In this article, three monitoring approaches using CUMULATIVE SUM (CUSUM) CONTROL CHARTs in phase two for zero inflated poisson-based processes are presented. The first approach is based on the zero inflated poisson distribution, the second on, a proportional hazard regression model, and the third integrates a proportional hazard (PH) regression model and a frailty model to consider both measurable and unmeasurable covariates. The performance of all three CONTROL CHARTs was evaluated separately and simultaneously by applying shifts to both parameters of the zero inflated poisson distribution. Extensive simulation studies were conducted to evaluate the performance of these monitoring methods in terms of the average run length (ARL) of the CONTROL CHARTs. The proposed CUMULATIVE SUM CONTROL CHART with simultaneous consideration of measurable and unmeasurable variables showed superior performance. Finally, a real case study in a label printing factory has been provided to show the effectiveness of the proposed CONTROL CHART.

In this paper, it is asSUMed that the mean of a normal process is monitored by a CUSUM CONTROL CHART. When the CONTROL CHART triggers a signal and declares that the process has gone out of CONTROL, a search process is started to find the time of change and the causes of going the process out of CONTROL. Several methods (plans) for finding the true (real) change point is proposed. It is shown that the plans which are based on the likelihood of the points in time perform better.

Usually, in monitoring a proportion p, the binary observations are considered independent; however, in many real cases, there is a continuous stream of autocorrelated binary observations in which a two-state Markov chain model is applied with first-order dependence. On the other hand, the Bernoulli CUSUM CONTROL CHART which is not robust to autocorrelation can be applied two-sided CONTROL CHART to able to detect either increases or decreases in the process parameter. In this paper, a twosided Bernoulli-based CUSUM CONTROL CHART is proposed based on a log-likelihood-ratio statistic using a Markov chain model and average run length relationship. The average run length relationship is set using the corresponding upper and lower Bernoulli CUSUM CHARTs. Simulation studies show the superior performance of the proposed monitoring scheme. Numerical results show the superior performance of the proposed CONTROL CHART.

A CONTROL CHART can be designed based on heuristic, statistical, economic or economic statistical asSUMptions. When a CONTROL CHART such as multivariate CUMULATIVE SUM (MCUSUM) CONTROL CHART is employed to monitor a production process, three parameters should be determined; subgroup size, sampling frequency and the CONTROL limits. This paper provides an algorithm for economic-statistical designing the PPCUSUM CONTROL CHARTs parameters based on simulation approach. Finally, example and sensivity analysis are presented.

Introduction & Objective: Developing the use of statistical process CONTROL (SPC) methods for the healthcare area is evaluated as an attractive contribution. Analyzing patient data using SPC approach plays an important role to monitor effectively a health care process, improving the quality surgical processes, and other medical service processes. Among SPC methods, CUMULATIVE SUM approach have been attracted more attention in the medical literature due to its simple formulation and interpretation, as well as more sensitivity to detect medium and small shifts compared to other methods. The aim of this study is to provide analytically positive effects of using CUSUM CHARTs for hospitals, surgical, and therapeutic processes.Materials & Methods: This study is a comprehensive literature review. This paper investigates comprehensively researches and results of the used CUSUM CHARTs in different areas of healthcare focusing on reported reliable scientific sources without any limitation of time.Results: This study reveals that different CUMULATIVE SUM CONTROL CHART types are proposed to use in therapeutic and surgical processes leading to improvement of the processes. The analysis indicates that risk adjustment methods considering patients’ risk before surgery is more superior compared to other CUSUM types. This approach focuses on homogenizing and adjusting the effect of physical and physiological conditions corresponding to patients.Conclusions: CUMULATIVE SUM CHARTs should be used considering strength and weakness points of each CHART as well as data probability distribution. This paper reveals that the use of risk-adjusted CUMULATIVE SUM CHARTs can be more accurately reflect the performance results of a surgery compared to other CHART types. Furthermore the use of CUSUM methods for learning curves is capable of monitoring effectively the performance of medical trainees.

In some applications a single variable, either a process variable or product variable, characterizes the state of the process. In the other applications, multiple variables characterize the state of the process. However, in some practical situations, the quality of a process or product is characterized by a relationship between two or more variables instead of by the distribution of a single quality characteristic. This relationship, which can be linear, nonlinear or even a complicated model, is referred to as profile by researchers. Up to now, several methods have been proposed for monitoring simple linear profiles in both Phases I and II. In this paper, for improving phase II monitoring of linear profiles, a method has been proposed which applies CUMULATIVE SUM CONTROL CHARTs. Average run length criterion and simulation studies are used in order to evaluate the performance of the proposed method. The results show the suitable performance of the proposed method. Finally, the effect of reference value on the performance of the proposed method is evaluated.

In this paper, a CONTROL method based on binomial distribution is proposed in which, by analyzing the cumulated data for a uni-variate quality characteristic, the possible mean shift is detected. In this method, the domain of observations is first divided into some specified intervals and then the number of observations in each interval is counted. CONTROL statistics are next defined using the counted values based on the approximation methods. Necessary adaptations are made to form an appropriate statistic for the process monitoring. Using a simulation technique, the performance of the proposed method is compared with the ones of the optimal EWMA, GEWMA, CUSUM and GLR CONTROL CHARTs. The results show that with an equal in-CONTROL average run length, the CUMULATIVE Binomial CONTROL method performs better than CONTROL CHARTs in detecting a mean shift of any size less than 3s. The analysis is also carried out for auto correlated data, showing that the proposed method performs better than other methods for small to moderate values of autocorrelation coefficients.