Applied Stochastic Models in Business and Industry最新文献

Dynamic fluctuation is a common phenomenon in degradation processes. Hence, how to model it properly has a great impact on the degradation modeling as well as the remaining useful lifetime prediction. To capture the dynamic features and to avoid the risk of the model mis-specification, a nonparametric degradation model based on functional variance process is proposed in this article. The model is composed of a unit-specific mean trend and a degradation fluctuation which follows a stochastic process. The mean trend is estimated by the local smoother method, while the stochastic fluctuation is estimated by the functional principal component analysis method. The asymptotic properties of the estimators are proved. Also, the prediction for the remaining useful lifetime is discussed and the estimator is proved to converge in distribution. Moreover, a Bayesian scheme is developed to forecast the remaining useful lifetime for units with incomplete degradation observations. Simulation results show the superiority of the proposed method by comparing it with some existing methods. Finally, two real data sets are analyzed and used to illustrate the application of the method.

The aim is to demonstrate the reliability of a population at consecutive points in time, where a sample at each current point must prove that at least 100$��p�$% of the devices function until the next point with a probability of at least $��1�-�\omega �$. To test the reliability of the population, we flexibilise standard lifetime models by allowing the unknown parameter(s) of the corresponding counting process to vary in time. At the same time, we assign a prior distribution that assumes the parameters to be constant within a certain interval. This flexibilisation has several advantages: it can be applied for all parametric lifetimes; its Markov property allows the efficient derivation of the number of defective devices, even for a large number of testing times; and the inference is less certain and hence more realistic and leads to less frequent acceptance of poor quality populations. On the other hand, the inference is stabilised by the informative prior. Based on the flexibilisation of the homogeneous Poisson process (HPP), we derive acceptance sampling plans to test the future reliability of a population. Applying the zero failure sampling plans on simulations of Weibull processes shows their good frequentist properties and their robustness. In the case of utility meters subject to German regulations (Mess- und Eichverordnung (MessEV). 2014: 2010–2073.), application of the derived sequential sampling plans when the conditions of these plans are met can lead to an extension of the verification validity period. These sampling plans protect the consumer better than those from an HPP and are still cost efficient.

In reliability engineering, different types of accelerated degradation tests have been used to obtain reliability information for evaluating highly reliable or expensive products. The step-stress accelerated degradation test (SSADT) is one of the useful experimental schemes that can be used to save the resources of an experiment. Motivated by the SSADT data for operational amplifiers collected in Xi'an Microelectronic Technology Institute, in which the underlying degradation mechanism of the operational amplifiers is unknown, we propose a semiparametric approach for SSADT data analysis that does not require strict distributional assumptions. Specifically, the empirical saddlepoint approximation method is proposed to estimate the items' lifetime (first-passage time) distribution at both stress levels included and not included in the SSADT experiment. Monte Carlo simulation studies are used to evaluate the performance and illustrate the advantages of the proposed approach. Finally, the proposed semiparametric approach is applied to analyze the motivating data set.

The Markovian arrival process (MAP) is a versatile counting process with dependent and non-identically distributed inter-arrival times following the phase-type distribution. In this article, we study the classical $��\delta �$-shock model and a mixed $��\delta �$-shock model by assuming the MAP of shocks. We derive explicit expressions for the reliability and the mean lifetime of the system. Further, we study an optimal replacement policy based on the MAP. We illustrate the developed results through several numerical examples.

Products are often offered with warranties, which have become a common marketing strategy intended to indicate that product quality is guaranteed by the firm. Warranties can attract consumer purchases, but they also incur warranty costs, especially when firms falsely claim that their products are high quality; therefore, the determination of an appropriate warranty policy is of particular importance. This study considers a two-dimensional warranty for complex repairable products, such as a vehicle, a lathe, or industrial machinery, with consideration of (1) burn-in (run-in), which is a supervised accelerating testing process performed before product launch to prevent defective products from being sold on the market, and (2) periodic preventive maintenance, which is performed during the usage period to prevent the occurrence of unexpected failures under normal usage conditions. The optimal burn-in (run-in) time and preventive maintenance intervals are determined with the aim of minimizing warranty costs for firms. The results of the study show that given a higher repair cost and a greater infant mortality failure rate, more frequent preventive maintenance is preferable, and the repair cost has the largest effect on the total warranty cost for the firm.

Spectral density analysis plays an important role in studying a stationary random process on a real line. In this paper, we extend this discussion for the random process with stationary increments. We investigate the properties of the method of moments structure function estimation, and propose a nonparametric spectral density function estimator. Our numerical results show that the proposed spectral density estimator performs comparable with the parametric counterpart when the underlying process is assumed to be band-limited. Additionally, this method is applied to analyze US Housing Starts Data, where the hidden periodicities are detected, providing consistent conclusions with previous economic studies.

Estimation of dynamic mixture distributions is a difficult task, because the density contains an intractable normalizing constant. To overcome this difficulty, we develop an approach that maximizes, by means of the cross-entropy method, a Monte Carlo approximation of the log-likelihood function. The proposed noisy cross-entropy approach is unsupervised, since it does not require the specification of a threshold between the distributions. Moreover, it bypasses the evaluation of the normalizing constant, combining good statistical properties with a modest computational burden. Both simulation-based evidence and empirical applications suggest that noisy cross-entropy estimation is comparable or preferable to existing methods in terms of statistical efficiency, but is less demanding from the computational point of view.

The model of extended sequential order statistics (ESOS) comprises of two valuable characteristics making the model powerful when modelling multi-component systems. First, components can be assumed to be heterogeneous and second, component lifetime distributions can change upon failure of other components. This degree of flexibility comes at the cost of a large number of parameters. The exact number depends on the system size and the observation depth and can quickly exceed the number of observations available. Consequently, the model would benefit from a reduction in the dimension of the parameter space to make it more readily applicable to real-world problems. In this article, we introduce link functions to the ESOS model to reduce the dimension of the parameter space while retaining the flexibility of the model. These functions model the relation between model parameters of a component across levels. By construction the proposed ‘link estimates’ conveniently yield ordered model estimates. We demonstrate how those ordered estimates lead to better results compared to their unordered counterparts, particularly when sample sizes are small.