Economic-Statistical Design of EWMA Control Charts Based on Taguchi's Loss Function

This paper proposes an economic-statistical design of the EWMA chart with time-varying control limits in which the Taguchi's quadratic loss function is incorporated into the economic-statistical design based on Lorenzen and Vance's economical model. A nonlinear programming with statistical performance constraints is developed and solved to minimize the expected total quality cost per unit time. This model, which is divided into three parts, depends on whether production continues during the period when the assignable cause is being searched for and/or repaired. Through a computational procedure, the optimal decision variables, including the sample size, the sampling interval, the control limit width, and the smoothing constant, can be solved for by each model. It is showed that the optimal economic-statistical design solution can be found from the set of optimal solutions obtained from the statistical design, and both the optimal sample size and sampling interval always decrease as the magnitude of shift increases.     

关于单变量统计过程控制图某些研究结果简介

文章仅对一元连续变量的静态与动态控制图研究现状进行了简单的总结和介绍,并给出了较详细的参考文献,希望为国内开展此方向的研究抛砖引玉。     

A control chart for COM-Poisson distribution using a modified EWMA statistic

In this paper, a control chart has been developed for the Conway–Maxwell Poisson (COM-Poisson) distribution using the modified exponentially weighted moving average statistic. The proposed chart provides an efficient detection of smaller changes in the location parameter of the COM-Poisson distribution. The performance of the proposed control chart has been evaluated by the average and the standard deviation of the run length distribution for various parameters. Better detecting ability has also been compared with the existing control chart using EWMA statistic. Using simulation, we also showed the detecting ability over the traditional EWMA chart.     

An Examination of the Robustness to Non Normality of the EWMA Control Charts for the Dispersion

ABSTRACT

The EWMA control chart is used to detect small shifts in a process. It has been shown that, for certain values of the smoothing parameter, the EWMA chart for the mean is robust to non normality. In this article, we examine the case of non normality in the EWMA charts for the dispersion. It is shown that we can have an EWMA chart for dispersion robust to non normality when non normality is not extreme.     

Multivariate EWMA Control Chart with Adaptive Sample Sizes

Standard multivariate control charts usually employ fixed sample sizes at equal sampling intervals to monitor a process. In this study, a multivariate exponential weighted moving average (MEWMA) chart with adaptive sample sizes is investigated. Performance measure of the adaptive-sample-size MEWMA chart is obtained through a Markov chain approach. The performance of the adaptive-sample-size MEWMA chart is compared with the fixed-sample-size control chart in terms of steady-state average run length for different magnitude of shifts in the process mean. It is shown that the adaptive-sample-size chart is more efficient than the fixed-sample-size MEWMA control chart in detecting shifts in the process mean.     

Conditional design of the EWMA median chart with estimated parameters

The exponentially weighted moving average (EWMA) chart is often designed assuming the process parameters are known. In practice, the parameters are rarely known and need to be estimated from Phase I samples. Different Phase I samples are used when practitioners construct their own control chart's limits, which leads to the “Phase I between-practitioners” variability in the in-control average run length (ARL) of control charts. The standard deviation of the ARL (SDARL) is a good alternative to quantify this variability in control charts. Based on the SDARL metric, the performance of the EWMA median chart with estimated parameters is investigated in this paper. Some recommendations are given based on the SDARL metric. The results show that the EWMA median chart requires a much larger amount of Phase I data in order to reduce the variation in the in-control ARL up to a reasonable level. Due to the limitation of the amount of the Phase I data, the suggested EWMA median chart is designed with the bootstrap method which provides a good balance between the in-control and out-of-control ARL values.     

EWMA Control Charts for Monitoring High Yield Processes

The main objective of this article is to scrutinize the efficiency and verify the performance superiority of the one-sided EWMA control chart on high-yield processes. The proposed control chart is designed to detect both upward and downward shifts of the fraction of non conforming products and is developed based on non transformed geometric counts. Its algorithmic function is theoretically established and numerous performance measures are extracted using analytical methods based on the Markov modeling of the chart. Comparisons with traditional high yield control charts are conducted. Optimality tables and nomograms are included to help graphical determination of the optimal chart parameters.     

Two parameter cuscore qualty control procedures

This paper is concerned with the problem of simultaneously monitoring the process mean and process variability of continuous production processes using combined Shewhart-cumulative score (cuscore) quality control procedures developed by Ncube and Woodall (1984). Two methods of approach are developed and their properties are investigated. One method uses two separate Shewhart-cuscore control charts, one for determining shifts in the process mean and the other for detecting shifts in process variability. The other method uses a single combined statistic which is sensitive to shifts in both the mean and the variance. Each procedure is compared to the corresponding Shewhart schemes. It will be shown by average run length calculations that the proposed Shewhart- cuscore schemes are considerably more efficient than the comparative Shewhart procedures for certain shifts in the process mean and process variability for the case when the underlying process control variable is assumed to be normally distributed.     

