A neural network-based procedure for the monitoring of exponential mean

Control charts are widely used for both manufacturing and service industries. Cumulative sum (CUSUM) charts are known to be very sensitive in detecting small shifts in the mean. In this paper, we propose a neural network as an alternative approach to CUSUM charts when monitoring exponential mean. The performance of neural network was evaluated by estimating the average run lengths (ARLs) using simulation. The results obtained with simulated data suggest that control scheme based on neural network is significantly more sensitive to process shifts than CUSUM charts. This research also examines the feasibility of using CUSUM chart and neural network together in detecting process mean shifts. The results indicate that using the two methods in combination is more effective than using the methods separately.     

Enhancing the performance of CUSUM scale chart

Control charts act as the most important statistical process monitoring tool, widely used for the purpose of identifying unusual variations in process parameters. Researchers have implemented different rules to increase the sensitivity of Shewhart, CUSUM and EWMA control charts for the detection of small shifts in process location. However, for the monitoring of process scale, the use of such rules has been limited to Shewhart charts. This study proposes the implementation of sensitizing rules in CUSUM scale charts to enhance their ability to detect smaller changes in process variability. The performance of the proposed schemes is evaluated and compared with the simple scale CUSUM scheme, the EWMS chart, the M-EWMS chart and the COMB chart, in terms of run length characteristics such as average run length (ARL) and standard deviation of the run length distribution (SDRL). Control chart coefficients to set the ARL at the desired level are also provided. Two numerical examples are given to illustrate the application of the proposed schemes on practical data sets.     

On efficient use of auxiliary information for control charting in SPC

In Statistical Process Control (SPC), monitoring of the process dispersion has a major impact on the performance of processes like manufacturing, management and services. Control charts act as the most important SPC tool, used to differentiate between common and special cause variations in the process. The use of auxiliary information can enhance the detection ability of control charts and hence an efficient monitoring of process parameter(s) can be done. This study deals with the Shewhart type variability control charts based on auxiliary characteristics for the non-cascading processes, assuming stability of auxiliary parameters. The control chart structures of these variability charts are provided and their performance evaluations are carried out in terms of average run length (ARL), relative average run length (RARL) and extra quadratic loss (EQL) under the normal and t distributed process environments. The comparisons have been made among different variability charts and superiorities are established based on their detection abilities for different amounts of shifts in process dispersion. An illustrative example is also provided in support of the theory, and finally the study ends with concluding remarks and suggestions for future research.     

Simultaneous process mean and variance monitoring using artificial neural networks

Control chart patterns (CCPs) can be employed to determine the behavior of a process. Hence, CCP recognition is an important issue for an effective process-monitoring system. Artificial neural networks (ANNs) have been applied to CCP recognition tasks and promising results have been obtained. It is well known that mean and variance control charts are usually implemented together and that these two charts are not independent of each other, especially for the individual measurements and moving range (X–R_m) charts. CCPs on the mean and variance charts can be associated independently with different assignable causes when corresponding process knowledge is available. However, ANN-based CCP recognition models for process mean and variance have mostly been developed separately in the literature with the other parameter assumed to be under control. Little attention has been given to the use of ANNs for monitoring the process mean and variance simultaneously. This study presents a real-time ANN-based model for the simultaneous recognition of both mean and variance CCPs. Three most common CCP types, namely shift, trend, and cycle, for both mean and variance are addressed in this work. Both direct data and selected statistical features extracted from the process are employed as the inputs of ANNs. The numerical results obtained using extensive simulation indicate that the proposed model can effectively recognize not only single mean or variance CCPs but also mixed CCPs in which mean and variance CCPs exist concurrently. Empirical comparisons show that the proposed model performs better than existing approaches in detecting mean and variance shifts, while also providing the capability of CCP recognition that is very useful for bringing the process back to the in-control condition. A demonstrative example is provided.     

