1. Process Control Charts By: Brian Murphy

2. Control Charts are an on-line process- monitoring technique. Used to determine if a process is capable or out of control. In control processes operate with only chance causes of variation. Out of control processes have assignable causes of variation and can be restructured when identified.

3. Control Chart Contains ◦A center line (usually the arithmetic mean or the average of a collection of sample ranges) ◦A Lower and Upper Control Limit (LCL and UCL) ◦Points beyond the control limits indicate that the process is out of control.

4. Formulas: ◦x ave = grand average of x = (x 1 +x 2 +…+x m )/m Or R=x max -x min R 1, R 2,…,R m : ranges of m samples R ave = (R 1 +R 2 +…+R m )/m

5. Control Limits for R chart: ◦UCL = D 4 *R ave ◦Center Line = R ave ◦LCL = D 3 *R ave Control Limits for x chart: ◦UCL = x ave + A 2 *R ave ◦Center Line = x ave ◦LCL = x ave –A 2 *R ave *See next slide for values of D 3, D 4 and A 2

6. nA2A2 D3D3 D4D4 21.8803.267 31.02302.574 40.72902.282 50.57702.114 60.48302.004 70.4190.0761.924 80.3730.1361.864 90.3370.1841.816 100.3080.2231.777 *n denotes sample size

7. Rules for determining out of control process: