Products or systems degrade over time. Degradation over time is frequently modeled by stochastic processes to account for inherent randomness. Based on the assumption of additive accumulation of degradation, a family of degradation processes based on the Lévy processes has been well studied in the literature. Recently, a stochastic degradation model based on the generalized inverse Gaussian (GIG) distribution shows good performance in the empirical evaluation studies based on some well-known real datasets. The likelihood function of this model can be seen a generalization of the likelihood function of the existing degradation processes including the Wiener, gamma, inverse Gaussian (IG) processes, which belong to Lévy process. However, it is not clear that which stochastic models are the best for modeling the degradation phenomena although the numerous papers have appeared in decades.
In this paper, we consider more flexible degradation stochastic model than the prominent models. Specifically, we propose new stochastic degradation models based on the powered inverse Gaussian (PIG) distribution, which can be seen a generalization of the IG distribution, and the powered generalized inverse Gaussian (PGIG) distribution. The likelihood function of this model can be seen a generalization of the likelihood function of GIG degradation model. The performances of the proposed models are assessed by comparing the proposed models with the prominent models, based on some well-known real datasets. The results of the evaluation show that the proposed models perform better than existing models. And a simulation study is conducted.
When system deterioration information is continuously available, it is convenient to use a continuous stochastic process to characterize the deterioration. The gamma process and inverse Gaussian process are usually used to model monotonic deterioration; however, if the system deterioration is measured frequently, the measured amount of deterioration may not be monotonic. A replacement problem is considered here for a system with a non-monotonic amount of deterioration. The deterioration is characterized by a geometric Brownian motion, which can capture deterioration with an increasing rate over time. The system is inspected at equal time intervals, and the deterioration amount can be specified exactly from the inspection results. An optimal replacement policy is derived in accordance with the age and deterioration amount that minimizes the total expected cost over an infinite time horizon. The cost structure includes replacement cost and operating cost, which both increase with age and the amount of deterioration. The optimization problem is formulated as a Markov decision process and provides a set of conditions with which the structural properties of the optimal replacement policy is characterized. The total expected cost is proven to be monotonically non-decreasing in both age and deterioration amount. Moreover, the optimal replacement policy is shown to be a control limit policy in which the optimal control limits do not monotonically increase with either the amount of deterioration or age. A numerical example is given that illustrates the effects of the cost of replacement and the parameters of geometric Brownian motion on the control limit policy.
Currently, a large amount of data accumulated in electronic commerce (EC) sites, and it is possible to customize a marketing strategy for each customer. This study focuses on an analytical model of purchasing data cumulated on a fresh flowers EC site for their marketing analysis. On an EC site providing fresh flower products, the purchase frequency per customer is much lower than that on EC sites selling commodity products or books. Therefore, the accumulated data for each customer on an EC site providing fresh flowers are limited and it is difficult to analyze the individual preferences of each user based on their purchasing history. On the other hand, fresh flower products are characterized by their purchase for several events in an individual’s life such as birthday and funeral. Moreover, the selected colors and prices of flowers tend to be different depending on the event. In this research, we focus on the relationship between the attributes of customers and purchasing actions, making it unnecessary to analyze the purchasing behavior of individual customers. We propose the analytical model considering the relationship between the event, the color and price of flower items, and other factors. Because customers’ purchase behaviors are very diverse, the variation in the relationship may be difficult to explain using conventional methods with hard clustering, wherein each datapoint belongs strictly to one class. Therefore, we propose a new latent class model to analyze purchasing behavior data. The proposed model is expected to reveal customers’ purchase behaviors and, thus, help to develop efficient marketing strategies. Moreover, we validate the effectiveness of our proposed method by applying it to the real purchase history data on the EC site.
Conway and Maxwell derived the Conway-Maxwell (COM)-Poisson distribution as generalization of the Poisson distribution. This distribution has been used in survival analysis. The probability mass function (pmf) of this distribution contains a normalizing constant expressed as sum of infinite series and therefore, not only the computation of the distribution but also the parameter estimation for the COM-Poisson is difficult. To remedy this problem, several methods have been appeared in the literature such as the methods based on Laplace approximation and linear regression. However, it is pointed out that the approximation accuracy of the Laplace approximation is poor, and the regression method cannot be applied if there are no covariates.
