A hybrid homogeneously weighted moving average control chart for process monitoring

Several modifications and enhancements to control charts in increasing the performance of small and moderate process shifts have been introduced in the quality control charting techniques. In this paper, a new hybrid control chart for monitoring process location is proposed by combining two homogeneously weighted moving average (HWMA) control charts. The hybrid homogeneously weighted moving average (HHWMA) statistic is derived using two smoothing constants λ₁ and λ₂ . The average run length (ARL) and the standard deviation of the run length (SDRL) values of the HHWMA control chart are obtained and compared with some existing control charts for monitoring small and moderate shifts in the process location. The results of study show that the HHWMA control chart outperforms the existing control charts in many situations. The application of the HHWMA chart is demonstrated using a simulated data.     

A sensitive non-parametric EWMA control chart

In practice, we may not always have normally distributed quality characteristics of interest. This leads to the need for non-parametric techniques which are not dependent on the assumptions about the parent distribution. This study develops a non-parametric exponentially weighted moving average (EWMA) chart (namely the NPSS_EWMA chart) for an improved monitoring of process location. The proposal is based on the use of sign statistics on a moving pattern in an EWMA setup. The design structure of the proposed chart is developed and its performance is evaluated in terms of different properties including average run length (ARL), standard deviation run length (SDRL), percentiles, relative ARL (RARL), extra quadratic loss (EQL), and performance comparison index (PCI). The proposal is compared with recently developed non-parametric counterparts namely NPS_EWMA, NPAS_EWMA, and NPS_CUSUM charts. It is observed that the design structure of the proposed NPSS_EWMA chart outshines the existing counterparts. An application example is also included in the study for practical demonstration.     

Economic and economic-statistical designs of the side sensitive group runs chart with auxiliary information

This article studies the economic and economic-statistical designs of the auxiliary information (AI) based side sensitive group runs (SSGR-AI) chart. The regression estimator that consists of information not only from the primary variable but also from the auxiliary variable is integrated into the control charting statistic. Optimal designs of the SSGR-AI chart, for the minimization of the expected cost function with and without statistical constraints, are developed based on (i) average run length (ARL) and (ii) expected average run length (EARL). Furthermore, sensitivity analyses are conducted, that is, the impact of various input parameters on the optimal parameters and costs for different values of correlation coefficients (ρ) between the primary and auxiliary variables are investigated. In addition, the effects of incorrect specification of the size of the shift on the optimal cost of the SSGR-AI chart are studied. The comparative study reveals that the SSGR-AI chart is superior to the exponentially weighted moving average-AI (EWMA-AI) and synthetic-AI (Syn-AI) charts, for both designs, by giving the smallest costs.     

Moving range charts for monitoring the Weibull shape parameter with single observation samples

This paper proposes an approach to monitor shifts in the Weibull shape parameter bfβ via control charts based on the moving range of single‐point samples from a smallest extreme value distribution. The average run length (ARL) of the proposed charts are computed using Fredholm integral equations of the second kind. The derived control limits for one‐sided and two‐sided control charts are unbiased in the sense that the ARL when β has shifted is shorter than the desired stable‐process ARL. These control limits depend only on the desired stable‐process ARL and the stable value of β. The paper also discusses the sample size requirements for Phase I so that the run length distributions are similar under standards‐given scenario (β is given) and retrospective scenario (β is estimated from past data). The proposed methods are then applied to data on the breaking strengths of carbon fibers. The results suggest that one‐sided control charts can detect small shifts in β sooner than two‐sided charts. Copyright © 2011 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.     

Memory‐Type Control Charts for Monitoring the Process Dispersion

Control charts have been broadly used for monitoring the process mean and dispersion. Cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts are memory control charts as they utilize the past information in setting up the control structure. This makes CUSUM and EWMA‐type charts good at detecting small disturbances in the process. This article proposes two new memory control charts for monitoring process dispersion, named as floating T ? S² and floating U ? S² control charts, respectively. The average run length (ARL) performance of the proposed charts is evaluated through a simulation study and is also compared with the CUSUM and EWMA charts for process dispersion. It is found that the proposed charts are better in detecting both positive as well as negative shifts. An additional comparison shows that the floating U ? S² chart has slightly smaller ARLs for larger shifts, while for smaller shifts, the floating T ? S² chart has better performance. An example is also provided which shows the application of the proposed charts on simulated datasets. Copyright © 2013 John Wiley & Sons, Ltd.     

A modified CUSUM control chart for monitoring industrial processes

Control charts are the most popular tool of statistical process control for monitoring variety of processes. The detection ability of these control charts can be improved by introducing various transformations. In this study, we have enhanced the performance of CUSUM charts by introducing a link relative variable transformation technique. Link relative variable converts the original process variable in a form which is relative to its mean. So, the link relative represents the relative positioning of the observations. Average run length (ARL ) is used to compare our technique with the previous studies. The comparison shows the overall good detection performance of our scheme for a span of shifts in the mean. A real‐world example from the electrical engineering process is also included to demonstrate the application of proposed control chart.     

