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Highlights • Three types of thresholds including alarm line and two different failure thresholds are used to model the system reliability. • Two degradation process models, Wiener-Gamma and Gamma-Gamma, are developed. • Explicit formulas for the system reliability in terms of duration thresholds for the degradation models are presented. Abstract Stochastic degradation process models are developed in terms of cumulative degradation signals of systems under three types of thresholds including alarm line and two different failure thresholds. One of the failure thresholds corresponds to the degradation amount, and the other corresponds to the duration. We assume that the degradation process can be separated into two distinctive stages by a change-point which is the first passage time of the degradation process with respect to the alarm line. For simplicity, the first stage is regarded as an age-dependent (or non-stationary) Wiener process or an age-dependent (or non-stationary) Gamma process, and the second stage is regarded as an age-dependent (or non-stationary) Gamma process; thus, two special degradation models, Wiener-Gamma and Gamma-Gamma, are constructed. Specially, two-stage stationary Wiener-Gamma and Gamma-Gamma models can be viewed as special cases. The system reliability is defined as the probability that the degradation signals do not exceed a failure threshold and the duration of exceeding the alarm line is less than the duration threshold. Some reliability results including two cases in terms of duration thresholds (constants and random variables) are derived. The moments of lifetime are also given based on the results. In addition, simulation is carried out to verify the given results. And some numerical examples are presented to illustrate the results obtained in the paper. [ABSTRACT FROM AUTHOR]

The use of degradation model to perform the reliability analysis has drawn much attention due to the fact that the performance of numerous highly reliable systems degrades over time. To describe the unit-to-unit variability for a population of systems, the random effect has been incorporated into the degradation model that plays an important part in assessing the reliability of deteriorating systems. In the existing literature, the normal distribution is commonly adopted to represent the random effect, but the assumption can be unsuitable for some practical applications, such as the degradation process of train wheels. In this paper, we present a degradation modeling and reliability estimation approach by using truncated normal distribution to characterize the unit-to-unit variability. A Wiener process with truncated normal distribution is firstly applied to model the degradation process of the deteriorating system, and the analytical expressions of probability density function and reliability function are derived. Expectation maximization algorithm is then used to estimate the model parameters. The effectiveness and feasibility of the presented approach are illustrated through a numerical example and practical case studies for laser devices and train wheels. The results indicate that the presented approach can obtain better reliability estimation results by considering the truncated normal distribution when the unit-to-unit variability has significant difference. [ABSTRACT FROM AUTHOR]

Degradation models are widely used to assess the lifetime information of highly reliable products possessing quality characteristics that both degrade over time and can be related to reliability. The performance of a degradation model largely depends on an appropriate model description of the product's degradation path. Conventionally, the random or mixed-effect model is one of the most well-known approaches presented in the literature in which the normal distribution is commonly adopted to represent unit-to-unit variability in the degradation model. However, this assumption may not appropriately signify accurate projections for practical applications. This paper is motivated by laser data wherein the normal distribution is relaxed with a skew-normal distribution that consequently provides greater flexibility as it can capture a broad range, non-normal, asymmetric behavior in unit-to-unit variability. Based on the proposed degradation model, we first derive analytical expressions for a product's lifetime distribution along with its corresponding mean-time-to-failure (MTTF). We then utilize the laser data to illustrate advantages gained by the proposed model. Finally, we address effects from the skewness parameter with regard to the accuracy of both a product's MTTF and its qth failure quantile; especially when the underlying skew-normal distribution is mis-specified as a normal distribution. The result demonstrates that effects from the skewness parameter on the tail probabilities of a product's lifetime distribution are not negligible when the random effect of the true degradation model follows a skew-normal distribution. [ABSTRACT FROM AUTHOR]

Burn-in test is a manufacturing process applied to products to eliminate latent failures or weak components in the factory before the products reach customers. The traditional burn-in test over a short period of time to collect time-to-failure or go/no-go data is rather inefficient. This decision problem can be solved if there exists a suitable quality characteristic (QC) whose degradation over time can be related to the lifetime of the product. Recently, optimal burn-in policies have been discussed in the literature assuming that the underlying degradation path follows a Wiener process. However, the degradation model of many materials (especially in the case of fatigue data) may be more appropriately modeled by a gamma process that exhibits a monotone-increasing pattern. Here, motivated by laser data, we first -propose a mixed gamma process to describe the degradation path of the product. Next, we present a decision rule for classifying a unit as typical or weak. A cost model is used to determine the optimal termination time of a burn-in test, and a motivating example is then presented to illustrate the proposed procedure. Finally, a simulation study is carried out to examine the effect of wrongly treating a mixed gamma process as a mixed Wiener process, and the obtained results reveal that the effect on the probabilities of misclassification is not negligible. [ABSTRACT FROM AUTHOR]