Adapting EWMA Control Charts for Batch-Correlated Data

Batch production is common in the chemical and process industries. This article demonstrates how EWMA charts should be modified to account for substantial batch-to-batch variation. A batch-correlation model is considered, and methods of estimation and hypothesis testing for the batch-correlation coefficient are developed. This discussion is most appealing for production processes in which items are processed in batches but are related within batch.     

Effective Control Charts for Monitoring the NGINAR(1) Process

In recent years, there has been a growing interest in the control of autocorrelated count data. Existing results focus on the Poisson integer‐valued autoregressive (INAR) process, but this process cannot deal with overdispersion (variance is greater than mean), which is a common phenomenon in count data. We propose to control the autocorrelated count data based on a new geometric INAR (NGINAR) process, which is an alternative to the Poisson one. In this paper, we use the combined jumps chart, the cumulative sum chart, and the combined exponentially weighted moving average chart to detect the shift of parameters in the process. We compare the performance of these charts for the case of an underlying NGINAR(1) process in terms of the average run lengths. One real example is presented to demonstrate good performances of the charts. Copyright © 2015 John Wiley & Sons, Ltd.     

Statistical Performance of a Control Chart for Individual Observations Monitoring the Ratio of Two Normal Variables

Statistical Process Control monitoring of the ratio Z of two normal variables X and Y has received too little attention in quality control literature. Several applications dealing with monitoring the ratio Z can be found in the industrial sector, when quality control of products consisting of several raw materials calls for monitoring their proportions (ratios) within a product. Tables about the statistical performance of these charts are still not available. This paper investigates the statistical performance of a Phase II Shewhart control chart monitoring the ratio of two normal variables in the case of individual observations. The obtained results show that the performance of the proposed chart is a function of the distribution parameters of the two normal variables. In particular, the Shewhart chart monitoring the ratio Z outperforms the (p = 2) multivariate T² control chart when a process shift affects the in‐control mean of X or, alternatively, of Y and the correlation among X and Y is high and when the in‐control means of X and Y shift contemporarily to opposite directions. The sensitivity of the proposed chart to a shift of the in‐control dispersion has been investigated, too. We also show that the standardization of the two variables before computing their ratio is not a good practice due to a significant loss in the chart's statistical performance. An illustrative example from the food industry details the implementation of the ratio control chart. Copyright © 2013 John Wiley & Sons, Ltd.     

A Synthetic Control Chart for Monitoring the Ratio of Two Normal Variables

Very recently, monitoring the ratio of two normal random variables by means of control charts has been investigated in statistical process control literature. The industrial implementation of these control charts involves monitoring of processes where the correct proportion of two ingredients or elements within a product should be maintained under statistical control, monitoring of quality characteristics measuring the performance of a product as the ratio before and after some specific operation, for example, a chemical reaction following the introduction of an additive in a product, and monitoring of a chemical or physical property of a product, which is itself defined and computed as a ratio. This paper presents a Phase II synthetic control chart with each subgroup consisting of n > 1 sample units. Several tables are generated and commented to show the statistical performance of the investigated chart for known and random shift sizes affecting the in‐control ratio. A performance comparison with another control chart already proposed in literature shows the advantages associated to the implementation of the synthetic control chart. An illustrative example from the food industry is given for illustration. Copyright © 2015 John Wiley & Sons, Ltd.     

New Synthetic EWMA and Synthetic CUSUM Control Charts for Monitoring the Process Mean

Exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts are potentially powerful statistical process monitoring tools because of their excellent speed in detecting small to moderate persistent process shifts. Recently, synthetic EWMA (SynEWMA) and synthetic CUSUM (SynCUSUM) control charts have been proposed based on simple random sampling (SRS) by integrating the EWMA and CUSUM control charts with the conforming run length control chart, respectively. These synthetic control charts provide overall superior detection over a range of mean shift sizes. In this article, we propose new SynEWMA and SynCUSUM control charts based on ranked set sampling (RSS) and median RSS (MRSS) schemes, named SynEWMA‐RSS and SynEWMA‐MRSS charts, respectively, for monitoring the process mean. Extensive Monte Carlo simulations are used to estimate the run length characteristics of the proposed control charts. The run length performances of these control charts are compared with their existing powerful counterparts based on SRS, RSS and MRSS schemes. It turns out that the proposed charts perform uniformly better than the Shewhart, optimal synthetic, optimal EWMA, optimal CUSUM, near‐optimal SynEWMA, near‐optimal SynCUSUM control charts based on SRS, and combined Shewhart‐EWMA control charts based on RSS and MRSS schemes. A similar trend is observed when constructing the proposed control charts based on imperfect RSS schemes. An application to a real data is also provided to demonstrate the implementations of the proposed SynEWMA and SynCUSUM control charts. Copyright © 2014 John Wiley & Sons, Ltd.     

