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Effective Use of Control Charts for Process Quality

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  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 LocationFor Known Parameters:> LCL = Lower Control Limit =  - 3  / n> UCL = Upper Control Limit =  + 3  / nn = sample size for one particular point

  4. Out of Control Process Warnings1. 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 ChartsA 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)Cp = USL – LSL 6 USL = Upper Specification Limit LSL = Lower Specification Limit

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

  8. Example R ChartPiston 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 = 0.023What are the 3-sigma control limits for the Rchart? c5 = .864 b5 = 2.325

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