Applying fast initial response features on GWMA control charts for monitoring autocorrelation data

ABSTRACT

A generally weighted moving average (GWMA) control chart with fast initial response (FIR) features is addressed to monitor an autoregressive process mean shift. Numerical simulations based on average run length (ARL) show that the GWMA control chart with additional FIR feature requires less time to detect small or moderate shifts than GWMA control chart at low level of autocorrelation; whereas these two control charts perform similarly at high level of autocorrelation. Regardless of any level of autocorrelation, GWMA control charts provided with additional FIR feature have a good performance in detecting large shifts during the initial stage.     

Generally weighted moving average control charts using repetitive sampling

Abstract

Generally weighted moving average (GWMA) control charts have been validated for effective detection of small process shifts, and perform better than exponentially weighted moving average (EWMA) control charts. These charts are available based on single sampling; however, repetitive sampling charts have received less attention. Here, a GWMA control chart based on repetitive sampling (namely an RS-GWMA chart) is proposed for enhancing detectability of small process shifts. Simulations show that the proposed RS-GWMA chart with large design and small adjustment parameters outperforms existing hybrid EWMA (HEWMA) control charts based on repetitive sampling. An in-silico example is considered for demonstrating the applicability of the proposed RS-GWMA chart.     

Exponentially weighted moving average control schemes with variable sampling intervals

The idea of using non-constant sampling intervals has been of interest in quality control applications since it was first suggested for the “skip-lot sampling plan” of Dodge. Recent interest has focused on the use of variable sampling interval (VSI) control schemes. VSI control schemes use a short sampling interval is given     

Exponentially weighted moving average charts for correlated multivariate Poisson processes

In 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.     

Effect of measurement error on exponentially weighted moving average control charts under ranked set sampling schemes

Control charts are a powerful statistical process monitoring tool often used to monitor the stability of manufacturing processes. In quality control applications, measurement errors adversely affect the performance of control charts. In this paper, we study the effect of measurement error on the detection abilities of the exponentially weighted moving average (EWMA) control charts for monitoring process mean based on ranked set sampling (RSS), median RSS (MRSS), imperfect RSS (IRSS) and imperfect MRSS (IMRSS) schemes. We also study the effect of multiple measurements and non-constant error variance on the performances of the EWMA control charts. The EWMA control chart based on simple random sampling is compared with the EWMA control charts based on RSS, MRSS, IRSS and IMRSS schemes. The performances of the EWMA control charts are evaluated in terms of out-of-control average run length and standard deviation of run lengths. It turns out that the EWMA control charts based on MRSS and IMRSS schemes are better than their counterparts for all measurement error cases considered here.     

An exponentially weighted moving average chart controlling false discovery rate

A new control chart is developed by using the exponentially weighted moving average (EWMA) statistics and a multiple testing procedure for controlling false discovery rate. The multiple testing procedure considers not only the current EWMA statistic, but also a given number of previous statistics at the same time. Numerical simulations are accomplished to evaluate the performance of the proposed control chart in terms of the average run length and the conditional expected delay. The results are compared with those of the existing control charts including the X-bar chart, EWMA, and cumulative sum control charts. Case studies with real data-sets are also presented.     

An adaptive exponentially weighted moving average control chart for monitoring process variances

The exponentially weighted moving average (EWMA) control chart is efficient in detecting small changes in process parameters but less efficient when the changes are relatively large, due to what is known as the inertia problem. To diminish the inertia, an adaptive EWMA (AEWMA) chart has been proposed for monitoring process locations to improve over the traditional EWMA charts. The basic idea of the AEWMA scheme is to dynamically weight the past observations according to a suitable function of the current prediction error. This article extends the idea of the AEWMA chart for monitoring process locations to the case of monitoring process dispersion. A Markov chain model is established to analyze and design the suggested chart. It is shown that the AEWMA dispersion chart performs better than the EWMA and other dispersion charts in terms of its ability to perform relatively well at both small and large changes in process dispersion.     