New CUSUM and dual CUSUM mean charts

The CUSUM (C) charts are well recognized as a potentially advanced process monitoring tools because of their sensitivity against small and moderate shifts. In this paper, we first improve the sensitivity of the Brownian motion–based C (BC) chart with an appropriate transformation, named new BC (NBC) chart, for monitoring moderate and large shifts in the mean of a normal process. Then, using the control charting structure of the Crosier C (CC) chart, we propose the NBCC (NBC with CC structure) chart. In addition, for efficiently detecting a mean shift within an interval, dual version of these control charts are also proposed, named the dual NBC (DNBC) and dual NBCC (DNBCC) charts. Moreover, the fast initial response feature is also incorporated into the proposed charts. Using the Monte Carlo simulation, the run length properties of the proposed charts are computed. The run length performances of the existing and proposed charts are compared using the extra quadratic loss and integral relative average run length as performance criterion. It turns out that the NBC and NBCC (DNBC and DNBCC) charts are uniformly more sensitive than the C, CC, and NBC (dual C and dual CC) charts when detecting the mean shifts in small, moderate, and large intervals, where the DNBCC chart outperforms all considered charts. The proposed charts are also applied on real data sets to support the proposed theory.     

Side-sensitive modified group runs charts with and without measurement errors for monitoring the coefficient of variation

The coefficient of variation (CV) is used in process monitoring when the process mean and standard deviation are proportional to each other. In this work, a side-sensitive modified group runs CV (SSMGR CV) chart is proposed for monitoring the process CV. The run length performance of the SSMGR CV chart is compared to those of the existing CV charts in terms of the average and standard deviation of the run length criteria. The SSMGR CV chart is found to outperform the existing CV charts. In addition, the run length performance of the SSMGR CV chart is also evaluated in the presence of measurement errors, as these errors are not only unavoidable in practice but they also affect the sensitivity of a control chart in detecting an out-of-control situation. The results obtained show that the accuracy and precision errors affect the performance of the SSMGR CV chart in detecting an out-of-control situation.     

Monitoring of Time‐Between‐Events with a Generalized Group Runs Control Chart

Control charting methods for time between events (TBE) is important in both manufacturing and nonmanufacturing fields. With the aim to enhance the speed for detecting shifts in the mean TBE, this paper proposes a generalized group runs TBE chart to monitor the mean TBE of a homogenous Poisson failure process. The proposed chart combines a TBE subchart and a generalized group conforming run length subchart. The zero‐state and steady‐state performances of the proposed chart were evaluated by applying a Markov chain method. Overall, it is found that the proposed chart outperforms the existing TBE charts, such as the T, T_r, EWMA‐T, Synth‐T_r, and GR‐T_r charts. Copyright © 2015 John Wiley & Sons, Ltd.     

On increasing the sensitivity of moving average control chart using auxiliary variable

In the statistical process control, the most useful tool to monitor the manufacturing processes in the industries is the control chart. Quality practitioners always desire the charting structure that identifies sustainable changes in the monitoring processes. The sensitivity of the control chart is improved when additional correlated auxiliary information about the study variable is introduced. The regression estimate in the form of auxiliary and supporting variables presents an unbiased and efficient statistic of the mean of the process variable. In this study, auxiliary information-based moving average (AB-MA) control chart is designed for efficient monitoring of shifts in the process location parameter. The performance of the AB-MA control chart is evaluated and compared with existing charts using average run length and other run length characteristics. The comparison reveals that the AB-MA control chart outperforms the competitors in detecting the small and medium changes in the process location parameter. The application of the proposal is also provided to implement it in real situation.     

Guaranteed in‐control performance of the EWMA chart for monitoring the mean

Research on the performance evaluation and the design of the Phase II EWMA control chart for monitoring the mean, when parameters are estimated, have mainly focused on the marginal in‐control average run‐length (ARL_IN). Recent research has highlighted the high variability in the in‐control performance of these charts. This has led to the recommendation of studying of the conditional in‐control average run‐length (CARL_IN) distribution. We study the performance and the design of the Phase II EWMA chart for the mean, using the CARL_IN distribution and the exceedance probability criterion (EPC). The CARL_IN distribution is approximated by the Markov Chain method and Monte Carlo simulations. Our results show that in‐order to design charts that guarantee a specified EPC, more Phase I data are needed than previously recommended in the literature. A method for adjusting the Phase II EWMA control chart limits, to achieve a specified EPC, for the available amount of data at hand, is presented. This method does not involve bootstrapping and produces results that are about the same as some existing results. Tables and graphs of the adjusted constants are provided. An in‐control and out‐of‐control performance evaluation of the adjusted limits EWMA chart is presented. Results show that, for moderate to large shifts, the performance of the adjusted limits EWMA chart is quite satisfactory. For small shifts, an in‐control and out‐of‐control performance tradeoff can be made to improve performance.     

