Enhanced EWMA charts for monitoring the process coefficient of variation

The coefficient of variation (CV) is an important quality characteristic when the process variance is a function of the process mean for a production process. In this paper, we develop an auxiliary information–based (AIB) estimator for estimating the squared CV, along with its approximated mean and variance. This estimator is then used to devise new one-sided EWMA charts for monitoring the increases or decreases in the squared CV of a normal process, named the AIB-EWMA CV charts. In addition, the sensitivities of these control charts are also enhanced with the fast initial response feature. The Monte Carlo simulation method is used to compute the run length characteristics of the proposed CV charts. Based on detailed run length comparisons, it is found that the proposed AIB-EWMA CV charts are uniformly and substantially better than the existing EWMA CV charts when detecting different kinds of upward/downward shifts in the squared CV. The proposed charts are also applied to a real dataset to support the proposed theory.     

A side-sensitive synthetic coefficient of variation chart

Control charts for monitoring the coefficient of variation (γ) are useful for processes with an inconsistent mean (μ) and a standard deviation (σ) which changes with μ, by monitoring the consistency in the ratio σ over μ. The synthetic-γ chart is one of the charts proposed to monitor γ, and its attractiveness lie in waiting until a second point to fall outside the control limits before a decision is made. However, existing synthetic-γ charts do not differentiate between the points falling outside the upper control limit (UCL) and lower control limit (LCL). Hence, this paper proposes a side-sensitive synthetic-γ chart, where successive nonconforming samples must either fall above the UCL or below the LCL. Formulae to compute the average run length (ARL), the standard deviation of the run length (SDRL) and expected average run length (EARL) are derived using the Markov chain approach, and the algorithms to obtain the optimal charting parameters are proposed. Subsequently, the optimal charting parameters, ARL, SDRL and EARL values for various numerical examples are shown. Comparisons show that the side-sensitive synthetic-γ chart consistently outperforms the existing synthetic-γ chart, especially for small shifts. The proposed chart also consistently outperforms the Shewhart-γ chart, while showing comparable or better performance than the Exponentially Weighted Moving Average (EWMA) chart for most shift sizes, except for very small shifts. Finally, this paper shows the implementation of the proposed chart on an industrial example.     

On developing sensitive nonparametric mixed control charts with application to manufacturing industry

Control charts are designed under the normality assumption of the quality characteristic of the process. However, the normality assumption rarely holds in practice. In non-normal conditions, parametric charts tend to display more false alarm rates and invalid out-of-control comparisons. The exponentially weighted moving average chart is a frequently used memory-type control chart for monitoring the process target that only performs effectively under the smoothing parameter's small choices. This study proposes a nonparametric mixed exponentially weighted moving average-progressive mean chart based on sign statistic (NPMEP_SN) under simple and ranked set sampling schemes to address this said drawback. Normal and non-normal distributions are included in this study to observe the proposed chart's in-control behavior and out-of-control efficacy. The prominent feature of the proposed schemes is that it works efficiently in detecting small and persistent shifts in the process location corresponding to the given values of the smoothing parameter. The proposed scheme is also tested under the ranked set sampling scheme to enhance the NPMEP_SN chart's performance (hereafter named “NPMEP_RSN”). The performance of the proposed charts is investigated through simulations using run-length profiles. The proposed schemes were seen to outperform other alternatives, specifically under the ranked set sampling scheme. A real data-set related to the diameter of a piston ring is included as a demonstration of the proposal.     

A control chart for monitoring the lognormal process variation using repetitive sampling

Control charts are developed to make the specific quality measures for a successful production process and follow normal distribution behaviors. But some real-life practices do not match such practices and exhibit some positively skewed behavior like lognormal distribution. The present study has considered this situation and proposed a monitoring control chart based on lognormal process variation using a repetitive sampling scheme. This concept proved better for detecting shifts as quickly as possible, and compared with the existing concept, results are elaborated through extensive tables. The average run lengths and standard deviations of the run lengths are being used as a performance evaluation measures and computed by using Monte Carlo simulations performed in R language. A real-life situation has been discussed in the example section to strengthen the proposed control chart concept in a real-life situation.     

Enhancing the performance of the EWMA control chart for monitoring the process mean using auxiliary information

When using control charts to monitor manufacturing processes, the exponentially weighted moving average (EWMA) control chart is useful for detecting persistent shifts in the process parameter. This paper proposes enhancements to the applications of the EWMA control chart for those scenarios where the exact measurement of process units is difficult and expensive, but the visual ordering of the units can be done easily. The proposed charts use an auxiliary variable that is correlated with the process variable to provide efficient monitoring of shifts in the process mean and are formulated based on ranked set sampling (RSS) and median RSS schemes (MRSS). Simulation results showed that the proposed charting schemes are more efficient in detecting a shift in the process mean than the classical EWMA control chart and its modification. An example is provided to show the application of the proposed charts using a simulated benchmark process: the continuous stirred tank reactor (CSTR).     

