During the last two decades, how to capture the degradation dynamics of complex systems and aid the subsequent decision-making has always been a popular topic in reliability modeling. By incorporating some considerations on uncertainty factors into such types of degradation modeling routes, we can improve the efficiency and roubustness of current models significantly when applied to practical issues. This thesis is aimed at developing some practical degradation models to help get access to optimal reliability tests design, failure time prediction or maintenance policies.

First, we study two issues concerning accelerated degradation tests. One issue allows the diversity of usage time of tested systems, while the other stresses sensor degradation under accelerated stress levels and the parameter uncertainty.

Accelerated degradation tests consider different usage time of the system and competing failure mode. For reliable products with a comparatively long lifetime, it is essential for us to assess certain reliability information of the products after a long period of usage time under specified stress levels. Compared with accelerated life test (ALT), in which more failure data is required, accelerated degradation test (ADT) shows its advantages in delivering more information with a shorter test duration and higher accuracy in reliability prediction. Two usage scenarios in this study are considered: one is to assume that systems are brand new to operate the mission and the other is that systems are randomly selected from used systems under pre-determined policies. The system to be tested is assumed to suffer from cumulative degradation and traumatic shocks with increasing intensity. We propose a new optimality criterion that minimizes the asymptotic variance of predicted reliability evaluated at the mission ending time. Optimal test plans for both scenarios are obtained via delta methods and the Fisher information. The global optimality of test plans is verified by the general equivalence theorems. A revisited example of carbon-film resistor is presented to illustrate the efficiency and robustness of optimal test plans for both new and randomly aged systems. The result shows that the test plan tends to explore more on lower stress levels for randomly aged systems. Further, we conduct simulation studies and explore compromise test plans for the example.

Accelerated degradation tests use sequential Bayesian planning consider sensor degradation and parameter uncertainty. Most classical accelerated degradation test (ADT) planning models implicitly overlook the errors when measuring the degradation levels of the test units. However, the sensor measurement errors are inevitable and the magnitude of the errors may have a trend to increase over time due to sensor degradation. As a consequence improperly overlooking the sensor degradation in ADT planning could result in a test plan with unsatisfactory performance. This study addresses this issue by proposing a sequential ADT planning model that factors in sensor degradation. The system degradation level is periodically measured, based on which we dynamically adjust the stress level during ADT. We adopt a Bayesian framework that periodically updates the posterior distribution of model parameters considering the sensor degradation. An approximate Bayesian computation algorithm is developed to circumvent the difficulty of directly evaluating the complicated likelihood function in our problem. Numerical studies on a gas turbine reveal that our sequential model outperforms several traditional ADT designs that overlook the sensor degradation.

Then we focus on the reliability analysis of discrete event data. The event log follows a cascading failure pattern and we propose a failure time prediction model to mitigate the potential cascading failure.

Lifetime prediction of systems with discrete event data considers a cascading failure patterns. With the popularization of big data, an increasing number of discrete event data is collected and recorded during system operations. These events are usually stored in the form of event logs. In manufacturing processes, there usually exist different levels of correlations among certain series of events, while we are often required to predict the occurrence time of certain events. Thus, two challenges remain to be solved for effective degradation modeling and reliability analysis: (1) how to leverage various information contained in the event log to predict the occurrence of certain event more precisely; (2) how to model the effects of multiple correlated events on the predicted event. To address these issues, this paper proposes a new modelling and analysis approach which integrates Cox proportional hazard model and association rule mining methodology. An algorithm to estimate unknown parameters and occurrence time prediction, based on reliability model, is discussed. Unlike the existing literature, our model focuses on the interactions between events. The effectiveness of our proposed model is demonstrated through a case study. Sensitivity analysis of the approach is also studied by changing some variables in the model.

Last but not least, we integrate the production planning and matintenance policy, motivated by the randomly occurred failures and uncertain demands issues existed in production planning horizon.

Integrated production and maintenance plan for a deteriorating system under uncertain demands. To deal with today’s tough competitions, many companies have put investments into highly automated production systems with sophisticated machines. To achieve optimum performance and economic benefits, the production system is desired to operate at the maximum capacity. To keep the production process at a low cost and to satisfy customer demands, manufacturing companies have to lay appropriate production plans. In most existing studies, it is often assumed that the production process is perfect and no machine failure occurs during production planning horizon. This, however, is not the case in practice. During production many machines deteriorate due to aging or wearing, and eventually lead to failures. When a failure occurs, maintenance actions have to be performed, which decreases the capacity of the machine and disturb the initial production plan. Perturbation of production planning in an emergency situation is costly and leads to deterioration of the product quality and the service level. Therefore, it is vital to integrate the production planning and maintenance policy into a coherent strategy so as to hedge against the unexpected failures and production re-planning.