An Empirical-Likelihood-Based Multivariate EWMA Control Scheme

Nonparametric control charts are useful in statistical process control (SPC) when there is a lack of or limited knowledge about the underlying process distribution, especially when the process measurement is multivariate. This article develops a new multivariate SPC methodology for monitoring location parameter based on adapting a well-known nonparametric method, empirical likelihood (EL), to on-line sequential monitoring. The weighted version of EL ratio test is used to formulate the charting statistic by incorporating the exponentially weighted moving average control (EWMA) scheme, which results in a nonparametric counterpart of the classical multivariate EWMA (MEWMA). Some theoretical and numerical studies show that benefiting from using EL, the proposed chart possesses some favorable features. First, it is a data-driven scheme and thus is more robust to various multivariate non-normal data than the MEWMA chart under the in-control (IC) situation. Second, it is transformation-invariant and avoids the estimation of covariance matrix from the historical data by studentizing internally, and hence its IC performance is less deteriorated when the number of reference sample is small. Third, in comparison with the existing approaches, it is more efficient in detecting small and moderate shifts for multivariate non-normal process.     

Monitoring Variability and Analyzing Multivariate Autocorrelated Processes

Traditional multivariate quality control charts are based on independent observations. In this paper, we explain how to extend univariate residual charts to multivariate cases and how to combine the traditional statistical process control (SPC) approaches to monitor changes in process variability in a dynamic environment. We propose using Alt's (1984) W chart on vector autoregressive (VAR) residuals to monitor the variability for multivariate processes in the presence of autocorrelation. We study examples jointly using the Hotelling T² chart on VAR residuals, the W chart, and the Portmanteau test to diagnose the types of shift in process parameters.     

On the Run Length of a State-Space Control Chart for Multivariate Autocorrelated Data

The literature on statistical process control (SPC) describes the negative effects of autocorrelation in terms of the increase in false alarms. This has been treated by the individual modeling of each series or the application of VAR models. In the former case, the analysis of the cross correlation structure between the variables is altered. In the latter, if the cross correlation is not strong, the filtering process may modify the weakest relations. In order to improve these aspects, state-space models have been introduced in multivariate statistical process control (MSPC). This article presents a proposal for building a control chart for innovations, estimating its average run length to highlight its advantages over the VAR approach mentioned above.     

Multivariate Control Chart Based on Multivariate Smirnov Test

Robust control charts are useful in statistical process control (SPC) when there is limited knowledge about the underlying process distribution, especially for multivariate observations. This article develops a new robust and self-starting multivariate procedure based on multivariate Smirnov test (MST), which integrates a multivariate two-sample goodness-of-fit (GOF) test based on multivariate empirical distribution function (MEDF) and the change-point model. As expected, simulation results show that our proposed control chart is robust to nonnormally distributed data, and moreover, it is efficient in detecting process shifts, especially large shifts, which is one of the main drawbacks of most robust control charts in the literature. As it avoids the need for a lengthy data-gathering step, the proposed chart is particularly useful in start-up or short-run situations. Comparison results and a real data example show that our proposed chart has great potential for application.     

One-Class Classification-Based Control Charts for Monitoring Autocorrelated Multivariate Processes

In recent years, statistical process control (SPC) of multivariate and autocorrelated processes has received a great deal of attention. Modern manufacturing/service systems with more advanced technology and higher production rates can generate complex processes in which consecutive observations are dependent and each variable is correlated. These processes obviously violate the assumption of the independence of each observation that underlies traditional SPC and thus deteriorate the performance of its traditional tools. The popular way to address this issue is to monitor the residuals—the difference between the actual value and the fitted value—with the traditional SPC approach. However, this residuals-based approach requires two steps: (1) finding the residuals; and (2) monitoring the process. Also, an accurate prediction model is necessary to obtain the uncorrelated residuals. Furthermore, these residuals are not the original values of the observations and consequently may have lost some useful information about the targeted process. The main purpose of this article is to examine the feasibility of using one-class classification-based control charts to handle multivariate and autocorrelated processes. The article uses simulated data to present an analysis and comparison of one-class classification-based control charts and the traditional Hotelling's T ² chart.     