The random intrinsic fast initial response of one-sided CUSUM charts

This article analyses the performance of a one-sided cumulative sum (CUSUM) chart that is initialized using a random starting point following the natural or intrinsic probability distribution of the CUSUM statistic. By definition, this probability distribution remains stable as the chart is used. The probability that the chart starts at zero according to this intrinsic distribution is always smaller than one, which confers on the chart a fast initial response feature. The article provides a fast and accurate algorithm to compute the in-control and out-of-control average run lengths and run-length probability distributions for one-sided CUSUM charts initialized using this random intrinsic fast initial response (RIFIR) scheme. The algorithm also computes the intrinsic distribution of the CUSUM statistic and random samples extracted from this distribution. Most importantly, no matter how the chart was initialized, if no level shifts and no alarms have occurred before time τ?>?0, the distribution of the run length remaining after τ is provided by this algorithm very accurately, provided that τ is not too small.     

Non parametric double generally weighted moving average sign charts based on process proportion

Non parametric control charts have received increasing attention in the field of statistical process control. This paper presents a non parametric double generally weighted moving average (DGWMA) sign chart for monitoring small deviations when the quality characteristics of a process are unknown. The statistical performance of the non parametric DGWMA sign chart is evaluated and compared with those of other charts, including the exponentially weighted moving average (EWMA), generally weighted moving average (GWMA), and double EWMA (DEWMA) sign charts. Simulation studies indicate that the non parametric DGWMA sign chart with a large design and median adjustment parameters is always more sensitive than other charts in detecting small changes.     

Grouped data exponentially weighted moving average control charts

In the manufacture of metal fasteners in a progressive die operation, and other industrial situations, important quality dimensions cannot be measured on a continuous scale, and manufactured parts are classified into groups by using a step gauge. This paper proposes a version of exponentially weighted moving average (EWMA) control charts that are applicable to monitoring the grouped data for process shifts. The run length properties of this new grouped data EWMA chart are compared with similar results previously obtained for EWMA charts for variables data and with those for cumulative sum (CUSUM) schemes based on grouped data. Grouped data EWMA charts are shown to be nearly as efficient as variables-based EWMA charts and are thus an attractive alternative when the collection of variables data is not feasible. In addition, grouped data EWMA charts are less affected by the discreteness that is inherent in grouped data than are grouped data CUSUM charts. In the metal fasteners application, grouped data EWMA charts were simple to implement and allowed the rapid detection of undesirable process shifts.     

The performance of multivariate CUSUM control charts with estimated parameters

In this paper, we study the effect of estimating the vector of means and the variance–covariance matrix on the performance of two of the most widely used multivariate cumulative sum (CUSUM) control charts, the MCUSUM chart proposed by Crosier [Multivariate generalizations of cumulative sum quality-control schemes, Technometrics 30 (1988), pp. 291–303] and the MC1 chart proposed by Pignatiello and Runger [Comparisons of multivariate CUSUM charts, J. Qual. Technol. 22 (1990), pp. 173–186]. Using simulation, we investigate and compare the in-control and out-of-control performances of the competing charts in terms of the average run length measure. The in-control and out-of-control performances of the competing charts deteriorate significantly if the estimated parameters are used with control limits intended for known parameters, especially when only a few Phase I samples are used to estimate the parameters. We recommend the use of the MC1 chart over that of the MCUSUM chart if the parameters are estimated from a small number of Phase I samples.     

On increasing the sensitivity of mixed EWMA–CUSUM control charts for location parameter

Control chart is an important statistical technique that is used to monitor the quality of a process. Shewhart control charts are used to detect larger disturbances in the process parameters, whereas cumulative sum (CUSUM) and exponential weighted moving average (EWMA) are meant for smaller and moderate changes. In this study, we enhanced mixed EWMA–CUSUM control charts with varying fast initial response (FIR) features and also with a runs rule of two out of three successive points that fall above the upper control limit. We investigate their run-length properties. The proposed control charting schemes are compared with the existing counterparts including classical CUSUM, classical EWMA, FIR CUSUM, FIR EWMA, mixed EWMA–CUSUM, 2/3 modified EWMA, and 2/3 CUSUM control charting schemes. A case study is presented for practical considerations using a real data set.     

