Question

1. What is the UCL for the XBar chart based on the data below, with n=4, and ten set of samples for the weight of soft drinks are given. USL for the product is 355 g and LSL is 345. Daily production is 15000 units.

Sample #	Observations
1	352	348	350	351
2	351	352	351	350
3	351	346	342	350
4	349	353	352	352
5	351	350	351	351
6	353	351	346	346
7	348	344	350	347
8	350	349	351	346
9	344	345	346	349
10	349	350	352	352

The UCL for the X-bar chart will be (circle the right answer).

a. 350.25

b. 345.92

c. 352.63

d. 349.27

2. What is the LCL for the Xbar chart for the problem with data given in question 1?

a. 352.63

b. 345.92

c. 349.27

d. 10.49

3. What is the UCL for the R-chart based on the data given in Problem 1?

a. 0

b. 4.6

c. 352.63

d. 10.50

4. What is LCL for the Rchart, based on the data given in problem?

a. -3.29

b. 0

c. 10.50

d. 4.6

Answer 1

Sample #	Observations				sample mean	range
1	352	348	350	351	350.25	4
2	351	352	351	350	351	2
3	351	346	342	350	347.25	9
4	349	353	352	352	351.5	4
5	351	350	351	351	350.75	1
6	353	351	346	346	349	7
7	348	344	350	347	347.25	6
8	350	349	351	346	349	5
9	344	345	346	349	346	5
10	349	350	352	352	350.75	3
				average	349.275	4.6

for mean chart:

sample mean x̅ =			349.275
average range R̅ =			4.6
sample size n   =			4
for sample size n=4, criitcal value of constant A2=					0.729
control line (CL) = x̅=			349.275
upper control limit =x̅+3*A2R̅ =			352.628
lower control limit =x̅-3*A2R̅ =			345.922

for Range chart:

average range R̅ =			4.6
sample size n   =			4
for sample size n=4, criitcal value of constant D3=					0
for sample size n=4, criitcal value of constant D4=					2.282
control line (CL) = R̅=			4.6
upper control limit =D4R̅ =			10.4972
lower control limit =D3R̅ =			0.0000

1()

UCL for the X-bar chart 352.63

2)

LCL for the Xbar chart =345.92

3)

UCL for the R-chart =10.50

4)

LCL for the Rchart =0