Robust design of adaptive control charts for manual manufacturing/inspection workstations

Often the manufacturing and the inspection workstations in a manufacturing process can coincide: thus, in these workstations the statistical process control (SPC) procedure of collecting sample statistics related to a critical-to-quality parameter is a task required to be done by the same worker who has to complete the working operations on a part. The aim of this study is to design a local SPC inspection procedure implementing an adaptive Shewhart control chart locally managed by the worker within the manufacturing workstation: the economic design of the inspection procedure is constrained by the expected number of false alarms issued and is restricted to those designs feasible with respect to the available shared labour resource. Furthermore, a robust approach that models the shift of the controlled parameter mean as a random variable is taken into account. The numerical analysis allows the most influencing environmental process factors to be captured and commented upon. The obtained results show that a few process operating parameters drive the choice of performing a robust optimization and the selection of the optimal SPC adaptive procedure.     

A Parameter-Tuned Genetic Algorithm for Economic-Statistical Design of Variable Sampling Interval X-Bar Control Charts for Non-Normal Correlated Samples

Among innovations and improvements that occurred in the past two decades on the techniques and tools used for statistical process control (SPC), adaptive control charts have shown to substantially improve the statistical and/or economical performances. Variable sampling intervals (VSI) control charts are one of the most applied types of the adaptive control charts and have shown to be faster than traditional Shewhart control charts in identifying small changes of concerned quality characteristics. While in the designing procedure of the VSI control charts the data or measurements are assumed independent normal observations, in real situations the validity of these assumptions is under question in many processes. This article develops an economic-statistical design of a VSI X-bar control chart under non-normality and correlation. Since the proposed design consists of a complex nonlinear cost model that cannot be solved using a classical optimization method, a genetic algorithm (GA) is employed to solve it. Moreover, to improve the performances, response surface methodology (RSM) is employed to calibrate GA parameters. The solution procedure, efficiency, and sensitivity analysis of the proposed design are demonstrated through a numerical illustration at the end.     

Monitoring simple linear profiles using variable sample size schemes

ABSTRACT

Profile monitoring is one of the new research areas in statistical process control. Most of the control charts in this area are designed with fixed sampling rate which makes the control chart slow in detecting small to moderate shifts. In order to improve the performance of the conventional fixed control charts, adaptive features are proposed in which, one or more design parameters vary during the process. In this paper the variable sample size feature of EWMA₃ and MEWMA schemes are proposed for monitoring simple linear profiles. The EWMA₃ method is based on the combination of three exponentially weighted moving average (EWMA) charts for monitoring three parameters of a simple linear profile separately and the Multivariate EWMA (MEWMA) chart is based on the using a single chart to monitor the coefficients and variance of a general linear profile. Also a two-sided control chart is proposed for monitoring the standard deviation in the EWMA₃ method. The performance of the proposed charts is compared in terms of the average time to signal. Numerical examples show that using adaptive features increase the power of control charts in detecting the parameter shifts. Finally, the performance of the proposed variable sample size schemes is illustrated through a real case in the leather industry.     

Profile Monitoring Using Nonparametric Bootstrap T 2 Control Chart

In certain statistical process control applications, performance of a product or process can be monitored effectively using a linear profile or a linear relationship between a response variable and one or more explanatory variables. In this article, we design a nonparametric bootstrap control chart for monitoring simple linear profiles based on T ² statistic. We evaluate the performance of the proposed method in phase II. The average and standard deviation of the run length under different shifts in the intercept, slope, and standard deviation are considered as the performance measures. Simulation results show that the performance of the proposed bootstrap control chart improves as the size of the available data increases.     

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.     

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 Variable Sample Size and Sampling Interval MSE Chart Based on Improved Square Root Transformation

In the field of statistical process control (SPC), control charts for attributes are widely used to detect the out-of-control condition by checking the number of nondefective units or nondefective in a sample. In this article, we use the average time to signal (ATS) and the average number of observations to signal (ANOS) to evaluate the performance of the optimal variable sample size and sampling interval (VSSI) improved square root transformation (ISRT) mean square error (MSE) (VSSI_ ISRT_ MSE) control chart for attribute data. In addition, this control chart will be used to monitor: (1) the difference between the process mean and the target value, and (2) the process variance shifts. We found that the optimal VSSI_ ISRT_ MSE chart performs better than the specific VSSI, the optimal variable sampling interval (VSI), and the fixed parameters (FP) ISRT_MSE charts. An example is given to illustrate this new proposed approach.     

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.     

EWNA charts for monitoring the mean and the autocovariances of stationary processes

In this paper various types of EWMA control charts are introduced for the simultaneous monitoring of the mean and the autocovariances. The target process is assumed to be a stationary process up to fourth-order or an ARMA process with heavy tailed innovations. The case of a Gaussian process is included in our results as well. The charts are compared within a simulation study. As a measure of the performance the average run length is taken. The target process is an ARMA (1,1) process with Student-t distributed innovations. The behavior of the charts is analyzed with respect to several out-of-control models. The best design parameters are determined for each chart. Our comparisons show that the multivariate EWMA chart applied to the residuals has the best overall performance.     

