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.     

A EWMA control chart based on an auxiliary variable and repetitive sampling for monitoring process location

ABSTRACT

This article develops an exponentially weighted moving average (EWMA) control chart using an auxiliary variable and repetitive sampling for efficient detection of small to moderate shifts in location. A EWMA statistic of a product estimator of the average (which utilities the information of auxiliary variables as well as repetitive sampling) is plotted on the proposed chart. The control chart coefficients of the proposed EWMA chart are determined for two strategic limits known as outer and inner control limits for the target in-control average run length. The performance of the proposed EWMA chart is studied using average run length when a shift occurs in the process average. The efficiency of the developed chart is compared with the competitive existing control charts. The results of the study revealed that proposed EWMA chart is more efficient than others to detect small changes in process mean.     

A new adaptive EWMA control chart using auxiliary information for monitoring the process mean

The adaptive memory-type control charts, including the adaptive exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts, have gained considerable attention because of their excellent speed in providing overall good detection over a range of mean shift sizes. In this paper, we propose a new adaptive EWMA (AEWMA) chart using the auxiliary information for efficiently monitoring the infrequent changes in the process mean. The idea is to first estimate the unknown process mean shift using an auxiliary information based mean estimator, and then adaptively update the smoothing constant of the EWMA chart. Using extensive Monte Carlo simulations, the run length profiles of the AEWMA chart are computed and explored. The AEWMA chart is compared with the existing control charts, including the classical EWMA, CUSUM, synthetic EWMA and synthetic CUSUM charts, in terms of the run length characteristics. It turns out that the AEWMA chart performs uniformly better than these control charts when detecting a range of mean shift sizes. An illustrative example is also presented to demonstrate the working and implementation of the proposed and existing control charts.     

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.     

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.     

A control chart for multivariate Poisson distribution using repetitive sampling

Control charts using repetitive group sampling have attracted a great deal of attention during the last few years. In the present article, we attempt to develop a control chart for the multivariate Poisson distribution using the repetitive group sampling scheme. In the proposed control chart, the monitoring statistic from the multivariate Poisson distribution has been used for the quick detection of the deteriorated process to avoid losses. The control coefficients have been estimated using the specified in-control average run lengths. The procedure of the proposed control chart has been explained by using the real-world example and a simulated data set. It has been observed that the proposed control chart is an efficient development for the quick detection of the nonrandom change in the manufacturing process.     

Globally applicable control chart for online monitoring of stability of process mean

The shape features of run chart patterns of the most recent m observations arising from stable and unstable processes are different. Using this fact, a new monitoring statistic is defined whose value for given m depends on the pattern parameters but not on the process parameters. A control chart for this statistic for given m, therefore, will be globally applicable to normal processes. The simulation study reveals that the proposed statistic approximately follows normal distribution. The performances of the globally applicable control chart in terms of average run lengths (ARLs) are evaluated and compared with the X chart. Both in-control ARL and out-of-control ARLs with respect to different abnormal process conditions are found to be larger than the X chart. However, the proposed concept is promising because it can eliminate the burden of designing separate control charts for different quality characteristics or processes in a manufacturing set-up.     

An EWMA chart for monitoring process mean

In the statistical process control literature, there exists several improved quality control charts based on cost-effective sampling schemes, including the ranked set sampling (RSS) and median RSS (MRSS). A generalized cost-effective RSS scheme has been recently introduced for efficiently estimating the population mean, namely varied L RSS (VLRSS). In this article, we propose a new exponentially weighted moving average (EWMA) control chart for monitoring the process mean using VLRSS, named the EWMA-VLRSS chart, under both perfect and imperfect rankings. The EWMA-VLRSS chart encompasses the existing EWMA charts based on RSS and MRSS (named the EWMA-RSS and EWMA-MRSS charts). We use extensive Monte Carlo simulations to compute the run length characteristics of the EWMA-VLRSS chart. The proposed chart is then compared with the existing EWMA charts. It is found that, with either perfect or imperfect rankings, the EWMA-VLRSS chart is more sensitive than the EWMA-RSS and EWMA-MRSS charts in detecting small to large shifts in the process mean. A real dataset is also used to explain the working of the EWMA-VLRSS chart.     

A control chart for monitoring process variation using multiple dependent state sampling

A control chart for monitoring process variation by using multiple dependent state (MDS) sampling is constructed in the present article. The operational formulas for in-control and out-of-control average run lengths (ARLs) are derived. Control constants are established by considering the target in-control ARL at a normal process. The extensive ARL tables are reported for various parameters and shifted values of process parameters. The performance of the proposed control chart has been evaluated with several existing charts in regard of ARLs, which empowered the presented chart and proved far better for timely detection of assignable causes. The application of the proposed concept is illustrated with a real-life industrial example and a simulation-based study to elaborate strength of the proposed chart over the existing concepts.     

