Detection of linear trends in process mean

In this paper, we develop a process control approach to detect linear trends in the process mean. A statistic based on the deviation between the target mean and the expected mean of the process is used in the development of the new approach. The statistic is shown to have a chi-square distribution. The approach is described and its performance is compared with cumulative sum (CUSUM), exponentially weighted moving average (EWMA), Shewhart, and generalized likelihood ratio (GLR) charts in detecting linear trends in the process mean. The results indicate that proposed approach is effective in detecting small to large trends. We also investigate the run length properties of the proposed approach under linear trends and compare its values with simulation results. Finally, we analyse the performance of the proposed approach in detecting the time when a drift occurs in the process and compare it with CUSUM and EWMA estimators. The results show that the proposed approach is more effective in detecting drift time for moderate and large trends.

[1]  A. R. Crathorne,et al.  Economic Control of Quality of Manufactured Product. , 1933 .

[2]  E. S. Page.  CONTINUOUS INSPECTION SCHEMES , 1954 .

[3]  D. A. Bell,et al.  Applied Statistics , 1953, Nature.

[4]  G. Box.  An analysis of transformations (with discussion) , 1964 .

[5]  D. A. Evans,et al.  An approach to the probability distribution of cusum run length , 1972 .

[6]  A. Willsky,et al.  A generalized likelihood ratio approach to the detection and estimation of jumps in linear systems , 1976 .

[7]  Donald J. Wheeler,et al.  Detecting a Shift in Process Average: Tables of the Power Function for X Charts , 1983 .

[8]  A. F. Bissell,et al.  The Performance of Control Charts and Cusums Under Linear Trend , 1984 .

[9]  Charles W. Champ,et al.  Exact results for shewhart control charts with supplementary runs rules , 1987 .

[10]  William H. Woodall,et al.  Performance of the Control Chart Trend Rule under Linear Shift , 1988 .

[11]  Charles W. Champ,et al.  Evaluation of control charts under linear trend , 1991 .

[12]  Fah Fatt Gan,et al.  Ewma control chart under linear drift , 1991 .

[13]  F. Gan.  Cusum Control Charts Under Linear Drift , 1992 .

[14]  Ken Nishina,et al.  A comparison of control charts from the viewpoint of change‐point estimation , 1992 .

[15]  Fah Fatt Gan.  Average Run Lengths for Cumulative Sum Control Charts Under Linear Trend , 1996 .

[16]  Tze Leung Lai,et al.  Efficient recursive algorithms for detection of abrupt changes in signals and control systems , 1999, IEEE Trans. Autom. Control..

[17]  Richard F. Gunst,et al.  Applied Regression Analysis , 1999, Technometrics.

[18]  Joseph J. Pignatiello,et al.  A magnitude‐robust control chart for monitoring and estimating step changes for normal process means , 2002 .

[19]  A Magnitude Robust Control Chart for Monitoring Process Dispersion Ogbonna Hopkins , 2002 .

[20]  George C. Runger,et al.  Control Charts for Monitoring Fault Signatures: Cuscore versus GLR , 2003 .

[21]  Fred Spiring,et al.  Introduction to Statistical Quality Control , 2007, Technometrics.