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Effective Use of Control Charts for Process Quality

This guide explores various quality control methods, focusing on X-Charts for process location, R-Charts for process variation, p-Charts for proportions, and c-Charts for known parameters. Learn how to identify and respond to out-of-control process warnings, with examples provided for better understanding. Discover how to calculate control limits and center line for different types of control charts based on sample sizes and process specifications. Ensure process capability using Process Capability Ratio (PCR) calculations. Gain insights into establishing control on natural variations before constructing control charts, with a detailed example on calculating 3-sigma control limits for the R-chart.

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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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