Surveillance of Poisson and Multinomial Processes
نویسندگان
چکیده
As time passes, change occurs. With this change comes the need for surveillance. One may be a technician on an assembly line and in need of a surveillance technique to monitor the number of defective components produced. On the other hand, one may be an administrator of a hospital in need of surveillance measures to monitor the number of patient falls in the hospital or to monitor surgical outcomes to detect changes in surgical failure rates. A natural choice for on-going surveillance is the control chart; however, the chart must be constructed in a way that accommodates the situation at hand. Two scenarios involving attribute control charting are investigated here. The first scenario involves Poisson count data where the area of opportunity changes. A modified exponentially weighted moving average (EWMA) chart is proposed to accommodate the varying sample sizes. The performance of this method is compared with the performance for several competing control chart techniques and recommendations are made regarding the best preforming control chart method. This research is a result of joint work with Dr. William H. Woodall (Department of Statistics, Virginia Tech). The second scenario involves monitoring a process where items are classified into more than two categories and the results for these classifications are readily available. A multinomial cumulative sum (CUSUM) chart is proposed to monitor these types of situations. The multinomial CUSUM chart is evaluated through comparisons of performance with competing control chart methods. This research is a result of joint work with Mr. Lee J. Wells (Grado Department of Industrial and Systems Engineering, Virginia Tech) and Dr. William H. Woodall (Department of Statistics, Virginia Tech).
منابع مشابه
Drift Change Point Estimation in the rate and dependence Parameters of Autocorrelated Poisson Count Processes Using MLE Approach: An Application to IP Counts Data
Change point estimation in the area of statistical process control has received considerable attentions in the recent decades because it helps process engineer to identify and remove assignable causes as quickly as possible. On the other hand, improving in measurement systems and data storage, lead to taking observations very close to each other in time and as a result increasing autocorrelatio...
متن کاملMonitoring Multinomial Logit Profiles via Log-Linear Models (Quality Engineering Conference Paper)
In certain statistical process control applications, quality of a process or product can be characterized by a function commonly referred to as profile. Some of the potential applications of profile monitoring are cases where quality characteristic of interest is modelled using binary,multinomial or ordinal variables. In this paper, profiles with multinomial response are studied. For this purpo...
متن کاملNumerical solution and simulation of random differential equations with Wiener and compound Poisson Processes
Ordinary differential equations(ODEs) with stochastic processes in their vector field, have lots of applications in science and engineering. The main purpose of this article is to investigate the numerical methods for ODEs with Wiener and Compound Poisson processes in more than one dimension. Ordinary differential equations with Ito diffusion which is a solution of an Ito stochastic differentia...
متن کاملBayesian Inference for Poisson and Multinomial Log-linear Models
Categorical data frequently arise in applications in the social sciences. In such applications,the class of log-linear models, based on either a Poisson or (product) multinomial response distribution, is a flexible model class for inference and prediction. In this paper we consider the Bayesian analysis of both Poisson and multinomial log-linear models. It is often convenient to model multinomi...
متن کاملPoisson-Lindley INAR(1) Processes: Some Estimation and Forecasting Methods
This paper focuses on different methods of estimation and forecasting in first-order integer-valued autoregressive processes with Poisson-Lindley (PLINAR(1)) marginal distribution. For this purpose, the parameters of the model are estimated using Whittle, maximum empirical likelihood and sieve bootstrap methods. Moreover, Bayesian and sieve bootstrap forecasting methods are proposed and predict...
متن کامل