Monitoring the ratio of two normal variables using variable sampling interval exponentially weighted moving average control charts

We investigate in this paper a new type of control chart called VSI EWMA‐RZ by integrating the variable sampling interval feature (VSI) with the exponentially weighted moving average (EWMA) scheme to monitor the ratio of two normal random variables. Because the distribution of the ratio is skewed, we suggest designing two separated one‐sided charts instead of one two‐sided chart. A new coefficient is introduced allowing us to be free to choose a sampling interval provided that it optimizes the performance of the control chart. We also make a direct comparison between the VSI EWMA‐RZ charts and standard EWMA‐RZ control charts. The numerical simulations show that the proposed charts outperform the standard EWMA charts in detecting process shifts. An application is illustrated for the implementation of the VSI EWMA‐RZ control charts in the food industry.     

Design of a Control Chart Using a Modified EWMA Statistic

In this paper, the design of a control chart is given using a modified exponentially weighted moving average statistic under the assumption that the quality characteristic of interest follows the normal distribution. The structure of the proposed control chart is developed, and the necessary measures are derived to find the average run length for in‐control and out‐of‐control processes. The efficiency of the proposed chart is compared with two existing control charts in terms of the average run length. The results are explained with the help of industrial example. Copyright © 2016 John Wiley & Sons, Ltd.     

Using Coupled EWMA Control Charts for Monitoring Processes with Linear Trends

The equations governing the construction of control charts for monitoring both the mean and the process variability of a process whose quality characteristic is subjected to a linear trend are presented. The Holt model for forecasting linear trends and a simple exponentially weighted moving average for monitoring process variability are combined to form a coupled system of nonlinear difference equations. The moments of the stationary solutions which lead to the computation of the control limits are presented. A table containing control chart constants is given for both consecutive and nonconsecutive observations of the process.     

New Synthetic CUSUM and Synthetic EWMA Control Charts for Monitoring the Process Mean using Auxiliary Information

The cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts are potentially powerful process monitoring tool because of their excellent speed in detecting small to moderate shifts in the process parameters. These control charts can be further improved by integrating them with the conforming run length control chart, resulting in the synthetic CUSUM (SynCUSUM) and synthetic EWMA (SynEWMA) charts. In this paper, we enhance the detection abilities of the SynCUSUM and SynEWMA charts using the auxiliary information. With suitable assumptions, the proposed control charts encompass the existing SynCUSUM, SynEWMA, CUSUM, and EWMA charts. Extensive Monte Carlo simulations are used to study the run length profiles of the proposed control charts. It turns out that the proposed near‐optimal control charts with the auxiliary information perform uniformly and substantially better than the existing near‐optimal SynCUSUM, SynEWMA, CUSUM, and EWMA charts. The proposed and existing control charts are also illustrated with the help of an example. Copyright © 2017 John Wiley & Sons, Ltd.     

Optimal one- and two-sided adaptive EWMA scheme for monitoring Poisson count data

The Poisson distribution assumption often arises in several industrial applications for modeling defects or nonconformities. In this work, we investigate the one- and two-sided performance of a new adaptive EWMA (exponentially weighted moving average)-type chart for monitoring Poisson count data. An appropriate discrete-state Markov chain technique is provided to compute the exact ARL (average run length) properties. Moreover, comparative studies are conducted to demonstrate the higher sensitivity of the proposed chart in the detection of shifts with various magnitudes. Advices on how to select the appropriate chart parameters are provided and an illustrative numerical example is proposed.     

CUSUM and EWMA Control Charts for Negative Binomial Distribution

In public health surveillance, control charts based on the daily number of hospitalizations may be monitored to detect outbreaks and/or to plan the offer of health assistance. A generalized linear model with negative binomial distribution is proposed to the number of hospitalizations, and it depends on the exposed population and covariates, as the day of week and sines and cosines to describe the seasonality. The objective of this study is to compare (in terms of ARL₁) the exponentially weighted moving average and the cumulative sum control charts for monitoring daily counts based on simulations of the daily number of hospitalizations due to respiratory diseases for people over 65 years old in São Paulo city (Brazil). Copyright © 2016 John Wiley & Sons, Ltd.     

EWMA and DEWMA Control Charts for Poisson‐Exponential Distribution: Conditional Median Approach for Censored Data

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.     

Enhancing the Performance of Combined Shewhart‐EWMA Charts

The combination of Shewhart control charts and an exponentially weighted moving average (EWMA) control charts to simultaneously monitor shifts in the mean output of a production process has proven very effective in handling both small and large shifts. To improve the sensitivity of the control chart to detect off‐target processes, we propose a combined Shewhart‐EWMA (CSEWMA) control chart for monitoring mean output using a more structured sampling technique, i.e. ranked set sampling (RSS) instead of the traditional simple random sampling. We evaluated the performance of the proposed charts in terms of different run length (RL) properties including average RL, standard deviation of the RL, and percentile of the RL. Comparisons of these charts with some existing control charts designed for monitoring small, large, or both shifts revealed that the RSS‐based CSEWMA charts are more sensitive and offer better protection against all types of shifts than other schemes considered in this study. Copyright © 2012 John Wiley & Sons, Ltd.     