A control chart based on likelihood ratio test for detecting patterned mean and variance shifts

Control charts based on generalized likelihood ratio test (GLRT) are attractive from both theoretical and practical points of view. Most of the existing works in the literature focusing on the detection of the process mean and variance are almost based on the assumption that the shifts remain constant over time. The case of the patterned mean and variance changes may not be well discussed. In this research, we propose a new control chart which integrates the exponentially weighted moving average (EWMA) procedure with the GLRT statistics to monitor the process with patterned mean and variance shifts. The attractive advantage of our control chart is its reference-free property. Due to the good properties of GLRT and EWMA procedures, our simulation results show that the proposed chart provides quite effective and robust detecting ability for various types of shifts. The implementation of our proposed control chart is illustrated by a real data example from chemical process control.     

Performance of t control charts in short runs with unknown shift sizes

Recently, control charts plotting a statistic having a Student’s t distribution have been proposed as an efficient solution to perform Statistical Process Control (SPC) in short production runs where the shift size of the in-control process mean from μ₀ to μ₁ is known a priori. The shift size is usually measured as a multiple δ of the in-control process standard deviation σ₀: but in practice, at the beginning of the production run, both the value of next shift δ and σ₀ are unknown. As a consequence, when the actual shift size differs from the value assumed at the chart design stage, the performance of the control chart can be seriously affected. To overcome this problem, this paper investigates the statistical performance of the Shewhart, EWMA and CUSUM t charts for short production runs when the shift size is unknown and modeled by means of a statistical distribution. An extensive numerical analysis allows the properties of the three charts to be compared and discussed when uniform and triangular distributions are used by quality practitioners to fit the unknown shift size. An illustrative example is utilized to demonstrate a practical implementation of the best performing among the three investigated charts.     

A study of process monitoring based on inverse Gaussian distribution

The inverse Gaussian distribution has considerable applications in describing product life, employee service times, and so on. In this paper, the average run length (ARL) unbiased control charts, which monitor the shape and location parameters of the inverse Gaussian distribution respectively, are proposed when the in-control parameters are known. The effects of parameter estimation on the performance of the proposed control charts are also studied. An ARL-unbiased control chart for the shape parameter with the desired ${\mathit{ARL}}_0$, which takes the variability of the parameter estimate into account, is further developed. The performance of the proposed control charts is investigated in terms of the ARL and standard deviation of the run length. Finally, an example is used to illustrate the proposed control charts.     

A phase II nonparametric control chart based on precedence statistics with runs-type signaling rules

Nonparametric control charts do not require knowledge about the shape of the underlying distribution and can thus be attractive in certain situations. Two new Shewhart-type nonparametric control charts are proposed for monitoring the unknown location parameter of a continuous population in Phase II (prospective) applications. The charts are based on control limits given by two specified order statistics from a reference sample, obtained from a Phase I (retrospective) analysis, and using some runs-type signaling rules. The plotting statistic can be any order statistic in a Phase II sample; the median is used here for simplicity and robustness. Exact run length distributions of the proposed charts are derived using conditioning and some results from the theory of runs. Tables are provided for practical implementation of the charts for a given in-control average run length between 300 and 500. Comparisons of the average run length ARL, the standard deviation of run length (SDRL) and some run length percentiles show that the charts have robust in-control performance and are more efficient when the underlying distribution is t (symmetric with heavier tails than the normal) or gamma (1, 1) (right-skewed). Even for the normal distribution, the new charts are quite competitive. An illustrative numerical example is given. An added advantage of these charts is that they can be applied before all the data are collected which might lead to savings in time and resources in certain applications.     

Online monitoring and fault identification of mean shifts in bivariate processes using decision tree learning techniques

With modern data collection system and computers used for on-line process monitoring and fault identification in manufacturing processes, it is common to monitor more than one correlated process variables simultaneously. The main problems in most multivariate control charts (e.g., T ² charts, MCUSUM charts, MEWMA charts) are that they cannot give direct information on which variable or subset of variables caused the out-of-control signals. A Decision Tree (DT) learning based model for bivariate process mean shift monitoring and fault identification is proposed in this paper under the assumption of constant variance-covariance matrix. Two DT classifiers based on the C5.0 algorithm are built, one for process monitoring and the other for fault identification. Simulation results show that the proposed model can not only detect the mean shifts but also give information on the variable or subset of variables that cause the out-of-control signals and its/their deviate directions. Finally a bivariate process example is presented and compared with the results of an existing model.     

A new approach to detecting the process changes for multistage systems

The study aims to develop a new control chart model suitable for monitoring the process quality of multistage manufacturing systems.Considering both the auto-correlated process outputs and the correlation occurring between neighboring stages in a multistage manufacturing system, we first propose a new multiple linear regression model to describe their relationship. Then, the multistage residual EWMA and CUSUM control charts are used to monitor the overall process quality of multistage systems. Moreover, an overall run length (ORL) concept is adopted to compare the detecting performance for various multistage residual control charts. Finally, a numerical example with oxide thickness measurements of a three-stage silicon wafer manufacturing process is given to demonstrate the usefulness of our proposed multistage residual control charts in the Phase II monitoring. A computerized algorithm can also be written based on our proposed scheme for the multistage residual EWMA/CUSUM control charts and it may be further converted to an expert and intelligent system. Hopefully, the results of this study can provide a better alternative for detecting process change and serve as a useful guideline for quality practitioners when monitoring and controlling the process quality of multistage systems with auto-correlated data.     

Improved quality of continuous flow manufacturing through the combination of statistical process control and conventional computer process control

This paper represents a portion of the evaluation of the use of Statistical Process Control within the realm of Conventional Computer Process Control. Various control charts commonly utilized in continuous processes are evaluated when subjected to process disturbances typical of continuous processes. The control charts considered are the Moving Average and Moving Range Chart combination, the Individual and Moving Range Chart combination, and the Exponentially Weighted moving Average Chart. The types of process disturbances considered are unit step and linear trend disturbances to the process average. The evaluation is based on the determination of the Average Run Lengths (ARLs) resulting from computer simulations.     

A hybrid fuzzy-statistical clustering approach for estimating the time of changes in fixed and variable sampling control charts

Control charts are the most popular Statistical Process Control (SPC) tools used to monitor process changes. When a control chart produces an out-of-control signal, it means that the process has changed. However, control chart signals do not indicate the real time of the process changes, which is essential for identifying and removing assignable causes and ultimately improving the process. Identifying the real time of the process change is known as change-point estimation problem. Most of the traditional change-point methods are based on maximum likelihood estimators (MLE) which need strict statistical assumptions. In this paper, first, we introduce clustering as a potential tool for change-point estimation. Next, we discuss the challenges of employing clustering methods for change-point estimation. Afterwards, based on the concepts of fuzzy clustering and statistical methods, we develop a novel hybrid approach which is able to effectively estimate change-points in processes with either fixed or variable sample size. Using extensive simulation studies, we also show that the proposed approach performs considerably well in all considered conditions in comparison to powerful statistical methods and popular fuzzy clustering techniques. The proposed approach can be employed for processes with either normal or non-normal distributions. It is also applicable to both phase-I and phase-II. Finally, it can estimate the true values of both in- and out-of-control states’ parameters.     

Adaptive CUSUM procedures with Markovian mean estimation

This paper proposes using a Markovian-type mean estimating procedure in the conventional cumulative sum (CUSUM) control scheme to update its reference value in an adaptive way. This generalizes a class of Markovian adaptive CUSUM (ACUSUM) schemes to achieve the aim of providing an overall good performance over a range of future expected but unknown mean shifts. A two-dimensional Markov chain model is developed to analyze the run length performance of the new scheme. A comparison of run length performance of the proposed ACUSUM scheme and other control charts is shown favorable to the former.     

A control point methodology for CUSUM control charts

A control point methodology (CPM) is proposed for implementation of graphical cumulative-sum (CUSUM) control charts on computers. Currently, most computer implementation of CUSUM charts is based on tabular form which loses the distinguished look of CUSUM statistics and V-mask. The more intuitive graphical CUSUM charts are not popular due to the difficulty of computer implementation. CPM removes the need to store all CUSUM points and thus reduces computing time. Examples are given to show that the proposed method can be applied to CUSUM for both means and ranges.     

