Economic design of non parametric sign control chart

An economic design of sign chart to control the median is proposed. Since the sign chart is distribution free, it can easily be applied to any process without prior knowledge of process quality distribution. The effect on loss cost observed for different shifts in location shows that the sign chart performs better for large shifts. The economic statistical performance study reveals that statistical performance of sign chart can be improved sufficiently for moderate shifts in the process. Sensitivity study shows that design is more sensitive for change in values of penalty loss cost and time required for search and repair of an assignable cause.     

On designing new optimal synthetic Tukey’s control charts

Tukey’s control chart is generally used for monitoring the processes where the measurement process physically damages the product. It is based on single observation and robust to outliers. In this paper, two optimal synthetic Tukey’s control charts are proposed by integrating the conforming run length chart with the Tukey’s control chart and its modification. The performance comparison of the proposed charts with the existing Tukey’s control charts is made by using out-of-control average run length and extra quadratic loss as performance metrics. The proposed charts offer better protection against the process shifts as compare to the existing Tukey’s control charts when the underlying process distribution is symmetric or asymmetric. Simulation studies also establish the supremacy of the proposed control charts over the existing Tukey’s control charts. In the end, an illustrative example based on a real data set of the combined cycle power plant is provided for practical implementation.     

A mean deviation-based approach to monitor process variability

The study proposes a Shewhart-type control chart, namely an MD chart, based on average absolute deviations taken from the median, for monitoring changes (especially moderate and large changes – a major concern of Shewhart control charts) in process dispersion assuming normality of the quality characteristic to be monitored. The design structure of the proposed MD chart is developed and its comparison is made with those of two well-known dispersion control charts, namely the R and S charts. Using power curves as a performance measure, it has been observed that the design structure of the proposed MD chart is more powerful than that of the R chart and is very close competitor to that of the S chart, in terms of discriminatory power for detecting shifts in the process dispersion. The non-normality effect is also examined on design structures of the three charts, and it has been observed that the design structure of the proposed MD chart is least affected by departure from normality.     

A new synthetic control chart for monitoring process mean using auxiliary information

ABSTRACT

Quality control charts have been widely recognized as a potentially powerful statistical process monitoring tool in statistical process control because of their superior ability in detecting shifts in the process parameters. Recently, auxiliary-information-based control charts have been proposed and shown to have excellent speed in detecting process shifts than those based without it. In this paper, we design a new synthetic control chart that is based on a statistic that utilizes information from both the study and auxiliary variables. The proposed synthetic chart encompasses the classical synthetic chart. The construction, optimal design, run length profiles, and the performance evaluation of the new chart are discussed in detail. It turns out that the proposed synthetic chart performs uniformly better than the classical synthetic chart when detecting different kinds of shifts in the process mean under both zero-state and steady-state run length performances. Moreover, with reasonable assumptions, the proposed chart also surpasses the exponentially weighted moving average control chart. An application with a simulated data set is also presented to explain the implementation of the proposed control chart.     

Synthetic double sampling s chart

This study proposes a synthetic double sampling s chart that integrates the double sampling (DS) s chart and the conforming run length chart. An optimization procedure is proposed to compute the optimal parameters of the synthetic DS s chart. The performance of the synthetic DS s chart is compared with other existing control charts for monitoring process standard deviation. The results show that the synthetic DS s chart is more effective for detecting increases in the process standard deviation for a wide range of shifts. An example is provided to illustrate the operation procedure of the synthetic DS s chart.     

A new double sampling control chart for monitoring process mean using auxiliary information

Statistical quality control charts have been widely accepted as a potentially powerful process monitoring tool because of their excellent speed in tracking shifts in the underlying process parameter(s). In recent studies, auxiliary-information-based (AIB) control charts have shown superior run length performances than those constructed without using it. In this paper, a new double sampling (DS) control chart is constructed whose plotting-statistics requires information on the study variable and on any correlated auxiliary variable for efficiently monitoring the process mean, namely AIB DS chart. The AIB DS chart also encompasses the classical DS chart. We discuss in detail the construction, optimal design, run length profiles, and the performance evaluations of the proposed chart. It turns out that the AIB DS chart performs uniformly better than the DS chart when detecting different kinds of shifts in the process mean. It is also more sensitive than the classical synthetic and AIB synthetic charts when detecting a particular shift in the process mean. Moreover, with some realistic beliefs, the proposed chart outperforms the exponentially weighted moving average chart. An illustrative example is also presented to explain the working and implementation of the proposed chart.     

