Variable Control Chart Constants Sample Size X-bar Chart ____________R Chart____
ID: 335505 • Letter: V
Question
Variable Control Chart Constants
Sample Size X-bar Chart ____________R Chart___________
N A2 D3 D4
2 1.880 0 3.267
3 1.023 0 2.574
4 0.729 0 2.282
5 0.577 0 2.114
6 0.483 0 2.004
7 0.419 0.076 1.924
8 0.373 0.136 1.864
9 0.337 0.184 1.816
10 0.308 0.223 1.777
12 0.266 0.283 1.717
14 0.235 0.328 1.672
16 0.212 0.363 1.637
18 0.194 0.391 1.608
20 0.180 0.415 1.585
22 0.167 0.434 1.566
24 0.157 0.451 1.548
Questions 1 - 3 are based on the following scenario:
The time to make beds at a motel is supposed to fall into an agreed-on range of times. A sample of five maids was selected to evaluate their efficiency, and the time needed to make a bed was observed on three different occasions:
Service Time (in seconds)
_____Maid Sample 1 Sample 2 Sample 3_____
Holland 110 90 150
Lindsey 180 120 140
Marie 155 130 175
Cindy 120 140 90
Manny 140 185 155
QUESTION 1
1. What are the upper and lower control limits for an X-bar chart with a sample size of five?
a.
UCL = 186.76, LCL = 90.64
b.
UCL = 191.87, LCL = 85.47
c.
UCL = 196.06, LCL = 96.44
d.
UCL = 168.67, LCL = 108.67
e.
None of the above
5 points
QUESTION 2
1. What are the upper and lower control limits for an R chart with a sample size of five?
a.
UCL = 109.93, LCL = 0
b.
UCL = 133.85, LCL = 0
c.
UCL = 155.93, LCL = 0
d.
UCL = 176.16, LCL = 0
e.
None of the above
5 points
QUESTION 3
1. After the control chart was established, a sample of five observations had the following time in seconds: 182, 150, 192, 178, 100. Is corrective action called for?
a.
X-bar = 160.2; process is out of control, corrective action is needed
b.
X-bar = 160.2.2, R-bar = 111; process is in control, no corrective action is needed
c.
X-bar = 160.2, R-bar = 111; process is out of control, corrective action is needed
d.
X-bar = 176.25, R-bar = 42; process is in control, no corrective action is needed
e.
None of the above
5 points
QUESTION 4
1. An operator of a mechanized sorting machine in the post office must read the zip code on a parcel and, knowing its location in the city, divert the package to its proper truck route. Based on past records, the error rate for skilled operators is approximately five errors per 100 parcels sorted - a defective rate of .05. Management wants to develop a control chart to monitor new operators to make sure that employees who are unsuited for the job can be identified. Over a nine-day probationary period, random samples of 100 parcels are drawn from the truck routes. What are the control limits for the sorting operation?
a.
UCL = .05, LCL = 0
b.
UCL = .09, LCL = .01
c.
UCL = .11, LCL = 0
d.
UCL = .37, LCL = 0
e.
None of the above
5 points
QUESTION 5
1. After becoming more experienced with their jobs, the machine operators in question 4 averaged only two sorting errors per 100 parcels sorted. What are the new control limits for the sorting operation?
a.
UCL = .02, LCL = 0
b.
UCL = .06, LCL = 0
c.
UCL = .35, LCL = 0
d.
UCL = .04, LCL = .004
e.
None of the above
a.
UCL = 186.76, LCL = 90.64
b.
UCL = 191.87, LCL = 85.47
c.
UCL = 196.06, LCL = 96.44
d.
UCL = 168.67, LCL = 108.67
e.
None of the above
Explanation / Answer
Q1
Find x bar of each maid by taking average of meantime of each sample
Calculate range of each sample by measuring difference between maximum and minimum value
For X bar chart
UCL = X-bar bar + A2 * R-bar
UCL = X-bar bar - A2 * R-bar
A2 is a factor corresponding to number of items in each sample
for this case n =5,
A2 = 0.577
X bar bar = 138.7
R bar = 52
UCL = 168.67
LCL = 108.66
Answer D
2.
Range Chart
Upper limit, UCL = D4 * R bar
Lower Limit, LCL = D3 * R bar
for n = 5 , value of
D4 = 2.114
D3 = 0
UCL = 2.114 * 52 =109.928 =109.93
LCL =0
Answer - A)
3.)
X bar = Sum of time / number of observation = (182+150+192+178+100)/5 = 160.4
R = Max(182,150,192,178,100) - Min(182,150,192,178,100) = 192-100 = 92
As sample mean x bar = 160.4 lies in between UCL & LCL of X bar bar and R = 92 also lies in between UCL and LCL of R chart so process is in control and no corrective action is required
Answer E
4.
p bar = 0.05 , nbar = 100
Upper Limit , UCL = p bar +3*sqrt( pbar*(1-pbar)/nbar) =0.11
Lower limit , LCL = p bar -3*sqrt( pbar*(1-pbar)/nbar) = -0.015 = 0
Answer C
5.
p bar = 0.02, nbar = 100
Upper Limit , UCL = p bar +3*sqrt( pbar*(1-pbar)/nbar) =0.06
Lower limit , LCL = p bar -3*sqrt( pbar*(1-pbar)/nbar) = -0.022 = 0
Answer : B
Maid Sample 1 Sample2 Sample3 X bar R Holland 110 90 150 116.7 60 Lindsey 180 120 140 146.7 60 Marie 155 130 175 153.3 45 Cindy 120 140 90 116.7 50 Manny 140 185 155 160.0 45 Average 138.7 52.0Related Questions
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