1. Section 14.3-1 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Lecture Slides Elementary Statistics Twelfth Edition and the Triola Statistics Series by Mario F. Triola

2. Section 14.3-2 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Chapter 14 Statistical Control Processes 14-1 Review and Preview 14-2 Control Charts for Variation and Mean 14-3 Control Charts for Attributes

3. Section 14.3-3 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Key Concept This section presents a method for constructing a control chart to monitor the proportion p for some attribute, such as whether a service or manufactured item is defective or nonconforming. The control chart is interpreted by using the same three criteria from Section 14-2 to determine whether the process is statistically stable.

4. Section 14.3-4 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Definition A control chart for p (or p chart) is a graph of proportions of some attribute (such as whether products are defective) plotted sequentially over time, and it includes a centerline, a lower control limit (LCL), and an upper control limit (UCL).

5. Section 14.3-5 Copyright © 2014, 2012, 2010 Pearson Education, Inc. 1.The data are process data consisting of a sequence of samples all of the same size n. 2.Each sample item belongs to one of two categories. 3.The individual sample data values are independent. Requirements

6. Section 14.3-6 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Notation

7. Section 14.3-7 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Center line: Upper control limit: Lower control limit: Graph (If the calculation for the lower control limit results in a negative value, use 0 instead. If the calculation for the upper control limit exceeds 1, use 1 instead.)

8. Section 14.3-8 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Upper and lower control limits of a control chart for a proportion p are based on the actual behavior of the process, not the desired behavior. Upper and lower control limits are totally unrelated to any process specifications that may have been decreed by the manufacturer. Caution

9. Section 14.3-9 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Let’s consider the proportion of defective quarters produced by the new production method at the United States Mint. Listed below are the number of defects in batches of 10,000 quarters randomly selected on each of 20 consecutive days. Construct a control chart for the proportion p of defective quarters and determine whether the process is within statistical control. Example

10. Section 14.3-10 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Example - Continued 87129610 51514 121496161820191824

11. Section 14.3-11 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Example - Continued Upper control limit: Lower control limit:

12. Section 14.3-12 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Example - Continued

13. Section 14.3-13 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Using the three out-of-control criteria listed in Section 14.2, we conclude this process is out of statistical control. Eight consecutive points lie below the centerline, and there is a point lying above the upper control limit. The control chart indicates that this process requires corrective action. Example - Continued