A synthetic double sampling control chart for process mean using auxiliary information

A control chart is a simple yet powerful tool that is extensively adopted to monitor shifts in the process mean. In recent years, auxiliary‐information–based (AIB) control charts have received considerable attention as these control charts outperform their counterparts in monitoring changes in the process parameter(s). In this article, we integrate the conforming run length chart with the existing AIB double sampling (AIB DS) chart to propose an AIB synthetic DS chart for the process mean. The AIB synthetic DS chart also encompasses the existing synthetic DS chart. A detailed discussion on the construction, optimization, and evaluation of the run length profiles is provided for the proposed control chart. It is found that the optimal AIB synthetic DS chart significantly outperforms the existing AIB Shewhart, optimal AIB synthetic, and AIB DS charts in detecting various shifts in the process mean. An illustrative example is given to demonstrate the implementation of the existing and proposed AIB control charts.     

On the effectiveness of the unit sample size for standard control charts: ARL VS. Aurl

In this paper we investigate the use of the average unit run length (AURL) as an important measure of the effectiveness of various quality control charting schemes. In particular we focus on its appropriateness for normally distributed processes that tend to produce units (or measurements) at slow rates. In our investigations with the standard Shewhart X? and R charts, as well as the CUSUM chart, AURL shows that a sample size of n=1 can yield the fastest means of detecting shifts.     

New Exponentially Weighted Moving Average Control Charts for Monitoring Process Mean and Process Dispersion

Exponentially weighted moving average (EWMA) control charts have been widely accepted because of their excellent performance in detecting small to moderate shifts in the process parameters. In this paper, we propose new EWMA control charts for monitoring the process mean and the process dispersion. These EWMA control charts are based on the best linear unbiased estimators obtained under ordered double ranked set sampling (ODRSS) and ordered imperfect double ranked set sampling (OIDRSS) schemes, named EWMA‐ODRSS and EWMA‐OIDRSS charts, respectively. We use Monte Carlo simulations to estimate the average run length, median run length, and standard deviation of run length of the proposed EWMA charts. We compare the performances of the proposed EWMA charts with the existing EWMA charts when detecting shifts in the process mean and in the process variability. It turns out that the EWMA‐ODRSS mean chart performs uniformly better than the classical EWMA, fast initial response‐based EWMA, Shewhart‐EWMA, and hybrid EWMA mean charts. The EWMA‐ODRSS mean chart also outperforms the Shewhart‐EWMA mean charts based on ranked set sampling (RSS) and median RSS schemes and the EWMA mean chart based on ordered RSS scheme. Moreover, the graphical comparisons of the EWMA dispersion charts reveal that the proposed EWMA‐ODRSS and EWMA‐OIDRSS charts are more sensitive than their counterparts. We also provide illuminating examples to illustrate the implementation of the proposed EWMA mean and dispersion charts. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Improving the Performance of Exponentially Weighted Moving Average Control Charts

A control chart is a graphical tool used for monitoring a production process and quality improvement. One such charting procedure is the Shewhart‐type control chart, which is sensitive mainly to the large shifts. For small shifts, the cumulative sum (CUSUM) control charts and exponentially weighted moving average (EWMA) control charts were proposed. To further enhance the ability of the EWMA control chart to quickly detect wide range process changes, we have developed an EWMA control chart using the median ranked set sampling (RSS), median double RSS and the double median RSS. The findings show that the proposed median‐ranked sampling procedures substantially increase the sensitivities of EWMA control charts. The newly developed control charts dominate most of their existing counterparts, in terms of the run‐length properties, the Average Extra Quadratic Loss and the Performance Comparison Index. These include the classical EWMA, fast initial response EWMA, double and triple EWMA, runs‐rules EWMA, the max EWMA with mean‐squared deviation, the mixed EWMA‐CUSUM, the hybrid EWMA and the combined Shewhart–EWMA based on ranks. An application of the proposed schemes on real data sets is also given to illustrate the implementation and procedural details of the proposed methodology. Copyright © 2013 John Wiley & Sons, Ltd.     

CUSUM Schemes for Monitoring Prespecified Changes in Linear Profiles

Because of the characteristics of a system or process, several prespecified changes may happen in some statistical process control applications. Thus, one possible and challenging problem in profile monitoring is detecting changes away from the ‘normal’ profile toward one of several prespecified ‘bad’ profiles. In this article, to monitor the prespecified changes in linear profiles, two two‐sided cumulative sum (CUSUM) schemes are proposed based on Student's t‐statistic, which use two separate statistics and a single statistic, respectively. Simulation results show that the CUSUM scheme with a single statistic uniformly outperforms that with two separate statistics. Besides, both CUSUM schemes perform better than alternative methods in detecting small shifts in prespecified changes, and become comparable on detecting moderate or large shifts when the number of observations in each profile is large. To overcome the weakness in the proposed CUSUM methods, two modified CUSUM schemes are developed using z‐statistic and studied when the in‐control parameters are estimated. Simulation results indicate that the modified CUSUM chart with a single charting statistic slightly outperforms that with two separate statistics in terms of the average run length and its standard deviation. Finally, illustrative examples indicate that the CUSUM schemes are effective. Copyright © 2016 John Wiley & Sons, Ltd.