1. Quality Control Methods

2. Control Charts > X (process location) >S (process variation) > R (process variation) > p (proportion) > c (proportion)

3. X Charts for Process Location For Known Parameters: > LCL = Lower Control Limit =  - 3  /  n > UCL = Upper Control Limit =  + 3  /  n n = sample size for one particular point

4. Out of Control Process Warnings 1. One point plots outside the 3  control limits. 2. Two out of three consecutive points plot beyond the 2  warning limits. 3. Four out of five consecutive points plot at a distance of 1  or beyond from the center line. 4. Eight consecutive points plot on one side of the center line.

5. Example: Process Charts A manufacturer is producing bolts and it is known that the length of the bolts from this process follows a Normal distribution with mean length = 0.50 inches and standard deviation = 0.03 in. What are the control limits and center line for a 3-sigma control chart with sample sizes of 9?

6. Process Capability Ratio (PCR) C p = USL – LSL 6  USL = Upper Specification Limit LSL = Lower Specification Limit

7. R Charts for Process Variation 3-Sigma Control Limits: UCL = r + 3 c n r / b n LCL = r – 3 c n r / b n For n  6, LCL = 0.

8. Example R Chart Piston rings for an automotive engine are produced by a forging process. We wish to establish control on natural variation before constructing an x chart because the control limits on the x chart depend on the process variability. Twenty-five samples, each of size five, have been taken when the process is considered in control. The inside diameter measurement data from these samples are summarized: x = 74.001 R = 0.023 What are the 3-sigma control limits for the R chart? c 5 =.864b 5 = 2.325