1. For the following data set, complete parts (a-f) and then complete the table for a tabular CUSUM chart assuming a target value of 12. (You may utilize EXCEL for the calculations)

FIR= FIR=

	X		Dev+			Dev-
1	10
2	12
3	11
4	10
5	11
6	14
7	15
8	11
9	13
10	11

Assuming an Individual-Moving Range chart yields the following [x-bar=11.8 MR-bar=1.889]

a. What is your estimate of the standard deviation of the statistic (x) you want to chart?

b. Assume that you would like to catch a shift of 0.6 standard deviations. What is your value for K?(note find k first)

c. What is the value for the “upper buffer”

d. What is the value for the “lower buffer”

e. Assuming a H=4σ , what are your Decision Limits for the chart?

f. Assuming a FIR=2σ complete the table of CUSUM values

g. Is there any evidence that the process has shift? Why?

2. For the following data set, complete parts (a-f) and then complete the table for a tabular CUSUM chart assuming a target value of 9. (You may utilize EXCEL for the calculations)

FIR= FIR=

	X1	X2	X3				Dev+			Dev-
1	7	12	11		10.00
2	9	12	10		10.33
3	11	9	11		10.33
4	10	7	7		8.00
5	8	10	10		9.33
6	8	12	12		10.67
7	7	9	7		7.67
8	9	8	9		8.67
9	11	7	9		9.00
10	10	7	11		9.33

Assuming an chart yields the following [ x-bar=9.333 r-bar=3.0]

a. What is your estimate of the standard deviation of the statistic(x-bar) you want to chart? (Don’t forget about including n!)

b. Assume that you would like to catch a shift of 1.4 standard deviations. What is your value for K? (find k first)

c. What is the value for the “upper buffer”

d. What is the value for the “lower buffer”

e. Assuming a H=4σ , what are your Decision Limits for the chart?

f. Assuming a FIR=2σ complete the table of CUSUM values

g. Is there any evidence that the process has shift? Why?