Exponentially Weighted Moving Average Hypergeometric np Control Scheme

ABSTRACTRuns rules are usually used with Shewhart-type charts to enhance the charts' sensitivities toward small and moderate shifts. Abbas et al. in 2011 took it a step further by proposing two runs rules schemes, applied to the exponentially weighted moving average (EWMA) chart and evaluated their average run length (ARL) performances using simulation. They showed that the proposed schemes are superior to the classical EWMA chart and other schemes being investigated. Besides pointing out some erroneous ARL and standard deviation of the run length (SDRL) computations in Abbas et al., this paper presents a Markov chain approach for computing the ARL, percentiles of the run length (RL) distribution and SDRL, for the two runs rules schemes of Abbas et al. Using Markov chain, we also propose two combined runs rules EWMA schemes to quicken the two schemes of Abbas et al. in responding to large shifts. The runs rules (basic and combined rules) EWMA schemes will be compared with some existing control charting methods, where the former charts are shown to prevail.

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The exponentially weighted moving average (EWMA) control charts with variable sampling intervals (VSIs) have been shown to be substantially quicker than the fixed sampling intervals (FSI) EWMA control charts in detecting process mean shifts. The usual assumption for designing a control chart is that the data or measurements are normally distributed. However, this assumption may not be true for some processes. In the present paper, the performances of the EWMA and combined X¯–EWMA control charts with VSIs are evaluated under non-normality. It is shown that adding the VSI feature to the EWMA control charts results in very substantial decreases in the expected time to detect shifts in process mean under both normality and non-normality. However, the combined X¯–EWMA chart has its false alarm rate and its detection ability is affected if the process data are not normally distributed.

Exponentially weighted moving average (EWMA) control charts are consistently used for the detection of small shifts contrary to Shewhart charts, which are commonly used for the detection of large shifts in the process. There are many interesting features of EWMA charts that have been studied for complete data in the literature. The aim of present study is to introduce and compare the double exponentially weighted moving average (DEWMA) and EWMA control charts under type-I censoring for Poisson-exponential distribution. The monitoring of mean level shifts using censored data is of a great interest in many applied problems. Moreover, a new idea of conditional median is introduced and further compared with the existing conditional expected values approach for monitoring the small mean level shifts. The performance of the DEWMA and EWMA charts is evaluated using the average run length, expected quadratic loss, and performance comparison index measures. The optimum sample size comparisons for the specified and unspecified parameters are also part of this study. Two applications for practical considerations are also discussed. It is observed that different censoring rates and the size of shifts significantly affect the performance of the EWMA and DEWMA charts. Copyright © 2016 John Wiley & Sons, Ltd.

In data-based method for fault detection, principal component analysis (PCA) has been used successfully for fault detection in system with highly correlated variables. The aim of this paper is to combine the exponentially weighted moving average (EWMA) control scheme with PCA model in order to improve fault detection performance. In fact, PCA is used to provide a modeling framework for the develop fault detection algorithm. Because of the ability of EWMA control scheme for detecting small changes, this technique is appropriate to improve the detection of a small fault in PCA model. The performance of the PCA-based EWMA fault detection algorithm is illustrated and compared to conventional fault detection methods using simulated continuously stirred tank reactor (CSTR) data. The results show the effectiveness of the developed algorithm.

Control chart is one of tools for quality control of production. control chart is one of tool that can be used to control the quality of production for variable data such as weight of product. However, there is a weakness of control chart, which is sensitivless in detecting small shift of the mean process. Exponentially Weighted Moving Average (EWMA) control chart is one of the quality control tool that can improve the weakness of control chart. EWMA control chart has a weight smoothing parameter (λ) which makes EWMA control chart more sensitive in detecting small shifts the process mean. Each production data will be weighted and past production data will be affected by present production data. EWMA control chart will be used to make a control chart by weight of cigarette data in Brak Megawon III PT Djarum Kudus. In this study, will be established to assist in the GUI Matlab computational EWMA methods chart controller to control the quality of production at PT Djarum Kudus.In this study showed that the most optimum weight refiner which is at a value of 0.6. Keyword : EWMA, Smoothing weight (λ), GUI, Weight of cigarette

A data-based technique for monitoring of wound rotor induction machines: A simulation study

In this paper we investigate control charts for monitoring a process to detect changes in the mean and/or variance of a normal quality variable when an individual observation is taken at each sampling point. The traditional X chart and moving range (MR) chart are evaluated. Also evaluated are the exponentially weighted moving average (EWMA) chart of the observations and the EWMA chart of the squared deviations of the observations from the target. It is shown that the combination of the X and MR charts will not detect small and moderate parameter shifts as fast as combinations involving the EWMA charts. The ability of charts to diagnose the type of parameter shift produced by a special cause is also investigated. It is shown that combinations involving the EWMA charts are just as effective at diagnosing the type of parameter shift as the traditional combination of the X and MR charts. The effect of adding the variable sampling interval (VSI) feature is also evaluated for some of the combinations of charts. The VSI feature allows the sampling interval to be varied as a function of the values of the statistics being plotted. It is shown that adding the VSI feature to the combinations of charts results in very substantial reductions in the expected time required to detect shifts in process parameters.