Runs tests for group control charts

When a process consists of several identical streams that are not highly correlated, an alternative to using separate control charts for each stream is to use a group control chart. Rather than plotting sample means from each stream at any time point, one could plot only the largest and/or smallest sample mean from among all the streams. Using the theory of stochastic processes and majorization together with numerical methods, the properties of a test that signals if r consecutive extreme values come from the same stream are examined. Both one and two-sided cases are considered. Average run lengths (ARL's), the least favorable configuration of the stream (population) means, and sample sizes necessary to have specified in-control and out-of-control ARL's are obtained. A test that signals if r-1 out of r consecutive extreme values come from the same stream is also considered     

A generally weighted moving average exceedance chart

Distribution-free control charts gained momentum in recent years as they are more efficient in detecting a shift when there is a lack of information regarding the underlying process distribution. However, a distribution-free control chart for monitoring the process location often requires information on the in-control process median. This is somewhat challenging because, in practice, any information on the location parameter might not be known in advance and estimation of the parameter is therefore required. In view of this, a time-weighted control chart, labelled as the Generally Weighted Moving Average (GWMA) exceedance (EX) chart (in short GWMA-EX chart), is proposed for detection of a shift in the unknown process location; this chart is based on exceedance statistic when there is no information available on the process distribution. An extensive performance analysis shows that the proposed GWMA-EX control chart is, in many cases, better than its contenders.     

Improving the performance of the zone control chart

A general model for the zone control chart is presented. Using this model, it is shown that there are score vectors for zone control charts which result in superior average run length performance in comparison to Shewhart charts with common runs rules.

A fast initial response (FIR) feature for the zone control chart is also proposed. Average run lengths of the zone control chart with this feature are calculated. It is shown that the FIR feature improves zone control chart performance by providing significantly earlier signals when the process is out of control.     

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 study of economic design of control charts for cumulative count of conforming items

In this paper the economic design of Cumulative Count of Conforming (CCC) control charts to maintain the current control of fraction nonconforming of a process is studied. CCC chart is an attribute chart for monitoring high quality processes by plotting the cumulative count of conforming items between two nonconforming ones on a suitable chart. A process model is proposed to obtain an appropriate loss function. An alogorithm to search for the optimal setting of the sampling and control parameters is derived. Numerical illustrations of the method and some properties of the optimal economic design are provided.     

An improved mean deviation exponentially weighted moving average control chart to monitor process dispersion under ranked set sampling

Quality-control charts are widely used to monitor and detect shifts in the process mean and dispersion. Abbasi and Miller [MDEWMA chart: an efficient and robust alternative to monitor process dispersion, J Stat Comput Simul 2013;83:247–268] suggested a robust mean deviation exponentially weighted moving average (MDEWMA) control chart for monitoring process dispersion under simple random sampling. In this study, an improved MDEWMA (IMDEWMA) control chart is proposed under ranked set sampling to monitor process dispersion. Detailed Monte Carlo simulations are performed from symmetric and asymmetric populations to investigate the performances of the proposed and existing control charts in terms of average run length (ARL), median run length and standard deviation of run length. An application to real-life data is also presented to illustrate the use of the IMDEWMA control chart. It is observed that the IMDEWMA control chart indicates a shift in process dispersion substantially quicker than the MDEWMA control chart, while maintaining comparable ARLs when the process is in control.     

Improved CUSUM charts for monitoring process mean

In this paper, we propose new cumulative sum (CUSUM) and Shewhart-CUSUM (SCUSUM) control charts for monitoring the process mean using ranked-set sampling (RSS) and ordered RSS (ORSS) schemes. The proposed CUSUM charts include the Crosier's CUSUM (CCUSUM) and Shewhart-CCUSUM (SCCUSUM) charts using RSS, and the CUSUM, CCUSUM, SCUSUM and SCCUSUM charts using ORSS. Moreover, fast initial response features are also attached with these CUSUM charts to improve their sensitivities for an initial out-of-control situation. Monte Carlo simulations are used to compute the run length characteristics of the proposed CUSUM charts. Upon comparing the run length performances of the CUSUM charts, it turns out that the proposed CUSUM charts are more sensitive than their existing counterparts. A real dataset is used to explain the implementation of the proposed CUSUM charts.     

Synthetic exponential control charts with unknown parameter

The existing synthetic exponential control charts are based on the assumption of known in-control parameter. However, the in-control parameter has to be estimated from a Phase I dataset. In this article, we use the exact probability distribution, especially the percentiles, mean, and standard deviation of the conditional average run length (ARL) to evaluate the effect of parameter estimation on the performance of the Phase II synthetic exponential charts. This approach accounts for the variability in the conditional ARL values of the synthetic chart obtained by different practitioners. Since parameter estimation results in more false alarms than expected, we develop an exact method to design the adjusted synthetic charts with desired conditional in-control performance. Results of known and unknown in-control parameter cases show that the control limit of the conforming run length sub-chart of the synthetic chart should be as small as possible.