# Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-1 Chapter 8: Statistical Quality Control.

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Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-1 Chapter 8: Statistical Quality Control

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-2 Variation Common causes – variation resulting from process factors such as people, materials, methods, and measurement systems Special causes – variation that occurs sporadically and can be identified or explained

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-3 Statistical Process Control When only common causes of variation are present, a process is in control. If special causes of variation occur, the process is out of control. SPC is focused on identifying when special causes are present, or if a process is in control.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-4 SPC Methodology 1. Select a sample of observations from a process 2. Measure a quality characteristic 3. Record data 4. Calculate key statistics 5. Plot statistics on a control chart 6. Examine the chart for out-of-control conditions 7. Determine the cause and take corrective action

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-5 Run Charts and Control Charts Run chart – a line chart where the independent variable is time and the dependent variables is the value of a sample statistic Control chart – a run chart with control limits that describe limits of common cause variation

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-6 Control Chart Structure

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-7  x- and R-charts The  x-chart monitors the centering of a process over time as measured by the mean of each sample The R-chart monitors the variability in data as measured by the range of each sample

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-8 Example: Syringe Samples File

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-9 Run Chart of Sample Means

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-10 Run Chart of Sample Ranges

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-11 Control Limit Calculations UCL R = D 4 R LCL R = D 3 R UCL  x = x + A 2 R LCL  x = x - A 2 R

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-12 PHStat Tool: Control Charts PHStat menu > Control Charts > R & Xbar Charts Enter sample size and specify data range for ranges Select type of chart; for R and Xbar, specify data range for means Note: You must first compute ranges and means in your worksheet

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-13 PHStat Results

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-14 Example: R-Chart

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-15 Example:  x-Chart

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-16 In-Control Indicators No points outside control limits Number of points above and below center line about the same Points fall randomly above and below center line No steady upward or downward trends Most points, but not all are near the center line; only a few are close to control limits

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-17 Out-of-Control Indicator: Shift

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-18 Out-of-Control Indicator: Cycles

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-19 Out-of-Control Indicator: Trend

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-20 Out-of-Control Indicator: Hugging the Center Line

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-21 Out-of-Control Indicator: Hugging the Control Limits

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-22 Illustration of Mixture

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-23 Second Shift Control Chart Calculations

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-24 Second Shift Range Chart

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-25 Second Shift x-Chart

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-26 p-Chart p-Chart monitors the fraction nonconforming (fraction defective) for attribute data Control limits UCL p = p + 3s LCL p = p - 3s

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-27 PHStat Tool: p-Chart PHStat menu > Control Charts > p-Chart Enter data range Specify sample size; if variable, enter range of data

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-28 Example: Room Inspection Data

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-29 PHStat p-Chart Output

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-30 p-Charts With Variable Sample Sizes One approach: compute the average sample size and use this for calculating the standard deviation Acceptable as long as the sample sizes fall within 25 percent of the average.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-31 Example: Surgery Infections Data (Average Sample Size)

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-32 Statistical Issues in Control Chart Design Selection of sample data Rational subgroups Sample size Size influences the ability to detect different size shifts in processes Frequency of sampling Economic trade-offs

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-33 Process Capability Analysis Compare the distribution of process output to design specifications when only common causes are present. Process capability is measured by the proportion of output that can be produced within design specifications.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-34 Capable Process

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-35 Marginally Capable Process

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-36 Incapable Process

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-37 Process Capability Index C p is the ratio of the specification range to the natural variability of the process as measured by the standard deviation

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall8-38 Example: Syringe Data Specifications of syringe lengths are 4.950  0.030 inches C p = (4.98 - 4.92)/(0.039) = 1.54