1. 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 pp
GMA Plans – Lecture 2/10/04 for Baltimore Section, ASQ
Group Moving Average Template Instructions
Group Moving Average Template
Link to Excel file

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

3. 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

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

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

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

8. 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

9. 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

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

11. Fig 9 - Plotted GMAs - .75 Shift
Cluttered

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

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

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

15. Fig 11 – 1.75 S shift
m=3 first

16. Fig 12 – X, MR charts
pt #3 caught it

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