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Lifetime prognostic based on the degradation data has been widely investigated and adopted for reliability assessment and maintenance policy. However, the measurement error (ME) is usually inevitable, which leads to the bias of lifetime estimation and erroneous evaluation of the safety risk. In this paper, we mainly focus on an inverse issue: how to specify the sensor's performance (i.e., the ME range) for satisfying a given requirement of the lifetime estimation. Under this consideration, we first analyze the probability distribution functions of the lifetime estimation with/without the ME based on Wiener process degradation model. Then a distance measure based on the relative entropy is formulated to evaluate the difference between these two lifetime estimations. Furthermore, the permissible ranges of the time-dependent and time-independent ME are attained under a given allowable bias of lifetime estimation according to the proposed distance measure. In addition, the influence of the ME on maintenance policy is discussed. Finally, numerical examples and a case study are provided to illustrate. [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]

Today, many products are designed to function for a long period of time before they fail. For such highly-reliable products, collecting accelerated degradation test (ADT) data can provide useful reliability information. However, it usually requires a moderate sample size to implement an ADT. Hence, ADT is not applicable for assessing the lifetime distribution of a newly developed or very expensive product which only has a few available test units on hand. Recently, a step-stress ADT (SSADT) has been suggested in the literature to overcome the above difficulty. However, in designing an efficient SSADT experiment, the issue about how to choose the optimal settings of variables was not discussed, such as sample size, measurement frequency, and termination time. In this study, we first use a stochastic diffusion process to model a typical SSADT problem. Next, under the constraint that the total experimental cost does not exceed a predetermined budget, the optimal settings of these variables are obtained by minimizing the asymptotic variance of the estimated 100pth percentile of the product's lifetime distribution. Finally, an example is used to illustrate the proposed method. [ABSTRACT FROM AUTHOR]