Statistical process control provides package of statistical tools applied for improving quality of manufacturing, production and services processes. Cumulative sum, exponentially weighted moving average (EWMA) and progressive mean charts belong to family of memory-type charts which effectively spot small and persistent shifts in the process parameter(s). EWMA chart requires normality and a proper choice of smoothing parameter to perform efficiently. Any deviation from these conditions affects its performance in terms of efficacy and robustness. For the said concerns, progressive exponentially weighted moving average (PEWMA) chart is developed to monitor the shifts in the process location. The performance of the proposed PEWMA chart is evaluated in terms of average run length and some other metrics of run length distribution. The assessment of the proposed chart has been made under standard normal, Student’s t, gamma, Laplace, logistic, exponential, contaminated normal and lognormal distributions. The performance of the proposed PEWMA chart is also compared with some existing competitors including the classical EWMA, classical CUSUM, HWMA, MEC, MCE and DEWMA charts. The analysis reveals that the proposal offers a design structure which has high sensitivity to small and persistent drifts in the process mean and has advantage of robustness under non-normal scenarios. An application from substrates manufacturing process (in which flow width of the resist is the key quality characteristic) is also provided for practical implementations.

Exponentially weighted moving average (EWMA) control chart can be designed to quickly detect small shifts in the mean of a sequence of independent normal observations. But this chart cannot perform well for skewed distribution. The main goal of this article is to suggest an EWMA control chart method that can be used to monitoring small shifts in a skewed distribution. Weighted variance method is introduced to construct a kind of EWMA chart for skewed distribution and the optimization design of this chart is given by using average run length as a performance assessment criteria. Pair of asymmetry control limits could be evaluated by sample dates in skewed distribution. The advantage of this method in detecting little drift for skewed distribution was illustrated by comparing with others control charts.

Control charts applied to simulated sow herd datasets

It is known that both the optimal exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts are based on a given reference value $\delta$, which, for the CUSUM chart, is the magnitude of a shift in the mean to be detected quickly. In this paper a generalized EWMA control chart (GEWMA) which does not depend on $\delta$ is proposed for detecting the mean shift. We compare theoretically the GEWMA control chart with the optimal EWMA, CUSUM and the generalized likelihood ratio (GLR) control charts. The results of the comparison in which the in-control average run length approaches infinity show that the GEWMA control chart is better than the optimal EWMA control chart in detecting a mean shift of any size and is also better than the CUSUM control chart in detecting the mean shift which is not in the interval $(0.7842\delta ,1.3798\delta )$. Moreover, the GLR control chart has the best performance in detecting mean shift among the four control charts except when detecting a particular mean shift $\delta,$ when the in-control average run length approaches infinity.

This paper proposes a new double sampling scheme for c control chart (DS-c), which was designed to improve the performance of c chart or to reduce the inspection cost. The mathematical expression required to do an exact evaluation of ARL and ASN is deduced. Further, a bi-objective genetic algorithm is implemented to obtain the optimal design of the DS-c scheme. This optimisation is aimed to simultaneously minimising the error probability type II and the ASN, guaranteeing a desired level for the error probability type I. A performance comparison between the double sampling (DS), fixed parameters (FP), variable simple size (VSS) and exponential weighted moving average (EWMA) schemes for the c chart is carried out. The comparison shows that with the implementation of DS-c scheme is obtained a significant reduction of the out of control ARL with a lower ASN respect to FP and a better ARL profile than VSS and EWMA. [Received: 4 February 2018; Accepted: 1 February 2019]

ABSTRACTIn this article, we study exponentially weighted moving average (EWMA) control schemes to monitor the multivariate Poisson distribution with a general covariance structure, so that the practitioner can simultaneously monitor multiple correlated attribute processes more effectively. The statistical performance of the charts is assessed in terms of the run length properties and compared against other mainstream attribute control schemes. The application of the proposed methods to real-life and simulated datasets is demonstrated.

Statistical process control (SPC) is the method that monitors process quality characteristics. Through control charts, one can detect whether the present process malfunction. However, some annoyances may arise while the engineers need to choose appropriately control chart under different levels of process variation. The Shewhart, cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts have been widely used for monitoring semiconductor manufacturing processes. Generally weighted moving average (GWMA) control chart is a new method of SPC, which was proposed by Sheu and Lin (2003). The main objective of this research is using step-by-step procedures to present a comparative study of the monitoring performance for Shewhart, CUSUM, EWMA and GWMA control charts. According to a specified in-control average run length (ARL), we determine the parameters of each control chart based on the Monte Carlo numerical simulation. The setting parameters in each control chart sre displayed and tabulated. While the process means or the process standard deviations are changing in different levels, the performance of each weighted control chart can be then compared by using the ARL. A rule of thumb for selecting better control schemes is provided as a truthfully reference to help engineers in choosing the more appropriate control charts immediately when the assignable causes occurred.