Question

Understanding Variation/Managing Chaos

Compute Average Moving Range, Natural Process Limits,Upper Range Limit

Please answer ONLY questions 5, 6 and 7. Page 60 and 137 formulas provided here in image 4 and 5. Thanks

Understanding Variation/Managing Chas WHAT SHOULD YOU DO NOW? Scatistics has never been a spectator sport. Process behavior chart no exception. You should see if you can compute the limits and an XmR chart 1、 The US. Trade Deficits for the last halfof 1988 are shown in Fi 6.7. Use the data of Figure 6.7, and the blank form in Figure 68 plot the time series graph for the U.S. Trade Deficits for the last hal of 1988. Jul Aug Sep Oct Now De 1988 10.5 11.2 9.2 10.1 10.4 10.5 Figure 6.7: Monthly U.S. Trade Deficits, 1988 (S billions) 2. Use the data in Figure 6.7 to compute the monthly moving ranges. Note that moving ranges are defined to be positive values, and are found by computing the differences between successive values. Write these values in the space provided in Figure 6.8, and plot the running record of the moving ranges. 3. Compute the average trade deficit for the last half of 1988. 4. Compute the Average Moving Range 5. Compute the Natural Process Limits for the X-chart using the for mulas on page 60 or on page 137 6. Compute the Upper Range Limit using the formula on page 60 or on 8. Page 137. 114 EmailSave

Answer 1

Xbar=sum of observation/Total no of observation

X bar= 10.5+11.2+9.2+10.1+10.4+10.5/6

Xbar=10.31

Average moving range

mR=| Xj-Xj-1|

mR bar = 1/m-1 * sum( mR )

=1/5*4

mR bar=0.8

	Jul	Aug	Sep	Oct	Nov	Dec
X	10.5	11.2	9.2	10.1	10.4	10.5
mR		0.7	2.0	0.9	0.3	0.1

5) upper natural process limit

UNPL=Xbar+(2.66*mRbar)

UNPL=10.31+(2.66*0.8)

UNPL=12.43

6) Lower natural process limit

LNPL=Xbar-(2.66*mRbar)

LNPL=10.31-(2.66*0.8)

LNPL=8.18

7) plot of limits

it 10 3 5 6