Efficient homogeneously weighted dispersion control charts with an application to distillation process

Monitoring disturbances in process dispersion using control chart is mostly based on the assumption that the quality characteristic follows normal distribution, which is not the case in many real-life situations. This paper proposes a set of new dispersion charts based on the homogeneously weighted moving average (HWMA) scheme, for efficient detection of shifts in process standard deviation (σ). These charts are based on a variety of σ estimators and are investigated for normal as well as heavy tailed symmetric and skewed distributions. The shift detection ability of the charts is evaluated using different run length characteristics, such as average run length (ARL), extra quadratic loss (EQL), and relative ARL measures. The performance of the proposed HWMA control charts is also compared with the existing EWMA dispersion charts, using different design parameters. Furthermore, an illustrative example is presented to monitor the vapor pressure in a distillation process.     

Percentile‐based control chart design with an application to Shewhart X̅ and S2 control charts

We present a method to design control charts such that in‐control and out‐of‐control run lengths are guaranteed with prespecified probabilities. We call this method the percentile‐based approach to control chart design. This method is an improvement over the classical and popular statistical design approach employing constraints on in‐control and out‐of‐control average run lengths since we can ensure with prespecified probability that the actual in‐control run length exceeds a desired magnitude. Similarly, we can ensure that the out‐of‐control run length is less than a desired magnitude with prespecified probability. Some numerical examples illustrate the efficacy of this design method.     

New Synthetic Control Charts for Monitoring Process Mean and Process Dispersion

A statistical quality control chart is widely recognized as a potentially powerful tool that is frequently used in many manufacturing and service industries to monitor the quality of the product or manufacturing processes. In this paper, we propose new synthetic control charts for monitoring the process mean and the process dispersion. The proposed synthetic charts are based on ranked set sampling (RSS), median RSS (MRSS), and ordered RSS (ORSS) schemes, named synthetic‐RSS, synthetic‐MRSS, and synthetic‐ORSS charts, respectively. Average run lengths are used to evaluate the performances of the control charts. It is found that the synthetic‐RSS and synthetic‐MRSS mean charts perform uniformly better than the Shewhart mean chart based on simple random sampling (Shewhart‐SRS), synthetic‐SRS, double sampling‐SRS, Shewhart‐RSS, and Shewhart‐MRSS mean charts. The proposed synthetic charts generally outperform the exponentially weighted moving average (EWMA) chart based on SRS in the detection of large mean shifts. We also compare the performance of the synthetic‐ORSS dispersion chart with the existing powerful dispersion charts. It turns out that the synthetic‐ORSS chart also performs uniformly better than the Shewhart‐R, Shewhart‐S, synthetic‐R, synthetic‐S, synthetic‐D, cumulative sum (CUSUM) ln S², CUSUM‐R, CUSUM‐S, EWMA‐ln S², and change point CUSUM charts for detecting increases in the process dispersion. A similar trend is observed when the proposed synthetic charts are constructed under imperfect RSS schemes. Illustrative examples are used to demonstrate the implementation of the proposed synthetic charts. Copyright © 2014 John Wiley & Sons, Ltd.     

A New Synthetic Exponentially Weighted Moving Average Control Chart for Monitoring Process Dispersion

Exponentially weighted moving average (EWMA) control charts have been widely recognized as a potentially powerful process monitoring tool of the statistical process control because of their excellent speed in detecting small to moderate shifts in the process parameters. Recently, new EWMA and synthetic control charts have been proposed based on the best linear unbiased estimator of the scale parameter using ordered ranked set sampling (ORSS) scheme, named EWMA‐ORSS and synthetic‐ORSS charts, respectively. In this paper, we extend the work and propose a new synthetic EWMA (SynEWMA) control chart for monitoring the process dispersion using ORSS, named SynEWMA‐ORSS chart. The SynEWMA‐ORSS chart is an integration of the EWMA‐ORSS chart and the conforming run length chart. Extensive Monte Carlo simulations are used to estimate the run length performances of the proposed control chart. A comprehensive comparison of the run length performances of the proposed and the existing powerful control charts reveals that the SynEWMA‐ORSS chart outperforms the synthetic‐R, synthetic‐S, synthetic‐D, synthetic‐ORSS, CUSUM‐R, CUSUM‐S, CUSUM‐ln S², EWMA‐ln S² and EWMA‐ORSS charts when detecting small shifts in the process dispersion. A similar trend is observed when the proposed control chart is constructed under imperfect rankings. An application to a real data is also provided to demonstrate the implementation and application of the proposed control chart. Copyright © 2014 John Wiley & Sons, Ltd.     