Control Charts for Binary Correlated Variables

To monitor the nonconforming fraction of a production process, usually np or p control charts are used for this purpose. However, in many practical situations, the binary variables are correlated but not easily perceived by practitioners. The aim of this article is to present the maximum likelihood and method of moment estimators of the correlation parameter ρ of an overdispersed binomial distribution. Inferential procedure is also introduced to test the null hypothesis H₀: ρ = 0 x H₁: ρ > 0. A Shewhart‐type control chart np_ρ and an Exponentiated Weighted Moving Average (EWMA)‐type control chart (EWMA np_ρ) are proposed to evaluate the nonconforming fraction when the binary variables are correlated. The traditional np chart is a particular case of the np_ρ control chart when ρ = 0. The misuse of control limits of np control in case of correlated binary variables will result a large number of false alarms. To have the same performance (in terms of average run length) of the traditional np control chart, the np_ρ control chart needs at least to double the sample size. Numerical example illustrates the proposal. Copyright © 2012 John Wiley & Sons, Ltd.     

Monitoring Weibull Quantiles by EWMA Charts Based on a Pivotal Quantity Conditioned on Ancillary Statistics

In this article, we study exponentially weighted moving average (EWMA) charts for monitoring Weibull quantiles (percentiles) based on a monitoring statistic conditioned on ancillary statistics when samples may be Type II censored. The monitoring statistic has a distribution form that is intractable, but analytic forms of the density and distribution functions can be derived when it is conditioned on ancillary statistics. We use these results to develop EWMA control charts and, in certain cases, evaluate their average run length without resorting to simulations. We compare the average run length performance of the EWMA charts with those of probability‐limit charts, studied by the authors, and probability‐limit charts enhanced with Western Electric alarm rules. We apply the charts to the breaking strength of carbon fibers to detect shifts in a specific Weibull quantile. Copyright © 2016 John Wiley & Sons, Ltd.     

A New S2‐EWMA Control Chart for Monitoring the Process Variance

This article demonstrates how a three‐parameter logarithmic transformation combined with an exponentially weighted moving average (EWMA) approach can be used to monitor the sample variance of a process. The computation of the parameters of the logarithmic transformation and the control limits are explained. An easy‐to‐use table is provided and an illustrative example is given. The performance of the logarithmic transformation is evaluated under the assumption of normality. An optimal design strategy based on the ARL is presented and comparisons with other procedures are performed. Copyright © 2005 John Wiley & Sons, Ltd.     

Linking EWMA p Charts and the Risk Adjustment Control Charts

This paper develops an adaptive exponentially weighted moving average (EWMA) chart that can be used as either a p chart for monitoring significant departures from in‐control non‐homogenous probabilities of failure or success or a risk‐adjusted control chart for success or failure of an event. An example of a risk adjustment process is monitoring the performance of a particular surgery over time where we need to adjust for the temporal changes in patient case mix. If the magnitude of this shift is known in advance, as would be the case in some hypothesis testing applications, then the paper offers a way of selecting the appropriate exponential weights to be efficient at detecting such a variable shift. The adaptive EWMA p chart is tested using extensive simulations. Processes for its efficient design are offered. The example application offers practitioners a means of evaluating a trial in real time rather than the traditional approach of evaluating the trial at the end of the study period. This is helpful in deciding how long the trial should run as well as potentially adapting the design over time as more is understood about the trial uncertainties. This may be particularly useful in evaluating expensive trials. Copyright © 2016 John Wiley & Sons, Ltd.     

EWMA Dispersion Control Charts for Normal and Non‐normal Processes

Process monitoring through control charts is a quite popular practice in statistical process control. This study is planned for monitoring the process dispersion parameter using exponentially weighted moving average (EWMA) control chart scheme. Most of the EWMA dispersion charts that have been proposed are based on the assumption that the parent distribution of the quality characteristic is normal, which is not always the case. In this study, we develop new EWMA charts based on a wide range of dispersion estimates for processes following normal and non‐normal parent distributions. The performance of all the charts is evaluated and compared using run length characteristics (such as the average run length). Extra quadratic loss, relative average run length, and performance comparison index measures are also used to examine the overall effectiveness of the EWMA dispersion charts.Copyright © 2014 John Wiley & Sons, Ltd.     

An EWMA signed ranks control chart with reliable run length performances

During the design phase of a control chart, the determination of its exact run length properties plays a vital role for its optimal operation. Markov chain or integral equation methods have been extensively applied in the design phase of conventional control charts. However, for distribution-free schemes, due to the discrete nature of the statistics being used (such as the sign or the Wilcoxon signed rank statistics, for instance), it is impossible to accurately compute their run length properties. In this work, a modified distribution-free phase II exponentially weighted moving average (EWMA)-type chart based on the Wilcoxon signed rank statistic is considered and its exact run length properties are discussed. A continuous transformation of the Wilcoxon signed rank statistic, combined with the classical Markov chain method, is used for the determination of the average run length in the in- and out-of control cases. Moreover, its exact performance is derived without any knowledge of the distribution of sample observations. Finally, an illustrative example is provided showing the practical implementation of our proposed chart.