In this paper, we propose a new method of parameter estimation for the COM-Poisson using the conditional likelihood functions in the COM-Poisson distribution. The key idea of the proposed method is to use the conditional likelihood functions, which does not have the complicated normalizing constant. We further prove that the estimates of all two parameters always exist uniquely and a conditional likelihood function of the shape parameter is a log-concave function. Through Monte Carlo simulations, we further show that the proposed method performs better than the existing method in terms of bias and root mean squared error (RMSE). In an illustrative example, we fit the COM-Poisson model to the real data set of carton by our proposed method.
Nowadays, many companies use business chat systems for communication among employees. With simple communication or information sharing, these online communication systems play an important role in improving work efficiency. Additionally, analyzing accumulated communication data on systems can be effective for human resource management to create further business value. In particular, the response interval between two employees reflects their relationship and work efficiency. Therefore, designing a model for analyzing the response interval between two employees as a minimum communication unit on a chat system can be effective. Our study proposes a new latent class model that quantitatively expresses the relationship between two users based on response interval. We also analyze the communication characteristics from a response interval perspective. By assuming that a combination of two users and their response intervals arise probabilistically from latent classes, we can express the difference in users’ behaviors that are affected by who are the chat partners and other conditions. Finally, we apply the actual data from a Japanese company to our model for a response interval analysis. Through actual data analysis, we revealed the communication characteristics of companies and the relationship between each employee pair and the company.
When a process demonstrates complex cause-and-effect relationships, process adjustments are often used, such as automatic process control (APC). On the other hand, a statistical process control (SPC) is used to identify the causes of abnormality. For example, we use control charts for process monitoring. However, in a process with process adjustments, careful consideration should be taken toward choosing control characteristics as abnormalities may go undetected through the sole monitoring of output.
In many cases, the complexity of the gear grinding process complicates the identification of abnormal causes. Therefore, we indicate a decreased deviation from a fixed target value by using feedback adjustments.
There are correlations among multivariate quality characteristics in cases where feedback adjustments are not used. However, in the process with feedback adjustments, the relationships are disappeared as a result of the controlled quality characteristics. In such a process, we cannot detect changes in the relationship by monitoring quality characteristics, and therefore, we allow abnormalities to continue in the process.
This research shows whether feedback adjustment is effective for the process and then shows appropriate control characteristics, other than quality characteristics, for the use of T2-Q control charts to monitor the relationships among variables using the case study of the gear grinding process.
Software defects cause big problems to our society because software is embedded in numerous products. Thus, defect detection via software testing is essential to prevent such problems and to improve the quality of software design. Within this context, methods for software test design which have frameworks for the test requirements analysis have been proposed to create effective and efficient test cases from various aspects, such as software behavior, use cases, usage environment, and so on. These frameworks are effective in designing test cases; however, the level of abstraction is high, and there is a lot of flexibility. So, the quality of test cases depends on the skill of testers, which is considered as a problem. This paper describes a test design method that includes more specific frameworks. We propose this method to understand the test object from both the static and dynamic aspects and to design test cases in the viewpoints of “weakness” and “adverse conditions.” We evaluated the effectiveness of the proposed method through an experiment wherein testers conducted the designing of test cases. It was confirmed that they derived more test cases that were related to weakness and adverse conditions using the proposed method than the empirical one.
This paper proposes hierarchical Bayesian control charts based on the spatial autoregressive model for trendy datasets in high-mix low-volume production. The control chart, which is a representative method of statistical process control, is plagued by sample shortages for each product type in high-mix low-volume production. In addition, during manufacturing processing equipment can deteriorate, which, in turn, can result in changing process averages, which, in turn, results in an increase in type I errors. Moreover, in high-mix, low-volume production, spatial dependence exists between different product types due to universal equipment being used. To address these problems, we design control charts that consider the spatial relationships among product types using hierarchical Bayesian modeling based on the spatial autoregressive model. To clarify the properties of the proposed method, we evaluate two production orders: completely random production orders and nonrandom production orders. The results suggest the proposed method is effective, especially in the case of a random production sequence and when there are large differences among product types.