wear resistance, which in turn affect material service lifetime. In the reliability literature, most existing research conducts reliability analysis based on either lifetime data or degradation data. However, none of these studies take the information contained in an image of the microstructure of the material into account when conducting reliability analysis. In this article, considering the strong effect on a materials reliability created by its microstructure, we conduct a reliability analysis of an advanced high-strength dual-phase steel by utilizing information about its microstructure. Specifically, the lifetime distribution of the steel, which is assumed to belong to a log-location-scale family, is predicted by utilizing the information contained in images of its microstructure. For the prediction, we propose a novel statistical model called the distribution-based functional linear model, in which the effect of the microstructure on both the location and scale parameters of lifetime distribution is formulated. The proposed model generalizes the existing functional linear regression model. A maximum penalized likelihood method is developed to estimate the model parameters. A simulation study is implemented to illustrate the developed methods. Physical experiments on dual-phase steel are designed and conducted to demonstrate the proposed model. The results show that the proposed model more precisely predicts the lifetime of the steel than existing methods that ignore the information contained in microstructure images.