1 Doing Statistics for Business Doing Statistics for Business Data, Inference, and Decision Making Marilyn K. Pelosi Theresa M. Sandifer Chapter 16 Improving and Managing Quality

2 Doing Statistics for Business Chapter 16 Objectives Ü Supplier/Customer Relations Ü The Language of Control charts Ü Types of Control charts Ü Individual or x-charts Ü Xbar and R-charts Ü The p-chart

3 Doing Statistics for Business A process is a series of actions that changes inputs to outputs.

4 Doing Statistics for Business A control chart is a graph that allows us to study variation in a product or service.

5 Doing Statistics for Business TRY IT NOW! Coffee and a Bagel Identifying Possible Sources of Variation Suppose you go to a donut shop for coffee and a bagel. Consider the service and quality of your food. Using the 6 categories of sources of variation, identify where variation might come from.

6 Doing Statistics for Business Figure 16.1 Different Possibilities for Changes in the Distribution of the Variable

7 Doing Statistics for Business A process whose distribution does not change over time is said to be in a state of statistical control or in control. If it does change over time, it is said to be out of statistical control or out of control.

8 Doing Statistics for Business Common causes of variation are the methods, machines, people, and environment that are an inherent part of a process. They are part of the design of the process.

9 Doing Statistics for Business Special causes of variation are events or actions that are not part of the process design.

10 Doing Statistics for Business An x-chart is a control chart used to monitor individual observations of a variable over time. Time is plotted on the x axis and the quality characteristic being monitored is plotted on the y axis. The graph also has 3 lines drawn parallel to the x axis. These are called the center line, upper control limit, and lower control limit.

11 Doing Statistics for Business TRY IT NOW! The Plastics Company x-Chart for the Customer Data Use the same upper and lower control chart limits but plot the first 10 melt flows that the customer observed. They are as follows:

12 Doing Statistics for Business The Xbar-chart is a control chart used to monitor the mean of a variable over time. Time is plotted on the (insert x with line over it) axis and the sample means are plotted on the y axis. The graph also has 3 lines drawn parallel to the x axis. These are called the center line, the upper control limit, and the lower control limit.

13 Doing Statistics for Business Figure 16.2 Three Key Characteristics of Sleeve Inside Diameter

14 Doing Statistics for Business TRY IT NOW! The Sleeve Company Xbar-chart for Characteristic b Using the sample averages shown in Example 16.8 from your textbook, create the Xbar-chart for characteristic b for the manufacturer of the sleeves.

15 Doing Statistics for Business The R-chart is a control chart used to monitor the variation of a process over time. Time is plotted on the x axis and the sample range, R = Max – Min, of the quality characteristic being monitored is plotted on the y axis. The graph also has 3 lines drawn parallel to the x axis. These are called the center line, upper control limit, and lower control limit.

16 Doing Statistics for Business TRY IT NOW! The Sleeve Company R-chart for Characteristic b Using the sample ranges shown in Example 16.8 from your textbook, create the R-chart for characteristic b for the manufacturer of the sleeves.

17 Doing Statistics for Business The p-chart is a control chart used to monitor the proportion, p, of items that have a particular attribute or characteristic over time. Time is plotted on the x axis and the sample proportion, p = number in the sample with the attribute /n, is plotted on the y axis. The graph also has 3 lines drawn parallel to the x axis. These are called the center line, upper control limit, and lower control limit.

18 Doing Statistics for Business TRY IT NOW! The Basketball Player p-chart for Proportion of Successful Free Throws A basketball player is monitoring his free throw percentage. He keeps track of the number of baskets made in 50 practice shots on each day. His data are shown below for the past 15 days of practice.

19 Doing Statistics for Business TRY IT NOW! The Basketball Player p-chart for Proportion of Successful Free Throws (con’t)

20 Doing Statistics for Business TRY IT NOW! The Basketball Player p-chart for Proportion of Successful Free Throws (con’t) Create the p-chart to monitor the percentage of free throw shots that he makes. Is this player consistent?

21 Doing Statistics for Business Creating Control Charts in Excel - Subgroup Statistics in Excel 1. Create a pivot table for the data by dragging the Sample field button to the Row area and the Weight field button to the Data area. Double click on Weight to open the Pivot Table Field box and change Summarize by: to Average. Finish making you selections and click Finish. 2. You cannot summarize the data in a pivot table using the range, but you can do it for the maximum and minimum values. Create pivot tables for the Max and Min of each sample and locate them adjacent to the one for average. 3. Use a formula in the cell adjacent to the minimum value to calculate the range for each sample by subtracting the minimum weight value from the maximum.

22 Doing Statistics for Business Creating Control Charts in Excel - Calculating the Control Limits 1. Use a formula to find the average of the sample ranges, (need R with line over it). The formula should be = AVERAGE (data range), where data range is the cell reference that contains the sample ranges. 2. Insert three new columns next to the column that contains the sample means and label them CD, LCL, and UCL. 3. In the first cell under the label CL, type “55.00” and copy it to the cells next to each of the sample means. 4. In the first cell under the label LCL, type in the formula “= *1.44”. Copy this formula down the column for each sample.

23 Doing Statistics for Business Creating Control Charts in Excel - Calculating the Control Limits (con’t) 5. In the first cell under the UCL, type in the formula “= *1.44”, and copy this formula to the cells below.

24 Doing Statistics for Business Creating Control Charts in Excel - Creating the Control Chart 1. Highlight the columns in the worksheet that contain the sample means, CL, LCL, UCL, and start the Chart Wizard. 2. From the list of Chart types, choose Line and Lines with Markers as the Chart sub-type. Click Next > twice to continue. 3. Add titles and other formatting changes, and click Finish. The chart will be placed on the worksheet.

25 Doing Statistics for Business Creating Control Charts in Excel - Creating the Control Chart (con’t) For control limits to be plotted without markers: 4. Click on the chart to select it, and then click on one of the three limits. The Format Data Series dialog box will open. Select the Patterns tab, and under Marker, click the radio button for None. 5. Repeat this for the two control lines.

26 Doing Statistics for Business Figure 16.4 Data and Summary Pivot Tables

27 Doing Statistics for Business Figure 16.5 Worksheet with CL, LCL and UCL

28 Doing Statistics for Business Figure 16.6 Choosing a Line Chart

29 Doing Statistics for Business Figure 16.7 Removing Markers from Lines

30 Doing Statistics for Business Figure 16.8 Control Chart for Diaper Weight

31 Doing Statistics for Business Chapter 16 Summary In this chapter you have learned: 4 Control charts are one of many quality tools being used with increasing frequency by both manufacturers and service companies. 4 In all cases of constructing and using control charts, a sample of data is collected periodically over time to monitor some characteristic of a process.

32 Doing Statistics for Business Chapter 16 Summary (con’t) 4 Control charts are used to detect the presence of special cause variation. If a process has some special cause variation, the one or more of the plotted points will go outside the upper and lower control limits. 4 The center line is located at the average value of the variable being plotted.

33 Doing Statistics for Business Chapter 16 Summary (con’t) 4 The upper and lower control limits are typically set three standard deviation above and below the center line. 4 A false alarm occurs when you conclude that there is some special variation in the process when there is not any.