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# Control Charts

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You have taken data from a production process in order to develop an Xbar control chart. You have 25 samples of data with 5 parts measured in each sample to get the Xbar. Use this data shown in the table.

Sample Xbar

1 2.12

2 2.22

3 1.98

4 2.24

5 1.97

6 1.99

7 2.13

8 2.11

9 2.03

10 1.96

11 1.92

12 2.01

13 2.03

14 2.14

15 1.95

16 2.20

17 1.88

18 1.82

19 2.19

20 2.16

21 2.14

22 1.97

23 1.95

24 2.10

25 2.03

1. First plot the data using Excel.

2. Then determine the UCL and LCL. Do any of the data points need to be thrown out? If so, then recalculate the UCL and LCL.

3. Then you begin to plot results on this chart. Here are the next 6 samples of data (sample size = 5).

Sample Xbar
1 2.24
2 2.22
3 1.95
4 2.06
5 1.99
6 2.05

Plot these on the control chart.

4. Is the process in control?

https://brainmass.com/statistics/statistical-figures/443370

#### Solution Preview

1. The plotted data is on the first tab of the Excel sheet.

2. With the information given nothing needs to be thrown out if you use 3-sigma as your only limit. However, some people would argue that two of three consecutive points outside the 2-s ...

\$2.19

## Performance: Control Chart for Process Mean

13-14
Boston-based Legal Seafoods prides itself on having instituted an advanced quality control system that includes the control of both food quality and service quality. The following are successive service times at one of the chain's restaurants on a Saturday night in May 2007 (time is stated in minutes from customer entry to appearance of waitperson)
5, 6, 5,5,5,7, 4, 12, 4, 4.5, 2, 5, 5, 5, 6, 6, 13, 2, 5, 4, 4.5, 6.5, 4, 1,
2 3, 5, 5, 4, 4, 8, 12 3, 4.5, 6.5, 6, 7, 10, 6, 6.5, 5, 3, 6.5 7,
Aggregate the data into groups of four, and construct a control chart for the process mean. Is the waiting time at the restaurant under control?

13-17
The following data are tensile strengths, in pounds, for a sample of string for industrial use made at a plant. Construct a control chart for the mean, using groups of 5 observations each. Test for statistical control of the process mean.
5, 6, 4, 6, 5, 7, 7, 7, 6, 5, 3, 5, 5, 5, 6, 5, 5, 6, 7, 7, 7, 7, 6, 7, 5,
5, 5, 6, 7, 7, 7, 7, 7, 5, 5, 6, 4 6, 6, 6, 7, 6, 6, 6, 6, 6, 7, 5, 7, 6,

13-23
Create R and s charts for problem 13-17. Is the process in control?

13-25

The capacity of the fuel tank of the 2007 Volvo S40 is designed to be 12.625 gallons. The actual capacity of tanks produced is controlled using a control chart. The data of 9 random samples of size 5 each collected on 9 different days are tabulated below. Draw X-bar, R, and s charts. Is the process in control? If it is not, remove the sample that is out of control, and redraw the charts.
1 2 3 4 5 6 7
12.667 12.600 12.599 12.607 12.738 12.557 12.646
12.598 12.711 12.583 12.524 12.605 12.745 12.647
12.685 12.653 12.515 12.718 12.640 12.626 12.651
12.700 12.703 12.653 12.615 12.653 12.694 12.607
12.722 12.579 12.599 12.554 12.507 12.574 12.589
8 9
12.710 12.529
12.627 12.725
12.605 12.306
12.648 12.551
12.545 12.600

13-29
BASF Inc. makes CDs for use in computers. A quality control engineer at the plant tests batches of 50 disks at a time and plots the proportions of defective disks on a control chart. The first 10 batches used to create the chart had the following numbers of defective disks: 8, 7, 6, 7, 8, 4, 3, 5, 5, 8. Construct the chart and interpret the results.

13-31

The following are the numbers of imperfections per yard of yarn produced in a mill in Pennsylvania in May 2007: 5, 3, 4, 8, 2, 3, 1, 2, 5, 9, 2, 2, 2, 3, 4, 2, 1. Is there evidence that the process is out of control?

13-32

The following are the numbers of blemishes in the coat of pain of new auto mobile made by Ford in June 2007: 12, 25, 13, 20, 5, 22, 8, 17, 31, 40, 9, 62, 14, 16, 9, 28. Is there evidence tat the painting process is out of control?

13-33

The following are the numbers of imperfection in rolls of wallpaper made by Laura Ashley: 5, 6, 3, 4, 5, 2, 7, 4, 5, 3, 5, 5, 3, 2, 0, 5, 5, 6, 7, 6, 9, 3, 3, 4, 2, 6. Construct a c chart for the process, and determine whether there is evidence that the process is out of control.

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