Improved quality control charts for monitoring the process mean,using double-ranked set sampling methods

Statistical control charts are widely used in the manufacturing industry. The Shewhart-type control charts are developed to improve the monitoring process mean by using the double quartile-ranked set sampling, quartile double-ranked set sampling, and double extreme-ranked set sampling methods. In terms of the average run length, the performance of the proposed control charts are compared with the existing control charts based on simple random sampling, ranked set sampling and extreme-ranked set sampling methods. An application of real data is also considered to investigate the performance of the suggested process mean control charts. The findings of the study revealed that the newly suggested control charts are superior to the existing counterparts.     

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 control chart using an auxiliary variable and repetitive sampling for monitoring process mean

In this paper, a new control chart is proposed by using an auxiliary variable and repetitive sampling in order to enhance the performance of detecting a shift in process mean. The product-difference type estimator of the mean is plotted on the proposed control chart, which utilizes the information of an auxiliary variable correlated with the main quality variable. The proposed control chart is based on the outer and inner control limits so that repetitive sampling is allowed when the plotted statistic falls between the two limits. The average run length (ARL) of the proposed control chart is evaluated using the Monte Carlo simulation. The proposed control chart is compared with the Riaz M control chart and the results show the outperformance of the proposed control chart in terms of the ARL.     

A weighted likelihood ratio test-based chart for monitoring process mean and variability

In this paper, a new single exponentially weighted moving average (EWMA) control chart based on the weighted likelihood ratio test, referred to as the WLRT chart, is proposed for the problem of monitoring the mean and variance of a normally distributed process variable. It is easy to design, fast to compute, and quite effective for diverse cases including the detection of the decrease in variability and individual observation case. The optimal parameters that can be used as a design aid in selecting specific parameter values based on the average run length (ARL) and the sample size are provided. The in-control (IC) and out-of-control (OC) performance properties of the new chart are compared with some other existing EWMA-type charts. Our simulation results show that the IC run length distribution of the proposed chart is similar to that of a geometric distribution, and it provides quite a robust and satisfactory overall performance for detecting a wide range of shifts in the process mean and/or variability.     

Time truncated attribute control chart for the Weibull distribution using multiple dependent state sampling

In this article, an attribute control chart is proposed for time truncated tests using the Weibull distribution. The design of proposed control chart is presented using the multiple dependent state (MDS) sampling. The control chart coefficients are determined for various specified average run length. The efficiency of the proposed control chart is elaborated with the help of a simulation data and a real data. The proposed control chart perform better than the existing control chart in terms of average run length.     

Enhanced adaptive CUSUM charts for process mean

A statistical quality control chart is an important tool of the statistical process control, which is widely used to control and monitor a production process. The CUSUM chart is designed to detect a specific shift, provided that the shift size is known in advance. In practice, however, shift sizes are rarely known. It is then customary to use an adaptive CUSUM chart, which can effectively detect a range of shift sizes. In this paper, we enhance the sensitivities of the improved adaptive CUSUM mean charts using an auxiliary-information-based (AIB) mean estimator. The run length performances of the proposed charts are compared with those of the AIB adaptive and non-adaptive CUSUM charts in terms of the average run length (ARL), extra quadratic loss, and integral relative ARL. These run length comparisons reveal that the proposed charts are more sensitive than the existing charts when detecting different kinds of shift in the process mean. An example is given to demonstrate the implementation of existing and proposed charts.     

Monitoring process mean and dispersion with one double generally weighted moving average control chart

Control charts are widely known quality tools used to detect and control industrial process deviations in Statistical Process Control. In the current paper, we propose a new single memory-type control chart, called the maximum double generally weighted moving average chart (referred as Max-DGWMA), that simultaneously detects shifts in the process mean and/or process dispersion. The run length performance of the proposed Max-DGWMA chart is compared with that of the Max-EWMA, Max-DEWMA, Max-GWMA and SS-DGWMA charts, using time-varying control limits, through Monte–Carlo simulations. The comparisons reveal that the proposed chart is more efficient than the Max-EWMA, Max-DEWMA and Max-GWMA charts, while it is comparable with the SS-DGWMA chart. An automotive industry application is presented in order to implement the Max-DGWMA chart. The goal is to establish statistical control of the manufacturing process of the automobile engine piston rings. The source of the out-of-control signals is interpreted and the efficiency of the proposed chart in detecting shifts faster is evident.