Adaptive CUSUM control chart with variable sampling intervals

The standard cumulative sum chart (CUSUM) is widely used for detecting small and moderate process mean shifts, and its optimal detection ability for any pre-specified mean shift has been demonstrated by its equivalence to continuous sequential tests. In real practice, the assumption of knowing the true mean shift in prior cannot be always met. So it is desirable to design a procedure that is efficient for detecting a range of future expected but unknown mean shifts. Adaptive CUSUM control chart, which can continuously adjust itself by a one-step forecasting operator, has been proposed to detect efficiently and robustly for a range of mean shifts in the early literature. Moreover, in terms of sampling time to signal, control chart with the VSI (variable sampling intervals) feature can detect the process changes more quickly than the traditional FSI (fixed sample intervals) chart. In this paper, a new CUSUM control chart which is based on both adaptive and VSI features is discussed. Also, a two-dimensional Markov chain model is developed to evaluate its run-time performance.     

Optimal linear combination of Poisson variables for multivariate statistical process control

In this paper we analyze the monitoring of p Poisson quality characteristics simultaneously, developing a new multivariate control chart based on the linear combination of the Poisson variables, the LCP control chart. The optimization of the coefficients of this linear combination (and control limit) for minimizing the out-of-control ARL is constrained by the desired in-control ARL. In order to facilitate the use of this new control chart the optimization is carried out employing user-friendly Windows© software, which also makes a comparison of performance between this chart and other schemes based on monitoring a set of Poisson variables; namely a control chart on the sum of the variables (MP chart), a control chart on their maximum (MX chart) and an optimized set of univariate Poisson charts (Multiple scheme). The LCP control chart shows very good performance. First, the desired in-control ARL (ARL₀) is perfectly matched because the linear combination of Poisson variables is not constrained to integer values, which is an advantage over the rest of charts, which cannot in general match the required ARL₀ value. Second, in the vast majority of cases this scheme signals process shifts faster than the rest of the charts.     

Statistical process control: what you don't measure can hurt you!

Statistical control charts are the most commonly used tools to analyze and monitor process variation and stability. Control charts help us isolate nonrandom causes of variation by plotting a measured attribute of the process over time; the upper and lower control limits are empirically derived from the measurements of process variation over time. If a data point falls outside the control limits, we assume that a nonrandom cause of variation is present. It is important that the control limits appropriately reflect the expected behavior of the process being measured. Measuring the number of escaped defects will alert us to problems in the inspection process even though the control charts might not be showing anything abnormal.     

Variable control scheme in the cascade processes

The article considers the variables process control scheme for cascade processes. We construct variable sample sizes and sampling intervals (VSSI) control charts to effectively monitor the input variable and the output variable produced by a cascade process. The performance of the proposed VSSI control charts is measured by the adjusted average time to signal derived by a Markov chain approach. An example of the metallic film thickness of the computer connectors system shows the application and the performance of the proposed VSSI control charts in detecting shifts in means of the cascade process. Furthermore, the performance of the proposed VSSI control charts and the fixed sample sizes and sampling intervals control charts are compared by numerical analysis results. These demonstrate that the former is much faster in detecting small and medium shifts. The optimum VSSI control charts are also proposed using optimization technique when quality engineers cannot specify the values of the variable sample sizes and sampling intervals. It has been found that the optimum VSSI control charts work and are thus suggested whenever quality engineers cannot specify the values of variable sample sizes and sampling intervals. Furthermore, the impacts of misusing Shewhart charts to monitoring the process means on the cascade process are also investigated.     

OWave control chart for monitoring the process mean

In this paper a control chart for monitoring the process mean, called OWave (Orthogonal Wavelets), is proposed. The statistic that is plotted in the proposed control chart is based on weighted wavelets coefficients, which are provided through the Discrete Wavelets Transform using Daubechies $\mathit{db}2$ wavelets family. The statistical behavior of the wavelets coefficients when the mean shifts are occurring is presented, and the distribution of wavelets coefficients in the case of normality and independence assumptions is provided. The on-line algorithm of implementing the proposed method is also provided. The detection performance is based on simulation studies, and the comparison result shows that OWave control chart performs slightly better than Fixed Sample Size and Sampling Intervals control charts ($\overline{X}$, EWMA, CUSUM) in terms of Average Run Length. In addition, illustrative examples of the new control chart are presented, and an application to Tennessee Eastman Process is also proposed.