Control chart for monitoring the coefficient of variation with an exponentially weighted moving average procedure

The coefficient of variation (CV) of a population is defined as the ratio of the population standard deviation to the population mean, which can be regarded as a measure of stability or uncertainty and can also indicate the relative dispersion of data to the population mean. This paper proposes a new exponentially weighted moving average chart for monitoring CV, which is constructed by truncating those negative normalized observations to 0 in the traditional exponentially weighted moving average CV statistics. The implementation and optimization procedures of the proposed chart are presented. The new chart is compared with some existing CV charts by means of average run length, and the comparison results show that the new chart outperforms other charts in most cases. Two examples illustrate the use of this chart on real data gathered from a metal sintering process and from a die casting hot chamber process.     

Increasing the Sensitivity of Cumulative Sum Charts for Location

The cumulative sum (CUSUM) chart is a very effective control charting procedure used for the quick detection of small‐sized and moderate‐sized changes. It can detect small process shifts missed by the Shewhart‐type control chart, which is sensitive mainly to large shifts. To further enhance the sensitivity of the CUSUM control chart at detecting very small process disturbances, this article presents CUSUM control charts based on well‐structured sampling procedures, double ranked set sampling, median‐double ranked set sampling, and double‐median ranked set sampling. These sampling techniques significantly improve the overall performance of the CUSUM chart over the entire process mean shift range, without increasing the false alarm rate. The newly developed control schemes do not only dominate most of the existing charts but are also easy to design and implement as illustrated through an application example of real datasets. The control schemes used for comparison in this study include the conventional CUSUM chart, a fast initial response CUSUM chart, a 2‐CUSUM chart, a 3‐CUSUM chart, a runs rules‐based CUSUM chart, the enhanced adaptive CUSUM chart, the CUSUM chart based on ranked set sampling (RSS), and the single CUSUM and combined Shewhart–CUSUM charts based on median RSS. Copyright © 2014 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.     

An Efficient Nonparametric EWMA Wilcoxon Signed‐Rank Chart for Monitoring Location

The statistical performance of traditional control charts for monitoring the process shifts is doubtful if the underlying process will not follow a normal distribution. So, in this situation, the use of a nonparametric control charts is considered to be an efficient alternative. In this paper, a nonparametric exponentially weighted moving average (EWMA) control chart is developed based on Wilcoxon signed‐rank statistic using ranked set sampling. The average run length and some other associated characteristics were used as the performance evaluation of the proposed chart. A major advantage of the proposed nonparametric EWMA signed‐rank chart is the robustness of its in‐control run length distribution. Moreover, it has been observed that the proposed version of the EWMA signed‐rank chart using ranked set sampling shows better detection ability than some of the competing counterparts including EWMA sign chart, EWMA signed‐rank chart, and the usual EWMA control chart using simple random sampling scheme. An illustrative example is also provided for practical consideration. Copyright © 2016 John Wiley & Sons, Ltd.     

New CUSUM and Shewhart-CUSUM charts for monitoring the process mean

The CUmulative SUM (CUSUM) charts have sensitive nature against small and moderate shifts that occur in the process parameter(s). In this article, we propose the CUSUM and combined Shewhart-CUSUM charts for monitoring the process mean using the best linear unbiased estimator of the location parameter based on ordered double-ranked set sampling (RSS) scheme, where the CUSUM chart refers to the Crosier's CUSUM chart. The run-length characteristics of the proposed CUSUM charts are computed with the Monte Carlo simulations. The run-length profiles of the proposed CUSUM charts are compared with those of the CUSUM charts based on simple random sampling, RSS, and ordered RSS schemes. It is found that the proposed CUSUM charts uniformly outperform their existing counterparts when detecting all different kinds of shifts in the process mean. A real data set is also considered to explain the implementation of the proposed CUSUM charts.     

A mixed HWMA-CUSUM mean chart with an application to manufacturing process

Memory-type control charts play a significant role to identify slight changes in the parameters of the production process. In this article, we have proposed a new cumulative sum chart that utilizes the statistic of the homogeneously weighted moving average chart. The performance of the proposed chart is studied using Monte Carlo simulations. The proposed chart is compared with some existing charts under different run length profiles. The run length profile comparisons reveal that the proposed chart performs superior as compared to the existing control charts. A real-life application using a manufacturing process dataset is also part of this study.     

