Benjamin M. Adams

An evaluation of forecast-based quality control schemes

High volume production processes and many processes using automated sampling technology yield process data which are autocorrelated. One technique proposed for monitoring autocorrelated data involves the application of the Individuals control chart to forecast residuals from an appropriate time series model of the process. This study examines the following issues concerning forecast-based monitoring schemes: (i) the affect of forecast recovery from step changes on the average run length (ARL) of control charts applied to forecast residuals (ii) the proposal of the cumulative distribution function (CDF) of the run lengths as an appropriate criterion for chart comparisons and (iii) the relative performance of the Individuals control chart, the Cumulative Sum (CUSUM) control chart and the Exponentially Weighted Moving Average control chart applied to forecast residuals using both the ARL and CDF criteria

An analysis of Taguchi's on-line process-control procedure under a random-walk model

The assumptions of the on-line process-control methods presented by Taguchi, Elsayed, and Hsiang (1989) are examined. Taguchis method for obtaining control strategies is evaluated for the random-walk case. A method for approximating optimal control strategies is presented and compared with results obtained using Taguchis method, with a new modification of Taguchis method, and with simulation results.

Combined Control Charts for Forecast-Based Monitoring Schemes

The problem of monitoring autocorrelated process data is discussed. Several forecast-based monitoring schemes are evaluated using a Markov chain approach to determine types of process shift and evaluation criteria. A combined exponentially weighte..

Robustness of Forecast-Based Monitoring Schemes

Forecast-based monitoring schemes for monitoring autocorrelated data are two stages processes. The first step is to determine an appropriate time-series model for the process data. The process is then monitored using control charts applied to the one-st..

Alternative Designs of the Hodges-Lehmann Control Chart

The Hodges-Lehmann control chart was proposed as a nonparametric alternative to the classical control chart. The proposed technique for establishing control limits produces control charts with in-control average run lengths (ARL~s) quite different from ..

Monitoring autocorrelated processes with an exponentially weighted moving average forecast

Traditional control charts such as the Shewhart chart, cumulative sum (CUSUM) chart and exponentially weighted moving average (EWMA) chart have been shown to be adversely affected by the presence of autocorrelation in data. Monitoring schemes which use these traditional control charts in conjunction with time series based forecasts have been proposed and shown to have properties superior to schemes based on traditional charts alone. The performance of the Shewhart, EWMA, and CUSUM charts on EWMA forecast errors is investigated. It is shown that the EWMA forecast does not adequately account for autocorrelation for processes following an AR(1) model. As a result, the standard control charts on forecast errors display unexpected statistical properties.

Robust Monitoring of Contaminated Data

Monitoring a process that has contaminated data with traditional control charts such as Shewharts X̄ chart and the Range chart results in an excessive number of false alarms. Robust control charts such as the Median and IQR charts are a better alternative to traditional charts for a process with contaminated data because the effects of the outlying data values are eliminated. However, process shifts are not detected as quickly with the robust charts. This paper introduces a diagnostic statistic technique that uses traditional control chart methods augmented by diagnostic tools. Performance measures for traditional, robust, and diagnostic statistic control chart systems for n = 5 are reported. Contour plots for n = 3 and n = 5 are provided to allow for interpolation of parameter values. The diagnostic statistic technique improves work stoppage (comparable to average run length) rates for contaminated data and maintains the ability to identify process shifts.

The reverse moving average control chart for monitoring autocorrelated processes

Forecast-based monitoring schemes have been researched extensively in regards to applying traditional control charts to forecast errors arising from various autocorrelated processes. The dynamic response and behavior of forecast errors after experiencing a shift in the process mean make it difficult to choose a suitable control chart. In this paper we propose the reverse moving average control chart as a new forecast-based monitoring scheme, compare the new control chart to traditional methods applied to various ARMA(1,1), AR(1), and MA(1) processes, and make recommendations concerning the most appropriate control chart to use in a variety of situations when charting autocorrelated processes.

THE MULTIVARIATE CONTROL WEB

The display of multivariate data has become a significant problem for the user of statistical process control (SPC) techniques. Though many graphical developments such as Chernoff faces, Andrews curves, STARs, and glyphs, among others, have appeared in ..

Multivariate SPC for recipe preservation of batch processes

The performances of the Hotellings T2 control chart and the squared prediction error control chart based on the multi-way principal component analysis are evaluated for monitoring within batch process variation for the purpose of recipe preservation. A nonlinear model for simulated batch process data is provided. The model allows for cross correlation of error terms at a given time period and serial correlation of error terms across time periods. The performance characterizations of the two monitoring schemes are provided for a variety of levels of cross correlation and serial correlation. The impact of the time period at which process shifts occur is also investigated for the monitoring schemes. The T2 control chart is recommended for the cases considered. Copyright