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AbstractIn engineering practice, some products start deteriorating only after a period of usage. Moreover, the degradation-free periods of different products show a phenomenon of clustering, that is, there are several heterogeneous subpopulations. Both the degradation-free period and its subpopulation label are often unobservable, which poses great challenges to the reliability modeling and evaluation. In this paper, a randomly delayed degradation model considering the heterogeneous initiation time is developed, where the mixture lognormal distribution and the Wiener process are integrated to characterize the overall degradation process. The model parameters are estimated by the stochastic expectation maximization algorithm which also produces the estimator of the degradation-free period for each product simultaneously. In addition, inferences on the choice of parameters’ initial values, interval estimation, determination of the number of subpopulations and classification of products are also presented. Finally, simulation studies are carried out to validate the proposed formulas and methods, and a practical example is provided for illustration. [ABSTRACT FROM AUTHOR]

Degradation tests have been used for the purpose of assessing reliability information. In this paper, we consider a degradation test design problem under a statistical model mis-specification scenario. The Wiener and gamma processes are considered in this research. A gamma process is suitable for describing degradation paths that exhibit monotone behavior. However, if one fits a Wiener process model to the data, the resulting statistical inferences may be affected. Tsai, Tseng, and Balakrishnan studied the effect on the estimated mean time to failure. However, the experimental design problem was not discussed. A lack of the explicit functional form of the estimation variances makes it difficult to find degradation plans that can improve test efficiency. In this paper, functional forms of optimal degradation test plans are proposed under model mis-specification. Furthermore, a weighted ratio objective function considering the prior probability of the true model is used to find robust test plans for practical use. The results from a numerical example show that, by using an appropriate degradation test plan, the estimation variance can be reduced, and the test efficiency can be improved. A simulation study is conducted to investigate the performance of the parameter estimates when the sample size is small. [ABSTRACT FROM AUTHOR]

Detecting the abnormal degradation rate of Wiener processes is important for quality control and reliability management. In this paper, we propose upper-side CUSUM control schemes for monitoring the abnormal degradation rate of three classes of Wiener processes. Average run length and standard deviation run length are applied to evaluating the efficiency of CUSUM control schemes. The results show that the proposed CUSUM control schemes can efficiently give out-of-control signals when the degradation rate of Wiener process accelerates. It is also shown that initial values of degradation rate and sampling frequency have significant influence on the performance of CUSUM control schemes. [ABSTRACT FROM AUTHOR]

For reliability-critical and expensive products, it is necessary to estimate their residual lives based on available information, such as the degradation data, so that proper maintenance actions can be arranged to reduce or even avoid the occurrence of failures. In this work, by assuming that the product-to-product variability of the degradation is characterized by a skew-normal distribution, a generalized Wiener process-based degradation model is developed. Following that, the issue of residual life (RL) estimation of the target product is addressed in detail. The proposed degradation model provides greater flexibility to capture a variety of degradation processes, since several commonly used Wiener process-based degradation models can be seen as special cases. Through the EM algorism, the population-based degradation information is used to estimate the parameters of the model. Whenever new degradation measurement information of the target product becomes available, the degradation model is first updated based on the Bayesian method. In this way, the RL of the target product can be estimated in an adaptive manner. Finally, the developed methodology is demonstrated by a simulation study. [ABSTRACT FROM AUTHOR]

Inverse Gaussian first hitting time regression models sometimes provide an attractive representation of lifetime data. Various authors comment that dependence of both parameters on the same covariate may imply multicollinearity. The frequent appearance of conflicting signs for the two coefficients of the same covariate may be related to this. We carry out simulation studies to examine the reality of this possible multicollinearity. Although there is some dependence between estimates, multicollinearity does not seem to be a major problem. Fitting this model to data generated by a Weibull regression suggests that conflicting signs of estimates may be due to model misspecification. [ABSTRACT FROM AUTHOR]

To assess the reliability of highly reliable products that have two or more performance characteristics (PCs) in an accurate manner, relations between the PCs should be taken duly into account. If they are not independent, it would then become important to describe the dependence of the PCs. For many products, the constant-stress degradation test cannot provide sufficient data for reliability evaluation and for this reason, accelerated degradation test is usually performed. In this article, we assume that a product has two PCs and that the PCs are governed by a Wiener process with a time scale transformation, and the relationship between the PCs is described by the Frank copula function. The copula parameter is dependent on stress and assumed to be a function of stress level that can be described by a logistic function. Based on these assumptions, a bivariate constant-stress accelerated degradation model is proposed here. The direct likelihood estimation of parameters of such a model becomes analytically intractable, and so the Bayesian Markov chain Monte Carlo (MCMC) method is developed here for this model for obtaining the maximum likelihood estimates (MLEs) efficiently. For an illustration of the proposed model and the method of inference, a simulated example is presented along with the associated computational results. [ABSTRACT FROM AUTHOR]

During the step-stress accelerated degradation test (SSADT) experiment, the operator usually elevates the stress level at a predetermined time-point for all tested products that had not failed. This time-point is determined by the experience of the operator and the test is carried on until the performance degradation value of the product crosses the threshold value. In fact, this mode only works when a lot of products have been used in the experiment. But in the SSADT experiment, the number of products is relatively few, and so the test control to the products should be done more carefully. Considering the differences in products, we think the time-point of elevating stress level varies randomly from product-to-product. We consider a situation in which when the degradation value crosses a pre-specified value, the stress level is elevated. Under the circumstances, the time at which the degradation path crosses the pre-specified value is uncertain, and so we may regard it as a random variable. We discuss multiple-steps step-stress accelerated degradation models based on Wiener and gamma processes, respectively, and we apply the Bayesian Markov chain Monte Carlo (MCMC) method for such analytically intractable models to obtain the maximum likelihood estimates (MLEs) efficiently and present some computational results obtained from our implementation. [ABSTRACT FROM AUTHOR]

The cumulative sum (CUSUM) chart is commonly used for detecting small or moderate shifts in the fraction of defective manufactured items. However, its construction relies on the error-free inspection assumption, which can seldom be met in practice. In this article, we discuss the construction of an upward CUSUM chart in the presence of inspection error, study the effects of inspection error on the out-of-control ARL of the CUSUM chart, and present a formula for determining the sampling size that compensates for the effect of inspection error on the out-of-control ARL. [ABSTRACT FROM AUTHOR]