Marcus B. Perry

Control chart pattern recognition using back propagation artificial neural networks

In this paper, control chart pattern recognition using artificial neural networks is presented. An important motivation of this research is the growing interest in intelligent manufacturing systems, specifically in the area of Statistical Process Control (SPC). Online automated process analysis is an important area of research since it allows the interfacing of process control with Computer Integrated Manufacturing (CIM) techniques. Two back-propagation artificial neural networks are used to model traditional Shewhart SPC charts and identify out-of-control situations as specified by the Western Electric Statistical Quality Control Handbook , including instability patterns, trends, cycles, mixtures and systematic variation. Using back propagation, patterns are presented to the network, and training results in a suitable model for the process. The implication of this research is that out-of-control situations can be detected automatically and corrected within a closed-loop environment. This research is the first step in an automated process monitoring and control system based on control chart methods. Results indicate that the performance of the back propagation neural networks is very accurate in identifying control chart patterns.

ESTIMATING THE CHANGE POINT OF A POISSON RATE PARAMETER WITH A LINEAR TREND DISTURBANCE

Knowing when a process changed would simplify the search and identification of the special cause. In this paper, we compare the maximum likelihood estimator (MLE) of the process change point designed for linear trends to the MLE of the process change point designed for step changes when a linear trend disturbance is present. We conclude that the MLE of the process change point designed for linear trends outperforms the MLE designed for step changes when a linear trend disturbance is present. We also present an approach based on the likelihood function for estimating a confidence set for the process change point. We study the performance of this estimator when it is used with a cumulative sum (CUSUM) control chart and make direct performance comparisons with the estimated confidence sets obtained from the MLE for step changes. The results show that better confidence can be obtained using the MLE for linear trends when a linear trend disturbance is present. Copyright

ESTIMATION OF THE CHANGE POINT OF A NORMAL PROCESS MEAN WITH A LINEAR TREND DISTURBANCE

Abstract Knowing when a process changed would simplify the search and identification of the special cause. In this paper, we compare the maximum likelihood estimator (MLE) of the process change point designed for linear trends to the MLE of the process change point designed for step changes when a linear trend disturbance is present. As expected, our conclusions show that the MLE of the process change point designed for linear trends outperforms the MLE designed for step changes when the change type is a linear trend. We also present an approach based on the likelihood function for estimating a confidence set for the process change point. We study the performance of this estimator when it is used with a Shewhart x control chart and make direct performance comparisons with the estimated confidence sets obtained from the MLE for step changes. As expected, results show that better confidence can be obtained using the MLE for linear trends when a linear trend disturbance is present.

Estimating the Change Point of the Process Fraction Non-conforming with a Monotonic Change Disturbance in SPC

Knowing when a process has changed would simplify the search for and identification of the special cause. In this paper, we propose a maximum-likelihood estimator for the change point of the process fraction non-conforming without requiring knowledge of the exact change type a priori. Instead, we assume the type of change present belongs to a family of monotonic changes. We compare the proposed change-point estimator to the maximum-likelihood estimator for the process change point derived under a simple step change assumption. We do this for a number of monotonic change types and following a signal from a binomial cumulative sum (CUSUM) control chart. We conclude that it is better to use the proposed change point estimator when the type of change present is only known to be monotonic. The results show that the proposed estimator provides process engineers with an accurate and useful estimate of the time of the process change regardless of the type of monotonic change that may be present. Copyright

CHANGE POINT ESTIMATION FOR MONOTONICALLY CHANGING POISSON RATES IN SPC

Knowing when a process has changed would simplify the search for and identification of the special cause. Although several change point methods have been suggested, many of them rely on the assumption that the effect present in the process output follows some known form (e.g. sudden shift or linear trend). Since processes are often influenced by several input factors, sudden shifts and linear trends do not always adequately describe the true nature of the process behavior. In this paper, we propose a maximum likelihood estimator for the change point of a Poisson rate parameter without requiring exact a priori knowledge regarding the form of the effect present. Instead, we assume the form of effect present can be characterized as belonging to the set of monotonic effects. We compare the proposed change point estimator to the commonly used maximum likelihood estimator for the process change point derived under a sudden and persistent shift assumption. We do this for a number of monotonic effects and following a signal from a Poisson CUSUM control chart. We conclude that it is better to use the proposed change point estimator when the form of the effect present is only known to be monotonic. The results show that the proposed estimator provides process engineers with an accurate and useful estimate of the last observation obtained from the unchanged process regardless of the form of monotonic effect that may be present.