The Synthetic Mean Square Error Control Chart

A synthetic mean square error (MSE) control chart is presented in this study for monitoring the changes in the mean and standard deviation of a normally distributed process. The synthetic MSE control chart is a combination of the standard MSE control chart and the conforming run length (CRL) control chart. From the numerical comparisons, the synthetic MSE control chart is always more efficient than the standard MSE control chart in detecting shifts in the process mean and standard deviation. The synthetic MSE chart also performs better than the exponentially weighted moving average-semicircle (EWMA-SC) chart, except for some cases where the process mean shifts are small.     

Nonparametric quality control charts based on the sign statistic

Nonparametric control chart are presented for the problem of detecting changes in the process median (or mean), or changes in the process variability when samples are taken at regular time intervals. The proposed procedures are based on sign-test statistics computed for each sample, and are used in Shewhart and cumulative sum control charts. When the process is in control the run length distributions for the proposed nonparametric control charts do not depend on the distribution of the observations. An additional advantage of the non-parametric control charts is that the variance of the process does not need to be established in order to set up a control chart for the mean. Comparisons with the corresponding parametric control charts are presented. It is also shown that curtailed sampling plans can considerably reduce the expected number of observations used in the Shewhart control schemes based on the sign statistic.     

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.     

Adjusted-loss-function charts with variable sample sizes and sampling intervals

Recent research has shown that the control charts with adaptive features are quicker than the traditional static Shewhart charts in detecting process shifts. This article presents the design and implementation of a control chart based on Adjusted Loss Function (AL) with Variable Sample Sizes and Sampling Intervals (VSSI). This single chart (called the VSSI AL chart) is able to monitor the process shifts in mean and variance simultaneously. Our studies show that the VSSI AL chart is not only easier to design and implement than the VSSI X¯ & S (or X¯ & R) charts, but is also 10% more effective than the latter in detecting the process shifts from an overall viewpoint.     

Optimal design of synthetic np control chart based on median run length

The synthetic np chart is a combination of the np sub-chart and the conforming run length sub-chart. A procedure for the optimal design of the synthetic np chart is provided by minimizing the out-of-control median run length (MRL). The comparative results show that the synthetic np chart performs better than the corresponding standard np chart for detecting process shifts in the fraction non conforming, in terms of the MRL. An example is given to illustrate the operation of the synthetic np chart.     

One-sided synthetic control charts for monitoring the multivariate coefficient of variation

Shewhart's type control charts for monitoring the Multivariate Coefficient of Variation (MCV) have recently been proposed in order to monitor the relative variability compared with the mean. These approaches are known to be rather slow in the detection of small or moderate process shifts. In this paper, in order to improve the detection efficiency, two one-sided Synthetic charts for the MCV are proposed. A Markov chain method is used to evaluate the statistical performance of the proposed charts. Furthermore, computational experiments reveal that the proposed control charts outperform the Shewhart MCV control chart in terms of the average run length to detect an out-of-control state. Finally, the implementation of the proposed chart is illustrated with an example using steel sleeves data.     

The effect of autocorrelation on the retrospective X-chart

Quality control chart interpretation is usually based on the assumption that successive observations are independent over time. In this article we show the effect of autocorrelation on the retrospective Shewhart chart for individuals, often referred to as the X-chart, with the control limits based on moving ranges. It is shown that the presence of positive first lag autocorrelation results in an increased number of false alarms from the control chart. Negative first lag autocorrelation can result in unnecessarily wide control limits such that significant shifts in the process mean may go undetected. We use first-order autoregressive and first-order moving average models in our simulation of small samples of autocorrelated data.     