Multivariate Exponentially Weighted Moving Average Charts for a Mean Based on Its Prediction Distribution

This article develops a control chart for a mean vector when it is monitored by a quadratic form in the exponentially weighted observation vector. A Bayesian approach is used to incorporate parameter uncertainty. We first use a Bayesian predictive distribution to construct the control chart, and we then use a sampling theory approach to evaluate it under various hypothetical specifications for the data generation model.     

Evaluation of control charts under linear trend

The performance of several control charting schemes is studied when the process mean changes as a linear trend. The control charts considered include the Shewhart chart, the Shewhart chart supplemented with runs rules, the cumulative sum (CUSUM) chart, the exponentially weighted moving average (EWMA) chart, and a generalized control chart.     

A New Adaptive Variable Sample Size Approach in EWMA Control Chart

Adaptive control charts have been developed for improving the capability of control charts in detecting small shifts. In this article, we propose a new exponential weighted moving average control chart with variable sample size, in which the sample size is determined as an integer linear function by EWMA statistic value. The performance of the proposed VSS EWMA control chart is compared with FSS EWMA as well as traditional VSS EWMA control charts. The results show the better performance of the proposed VSS strategy respect to the traditional one and fixed sample size.     

A Sequential Rank-Based Nonparametric Adaptive EWMA Control Chart

Nonparametric control chart is useful when the underlying distribution is unknown, or is not likely to be normal. In this article, we provide a sequential rank-based nonparametric adaptive EWMA (NAE) control chart for detecting the persistent shift in the location parameter. This NAE chart is a self-starting scheme and thus can be used to monitor processes at the start-up stages rather than waiting for the accumulation of sufficiently large calibration samples. Moreover, we do not require any prior knowledge of the underlying distribution, and to prespecify any tuning parameter either. A Markov chain model is suggested to calibrate the run-length distribution of NAE, which is shown to have approximate tail probability as a geometric distribution. A simulation study demonstrates that the proposed control chart not only performs robustly for different distributions, but also is efficient in detecting various magnitude of shifts. A real-data example from manufacturing shows that it performs quite well in practical applications.     

A Design of s Control Charts with a Combined Double Sampling and Variable Sampling Interval Scheme

In this paper, we propose new estimation techniques in connection with the system of S-distributions. Besides “exact” maximum likelihood (ML), we propose simulated ML and a characteristic function-based procedure. The “exact” and simulated likelihoods can be used to provide numerical, MCMC-based Bayesian inferences.     

Grey Predictive Process Control Charts

The present article intends to develop some imputation methods to reduce the impact of non response at both the occasions in two-occasion successive (rotation) sampling. Utilizing the auxiliary information, which is only available at the current occasion, estimators have been proposed for estimating the population mean at the current occasion. Estimators for the current occasion are also derived as a particular case when there is non response either on the first occasion or second occasion. Behaviors of the proposed estimators are studied and their respective optimum replacement policies are also discussed. To study the effectiveness of the suggested imputation methods, performances of the proposed estimators are compared in two different situations, with and without non response. The results obtained are demonstrated with the help of empirical studies.     

The EWMA sign chart revisited: performance and alternatives without and with ties

The EWMA Sign control chart is an efficient tool for monitoring shifts in a process regardless the observations'' underlying distribution. Recent studies have shown that, for nonparametric control charts, due to the discrete nature of the statistics being used (such as the Sign statistic), it is impossible to accurately compute their Run Length properties using Markov chain or integral equation methods. In this work, a modified nonparametric Phase II EWMA chart based on the Sign statistic is proposed and its exact Run Length properties are discussed. A continuous transformation of the Sign statistic, combined with the classical Markov Chain method, is used for the determination of the chart''s in- and out-of-control Run Length properties. Additionally, we show that when ties occur due to measurement rounding-off errors, the EWMA Sign control chart is no longer distribution-free and a Bernoulli trial approach is discussed to handle the occurrence of ties and makes the proposed chart almost distribution-free. Finally, an illustrative example is provided to show the practical implementation of our proposed chart.     

Multivariate CUSUM and EWMA Control Charts for Skewed Populations Using Weighted Standard Deviations

This article proposes a heuristic method of constructing multivariate cumulative sum and exponentially weighted moving average control charts for skewed populations based on the weighted standard deviation method which adjusts the variance–covariance matrix of quality characteristics and approximates the probability density function using several multivariate normal distributions. These control charts, however, reduce to the conventional control charts when the underlying distribution is symmetric. In-control and out-of-control average run lengths of the proposed control charts are compared with those of the conventional control charts for multivariate lognormal and Weibull distributions. Simulation results show that considerable improvements over the standard method can be achieved when the underlying distribution is skewed.