Multivariate Quality Control Chart for Autocorrelated Processes

Traditional multivariate statistical process control (SPC) techniques are based on the assumption that the successive observation vectors are independent. In recent years, due to automation of measurement and data collection systems, a process can be sampled at higher rates, which ultimately leads to autocorrelation. Consequently, when the autocorrelation is present in the data, it can have a serious impact on the performance of classical control charts. This paper considers the problem of monitoring the mean vector of a process in which observations can be modelled as a first-order vector autoregressive VAR (1) process. We propose a control chart called Z-chart which is based on the single step finite intersection test (Timm, 1996). An important feature of the proposed method is that it not only detects an out of control status but also helps in identifying variable(s) responsible for the out of control situation. The proposed method is illustrated with the help of suitable illustrations.     

Statistical control charts for monitoring the mean of a stationary process

Recently statistical process control (SPC) methodologies have been developed to accommodate autocorrelated data. A primary method to deal with autocorrelated data is the use of residual charts. Although this methodology has the advantage that it can be applied to any autocorrelated data it needs time series modeling efforts. In addition for a X residual chart the detection capability is sometimes small compared to the X chart and EWMA chart. Zhang (1998) proposed the EWMAST chart which is constructed by charting the EWMA statistic for stationary processes to monitor the process mean. The performance of the EWMAST chart the X chart the X residual chart and other charts were compared in Zhang (1998). In this paper comparisons are made among the EWMAST chart the CUSUM residual chart and EWMA residual chart as well as the X residual chart and X chart via the average run length.     

An integrated model based on statistical process control and maintenance for two-stage dependent processes

The close relationship between quality and maintenance of manufacturing systems has contributed to the development of integrated models which use the concept of statistical process control (SPC) and maintenance. This article demonstrates the integration of the Shewhart individual-residual (Z_X ? Z_e) joint control chart and maintenance for two-stage dependent processes by jointly optimizing their policies to minimize the expected total costs associated with quality, maintenance and inspection. To evaluate the effectiveness of the proposed model, two stand-alone models—a maintenance model and an SPC model—are proposed. Then a numerical example is given to illustrate the application of the proposed integrated model. The results show that the integrated model outperforms the two stand-alone models with regard to the expected cost per unit time. Finally, a sensitivity analysis is conducted to develop insights into time parameters and cost parameters that influence the integration efforts.     

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.     

Optimization of design parameters for control charts with multiple assignable causes

Duncan's economic model of Shewhart's original x¯ chart has established its optimal and economic application for processes with the Markovian failure characteristic. As the sample statistics show some indications of process variations, the variable-sampling-interval (VSI) control charts perform more effectively than the fixed sampling interval (FSI) ones due to a higher frequency in the sampling rate. Regarding the economic design of control charts, most studies have been dedicated to the FSI scheme. In 1998, Bai & Lee considered the production process with a single assignable cause and proposed an economic VSI design for a general x¯ control chart. However, in real cases, there are multiple assignable causes in the production process. Therefore, concerning the operation characteristics of the real industry, this research develops an economic model for the VSI control chart with multiple assignable causes based on stochastic and statistics theory and determines the optimal design parameters of the chart. A numerical example is also provided to demonstrate the effectiveness of the proposed model and the result indicates that VSI performs more effectively than a FSI control chart.     

An NP Control Chart Using Double Inspections

The np control chart is used widely in Statistical Process Control (SPC) for attributes. It is difficult to design an np chart that simultaneously satisfies a requirement on false alarm rate and has high detection effectiveness. This is mainly because one is often unable to make the in-control Average Run Length ARL₀ of an np chart close to a specified or desired value. This article proposes a new np control chart which is able to overcome the problems suffered by the conventional np chart. It is called the Double Inspection (DI) np chart, because it uses a double inspection scheme to decide the process status (in control or out of control). The first inspection decides the process status according to the number of non-conforming units found in a sample; and the second inspection makes a decision based on the location of a particular non-conforming unit in the sample. The double inspection scheme makes the in-control ARL₀ very close to a specified value and the out-of-control Average Run Length ARL₁ quite small. As a result, the requirement on a false alarm rate is satisfied and the detection effectiveness also achieves a high level. Moreover, the DI np chart retains the operational simplicity of the np chart to a large degree and achieves the performance improvement without requiring extra inspection (testing whether a unit is conforming or not).