A Multivariate Adaptive Exponentially Weighted Moving Average Control Chart

A multivariate extension of the adaptive exponentially weighted moving average (AEWMA) control chart is proposed. The new multivariate scheme can detect small and large shifts in the process mean vector effectively. The proposed scheme can be viewed as a smooth combination of a multivariate exponentially weighted moving average (MEWMA) chart and a Shewhart χ²-chart. The optimal design of the proposed chart is given according to a pre-specified in-control average run length and two shift sizes; a small and large shift each measured in terms of the non centrality parameter. The signal resistance of the newly proposed multivariate chart is also given. Comparisons among the new chart, the MEWMA chart, and the combined Shewhart-MEWMA (S-MEWMA) chart in terms of the standard and worst-case average run length profiles are presented. In addition, the three charts are compared with respect to their worst-case signal resistance values. The proposed chart gives somewhat better worst-case ARL and signal resistance values than the competing charts. It also gives better standard ARL performance especially for moderate and large shifts. The effectiveness of our proposed chart is illustrated through an example with simulated data set.     

Multivariate Synthetic |S| Control Chart with Variable Sampling Interval

A variable sampling interval (VSI) feature is introduced to the multivariate synthetic generalized sample variance |S| control chart. This multivariate synthetic control chart is a combination of the |S| sub-chart and the conforming run length sub-chart. The VSI feature enhances the performance of the multivariate synthetic control chart. The comparative results show that the VSI multivariate synthetic control chart performs better than other types of multivariate control charts for detecting shifts in the covariance matrix of a multivariate normally distributed process. An example is given to illustrate the operation of the VSI multivariate synthetic chart.     

A new nonparametric synthetic EWMA control chart for monitoring process mean

The exponentially weighted moving average (EWMA) control charts are widely used in chemical and process industries because of their excellent speed in catching small to moderate shifts in the process target. In usual practice, many data come from a process where the monitoring statistic is non-normally distributed or it follows an unknown probability distribution. This necessitates the use of distribution-free/nonparametric control charts for monitoring the deviations from the process target. In this paper, we integrate the existing EWMA sign chart with the conforming run length chart to propose a new synthetic EWMA (SynEWMA) sign chart for monitoring the process mean. The SynEWMA sign chart encompasses the synthetic sign and EWMA sign charts. Monte Carlo simulations are used to compute the run length profiles of the SynEWMA sign chart. Based on a comprehensive comparison, it turns out that the SynEWMA sign chart is able to perform substantially better than the existing EWMA sign chart. Both real and simulated data sets are used to explain the working and implementation of existing and proposed control charts.     

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.     

A new S2 control chart using repetitive sampling

A new S² control chart is presented for monitoring the process variance by utilizing a repetitive sampling scheme. The double control limits called inner and outer control limits are proposed, whose coefficients are determined by considering the average run length (ARL) and the average sample number when the process is in control. The proposed control chart is compared with the existing Shewhart S² control chart in terms of the ARLs. The result shows that the proposed control chart is more efficient than the existing control chart in detecting the process shift.     

The effect of Phase I sample size on the run length performance of control charts for autocorrelated data

Traditional control charts assume independence of observations obtained from the monitored process. However, if the observations are autocorrelated, these charts often do not perform as intended by the design requirements. Recently, several control charts have been proposed to deal with autocorrelated observations. The residual chart, modified Shewhart chart, EWMAST chart, and ARMA chart are such charts widely used for monitoring the occurrence of assignable causes in a process when the process exhibits inherent autocorrelation. Besides autocorrelation, one other issue is the unknown values of true process parameters to be used in the control chart design, which are often estimated from a reference sample of in-control observations. Performances of the above-mentioned control charts for autocorrelated processes are significantly affected by the sample size used in a Phase I study to estimate the control chart parameters. In this study, we investigate the effect of Phase I sample size on the run length performance of these four charts for monitoring the changes in the mean of an autocorrelated process, namely an AR(1) process. A discussion of the practical implications of the results and suggestions on the sample size requirements for effective process monitoring are provided.     

Double moving average–EWMA control chart for exponentially distributed quality

A control chart is an ever-popular tool for monitoring the production process. The early detection of a process shift, if any, is the desire of the quality control personnel. In this article, an effective alternative control charting procedure has been developed for the monitoring of exponentially distributed quality characteristic using the double moving average combined with EWMA statistic. The performance of the proposed control chart is examined for different combinations of the shift constant, the EWMA smoothing parameter, the moving average span, and the target in-control average run lengths. It has been observed that the proposed control chart is more efficient in the detection of process shifts as compared to control chart suggested by Khoo and Wang for the same purpose. The proposed control chart is illustrated for practical usage with the help of a synthetic and a real dataset.