Auxiliary information-based maximum generally weighted moving average chart for simultaneously monitoring process mean and variability

An auxiliary information-based (AIB) maximum exponentially weighted moving average (MaxEWMA) chart has been proposed to simultaneously monitor both increases and decreases in the process mean and/or variability, called the AIB-MaxEWMA chart, which is superior to the existing MaxEWMA chart. In this paper, we propose the AIB maximum generally weighted moving average chart, called the AIB-MaxGWMA chart, to further enhance the sensitivity of the AIB-MaxEWMA chart. Numerical simulation studies indicate that the AIB-MaxGWMA chart is sensitive to small shifts in the process mean and/or variability. The performance of the AIB-MaxGWMA chart based on average run lengths (ARLs) also outperforms than its counterparts including AIB-MaxEWMA, MaxGWMA and MaxEWMA charts. An example is used to illustrate the efficiency of the proposed AIB-MaxGWMA chart in detecting small process shifts.     

Combined Application of Shewhart and Cumulative Sum R Chart for Monitoring Process Dispersion

This study analyzes the performance of combined applications of the Shewhart and cumulative sum (CUSUM) range R chart and proposes modifications based on well‐structured sampling techniques, the extreme variations of ranked set sampling, for efficient monitoring of changes in the process dispersion. In this combined scheme, the Shewhart feature enables quick detection of large shifts from the target standard deviation while the CUSUM feature takes care of small to moderate shifts from the target value. We evaluate the numerical performance of the proposed scheme in terms of the average run length, standard deviation of run length, the average ratio average run length, and average extra quadratic loss. The results show that the combined scheme can detect changes in the process that were small or large enough to escape detection by the lone Shewhart R chart or CUSUM R chart, respectively. We present a comparison of the proposed schemes with several dispersion charts for monitoring changes in process variability. The practical application of the proposed scheme is demonstrated using real industrial data. Copyright © 2014 John Wiley & Sons, Ltd.     

A new adaptive EWMA control chart for monitoring the process dispersion

The exponentially weighted moving average (EWMA), cumulative sum (CUSUM), and adaptive EWMA (AEWMA) control charts have had wide popularity because of their excellent speed in tracking infrequent process shifts, which are expected to lie within certain ranges. In this paper, we propose a new AEWMA dispersion chart that may achieve better performance over a range of dispersion shifts. The idea is to first consider an unbiased estimator of the dispersion shift using the EWMA statistic, and then based on the magnitude of this shift, select an appropriate value of the smoothing parameter to design an EWMA chart, named the AEWMA chart. The run length characteristics of the AEWMA chart are computed with the help of extensive Monte Carlo simulations. The AEWMA chart is compared with some of the existing powerful competitor control charts. It turns out that the AEWMA chart performs substantially and uniformly better than the EWMA‐S², CUSUM‐S², existing AEWMA, and HHW‐EWMA charts when detecting different kinds of shifts in the process dispersion. Moreover, an example is also used to explain the working and implementation of the proposed AEWMA chart.     

An efficient adaptive EWMA control chart for monitoring the process mean

In recent years, the memory‐type control charts—exponentially weighted moving average (EWMA) and cumulative sum (CUSUM)—along with the adaptive and dual control‐charting structures have received considerable attention because of their excellent ability in providing an overall good detection over a range of mean‐shift sizes. These adaptive memory‐type control charts include the adaptive exponentially weighted moving average (AEWMA), dual CUSUM, and adaptive CUSUM charts. In this paper, we propose a new AEWMA chart for efficiently monitoring the process mean. The idea is to first design an unbiased estimator of the mean shift using the EWMA statistic and then adaptively update the smoothing constant of the EWMA chart. The run length profiles of the proposed AEWMA chart are computed using extensive Monte Carlo simulations. Based on a comprehensive comparative study, it turns out that the proposed AEWMA chart performs better than the existing AEWMA, adaptive CUSUM, dual CUSUM, and Shewhart‐CUSUM charts, in terms of offering more balanced protection against mean shifts of different sizes. An example is also used to explain the working of the existing and proposed control charts.     

Improved CUSUM monitoring of Markov counting process with frequent zeros

There has been a growing interest in monitoring processes featuring serial dependence and zero inflation. The phenomenon of excessive zeros often occurs in count time series because of the advancement of quality in manufacturing process. In this study, we propose three control charts, such as the cumulative sum chart with delay rule (CUSUM‐DR), conforming run length (CRL)‐CUSUM chart, and combined Shewhart CRL‐CUSUM chart, to enhance the performance of monitoring Markov counting processes with excessive zeros. Numerical experiments are conducted based on integer‐valued autoregressive time series models, for example, zero‐inflated Poisson INAR and INARCH, to evaluate the performance of the proposed charts designed for the detection of mean increase. A real example is also illustrated to demonstrate the usability of our proposed charts.