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(ultimately determining their strength). Below is the results of this day\'s tes

ID: 3204454 • Letter: #

Question

(ultimately determining their strength). Below is the results of this day's tests.

7

b. Is this process in statistical control? Why or why not?

Any assistance would be greatly appreciated.

The Langley tire company measures their tire strength on a scale from 1 to 10 every 4 hours.   They do this by randomly selecting three tires for each test period and destroying them

(ultimately determining their strength). Below is the results of this day's tests.

Hour A B C 4 8 6 7 8 6 8 8 12 7 8 7 16 6 8

7

a. Find the 3 sigma UCL and LCL for the mean and range charts.

b. Is this process in statistical control? Why or why not?

Any assistance would be greatly appreciated.

Explanation / Answer

Part a

Here, we have to find the 3 sigma UCL and LCL for the mean and range charts.

The UCL and LCL for mean chart is given as below:

UCL = X-double-bar + A2R-bar

LCL = X-double-bar – A2R-bar

The UCL and LCL for range chart is given as below:

UCL = D4R-bar

LCL = D3R-bar

Calculation table is given as below:

Hour

A

B

C

Xbar

Range

4

8

6

7

7

2

8

6

8

8

7.333333

2

12

7

8

7

7.333333

1

16

6

8

7

7

2

X-double-Bar =

7.222222

R-bar = 1.75

We are given n = 4

The coefficients A2, D3 and D4 are given as below:

A2 = 0.73

D3 = 0

D4 = 2.28

Now, plug all values and find out the limits given as below:

The UCL and LCL for mean chart is given as below:

UCL = X-double-bar + A2R-bar = 7.222222 + 0.73*1.75 = 8.499722

LCL = X-double-bar – A2R-bar = 7.222222 – 0.73*1.75 = 5.944722

The UCL and LCL for range chart is given as below:

UCL = D4R-bar = 2.28*1.75 = 3.99

LCL = D3R-bar = 0*1.75 = 0.00

Part b

All range points are lies between 0.00 and 3.99.

All Xbar points are lies between 5.944722 and 8.499722.

So, this process is in statistical control.

Hour

A

B

C

Xbar

Range

4

8

6

7

7

2

8

6

8

8

7.333333

2

12

7

8

7

7.333333

1

16

6

8

7

7

2

X-double-Bar =

7.222222

R-bar = 1.75