ESTIMATION OF THE CHANGE POINT OF THE PROCESS FRACTION NONCONFORMING IN SPC APPLICATIONS

Knowing when a process has changed would simplify the search for and identification of the special cause. In this paper, we compare the maximum likelihood estimator (MLE) of the process change point (that is, when the process changed) to built-in change point estimators from binomial CUSUM and EWMA control charts. We conclude that it is better to use the maximum likelihood change point estimator when a CUSUM or EWMA control chart signals a change in the process fraction nonconforming. The results show that the MLE provides process engineers with an accurate and useful estimate of the last subgroup from the unchanged process.

A change point model for the location parameter of exponential family densities

Knowing when a process has changed would simplify the search for and identification of the special cause. Consequently, having an estimate of the process change point following a control chart signal would be useful to process engineers. In this research a maximum likelihood change point estimator is proposed for the natural location parameter of densities belonging to the exponential family. It is assumed that the behavior in the location parameter over discrete sampling intervals is adequately modeled by a linear predictor. The estimator is intended to be applied to data obtained following signals from univariate statistical process control charts in an effort to aid process engineers diagnose the root cause of process change.

Identifying the time of step change in the mean of autocorrelated processes

Control charts are used to detect changes in a process. Once a change is detected, knowledge of the change point would simplify the search for and identification of the special cause. Consequently, having an estimate of the process change point following a control chart signal would be useful to process analysts. Change-point methods for the uncorrelated process have been studied extensively in the literature; however, less attention has been given to change-point methods for autocorrelated processes. Autocorrelation is common in practice and is often modeled via the class of autoregressive moving average (ARMA) models. In this article, a maximum likelihood estimator for the time of step change in the mean of covariance-stationary processes that fall within the general ARMA framework is developed. The estimator is intended to be used as an “add-on” following a signal from a phase II control chart. Considering first-order pure and mixed ARMA processes, Monte Carlo simulation is used to evaluate the performance of the proposed change-point estimator across a range of step change magnitudes following a genuine signal from a control chart. Results indicate that the estimator provides process analysts with an accurate and useful estimate of the last sample obtained from the unchanged process. Additionally, results indicate that if a change-point estimator designed for the uncorrelated process is applied to an autocorrelated process, the performance of the estimator can suffer dramatically.

Identifying the time of polynomial drift in the mean of autocorrelated processes

Control charts are used to detect changes in a process. Once a change is detected, knowledge of the change point would simplify the search for and identification of the special ause. Consequently, having an estimate of the process change point following a control chart signal would be useful to process engineers. This paper addresses change point estimation for covariance-stationary autocorrelated processes where the mean drifts deterministically with time. For example, the mean of a chemical process might drift linearly over time as a result of a constant pressure leak. The goal of this paper is to derive and evaluate an MLE for the time of polynomial drift in the mean of autocorrelated processes. It is assumed that the behavior in the process mean over time is adequately modeled by the kth-order polynomial trend model. Further, it is assumed that the autocorrelation structure is adequately modeled by the general (stationary and invertible) mixed autoregressive-moving-average model. The estimator is intended to be applied to data obtained following a genuine control chart signal in efforts to help pinpoint the root cause of process change. Application of the estimator is demonstrated using a simulated data set. The performance of the estimator is evaluated through Monte Carlo simulation studies for the k=1 case and across several processes yielding various levels of positive autocorrelation. Results suggest that the proposed estimator provides process engineers with an accurate and useful estimate for the last sample obtained from the unchanged process. Copyright

Estimating the time of step change with Poisson CUSUM and EWMA control charts

Knowing when a process has changed would simplify the search for and identification of the special cause. Consequently, having an estimate of the process change point following a control chart signal would be useful to process engineers. Much of the literature on change point models and techniques for statistical process control applications consider processes well modelled by the normal distribution. However, the Poisson distribution is commonly used in industrial quality control applications for modelling attribute-based process quality characteristics (e.g., counts of non-conformities). Some commonly used control charts for monitoring Poisson distributed data are the Poisson cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts. In this paper, we study the effect of changes in the design of the control chart on the performances of the change point estimators offered by these procedures. In particular, we compare root mean square error performances of the change point estimators offered by the Poisson CUSUM and EWMA control charts relative to that achieved by a maximum likelihood estimator for the process change point. Results indicate that the relative performance achieved by each change point estimator is a function of the corresponding control chart design. Relative mean index plots are provided to enable users of these control charts to choose a control chart design and change point estimator combination that will yield robust change point estimation performance across a range of potential change magnitudes.