Group Moving Average Template Instructions x Group Moving Averages (GMA) Process Control Plans by Sidney J. Lewis For ASQ, Baltimore Section February 10, 2004 Reference: Ross, S. Sparks, “ A group of Moving Averages Control Plan for Signaling Varying Location Shifts”, Quality Engineering, Vol. 15, No. 4, 2003 pp519-532 GMA Plans – Lecture 2/10/04 for Baltimore Section, ASQ   Group Moving Average Template Instructions Group Moving Average Template Link to Excel file

Introduction A control chart type Purposes of CC: shifts, trends, changes of variation Identifies extend of random variation: Control Limits

Fig 1A - Raw data, and GMA Explain M A Fig 1A - data statistics note the variation in n=50 samples Fig 2 - Control Limits vs sample size Extent of R.V. determined by size

Fig 3 - Detect Shifts vs Sample Size Fig 4 - ARL vs Probability

Fig 5 - X, MR Charts: In control Excel generated: Mean 65, Sigma 2

Fig 1C - Limits, Z-Scores Limits Z-scores Scaled Z-scores Significance test column

Fig. 6 Fig 6 - Detecting shifts with GMAs Each GMA starts with target plus data points Plot Probability of an alarm vs sample size shift of .75: may be detected first with small samples, but most likely with large (m=8) Shift = 1.75: m=3 should signal by 2nd point (n=6) P=50% equiv to ARL=2 Can’t use runs! need independent points Large shifts caught by small samples; Small shifts need large samples

Fig 7 – .75 shift at #21 First by m=18 (pt 15) Last by m=3 (pt 17) GMA plots Fig 7 - different limits for GMAs, Z-scores same limits for Scaled

Fig 8 - X, MR chart of .75 shift pt 17

Fig 9 - Plotted GMAs - .75 Shift Cluttered

Fig 9A - Z-scores - .75 Shift Less cluttered

 Fig 9B - Scaled Z-Scores - .75 Shift Clean m=18 first signal Options: table form (Fig 7) or Plot (9B)

Fig 10 – In-Control GMAs, Scaled Z All points w/i limits

Fig 11 – 1.75 S shift m=3 first

Fig 12 – X, MR charts pt #3 caught it

Fig 13 – 1.75 Shift, GMA and Scaled Z-Scores plots