Question
In: Statistics and Probability
An X-bar chart with three-sigma limits has parameters as follows: • UCL = 104 • Center...
An X-bar chart with three-sigma limits has parameters as follows:
• UCL = 104
• Center line = 100
• LCL = 96
• n = 9
Suppose that mean of the process quality characteristic shifts to 102, assume standard deviation does not change.
(a) What is average run length until the first point is plotted out of control?
(b) What is the probability that the control chart would exhibit lack of control by at least the third point plotted?
Solutions
orchestra answered 2 years agoRelated Solutions
An x ̅ chart with three-sigma limits has parameters as follows: UCL = 109 Center Line...
An x ̅ chart with three-sigma limits has parameters as follows:
UCL = 109 Center Line = 101 LCL = 100 n = 5 Find the ARL1 for the
chart. (10 points) What information does ARL convey that the
statistical error probabilities do not?
Calculate the control limits for the X-bar chart with 0.005 probability limits (instead of 3-sigma limits)....
Calculate the control limits for the X-bar chart with 0.005
probability limits (instead of 3-sigma limits). That is, here the
type I error rate (false alarm rate) is now set to α =
0.005. Use Excel for any calculations, not Minitab.
Day
x1
x2
x3
x4
x5
1
839
585
583
613
768
2
706
527
956
644
612
3
322
614
807
282
170
4
1001
904
419
522
430
5
259
811
847
603
572
6
681
523...
Define the "center line", "LCL" and "UCL" for an p chart and a p bar chart.
Define the "center line", "LCL" and "UCL" for an p chart and a p
bar chart.
Determine the Average Run Length (ARL) of a x-bar chart with limits where the process has...
Determine the Average Run Length (ARL) of a x-bar chart with
limits where the process has shifted one standard deviation in one
direction
what is the type 1 error of an x bar chart with 1 - sigma control...
what is the type 1 error of an x bar chart with 1 - sigma
control limits?
what is the type 1 error of an x bar chart with 2 - sigma
control limits?
what is the type 1 error of an x bar chart with 3 - sigma
control limits?
what is the type 1 error of an x bar chart with 4 - sigma
control limits?
Miller Inc. has decided to use a p-Chart with 3-sigma control limits to monitor the proportion...
Miller Inc. has decided to use a p-Chart with 3-sigma control
limits to monitor the proportion of defective metal shafts produced
by their production process. The quality control manager randomly
samples 150 metal shafts at 14 successively selected time periods
and counts the number of defective metal shafts in the sample.
Step 1 of 8: What is the Center Line of the control chart? Round
your answer to three decimal places.
Step 2 of 8: What value of z should...
Given the data provided below, calculate the control limits (X-bar and r-chart, Capability Index, create a...
Given the data provided below, calculate the control limits
(X-bar and r-chart, Capability Index, create a control chart, and
calculate the percentage of units that are expected to be out of
spec (z-value). Please show all work for how all calculations
were computed.
Filling
Line Checks - ounces
Specification: 12
ounces min; max - 15 ounces
Sample
Sample Times
Number
1pm
2pm
3pm
4pm
5pm
6pm
7pm
8pm
1
12.5
12.4
12.4
12.8
13
12.8
12.8
13
2
12.4
12.4...
Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma) LOADING... for this...
Refer to Table S6.1 - Factors for Computing Control Chart Limits
(3 sigma)
LOADING...
for this problem.
Sampling
44
pieces of precision-cut wire (to be used in computer assembly)
every hour for the past 24 hours has produced the following
results:
Hour
Bold x overbarx
R
Hour
Bold x overbarx
R
Hour
Bold x overbarx
R
Hour
Bold x overbarx
R
1
3.153.15 "
0.650.65 "
7
3.053.05 "
0.580.58 "
13
3.113.11 "
0.800.80 "
19
4.514.51 "...
Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma) LOADING... for this...
Refer to Table S6.1 - Factors for Computing Control Chart Limits
(3 sigma) LOADING... for this problem. Sampling 4 pieces of
precision-cut wire (to be used in computer assembly) every hour
for the past 24 hours has produced the following results:
Hour Bold x overbar R Hour Bold x overbar R Hour Bold x overbar R
Hour Bold x overbar R 1 3.15" 0.65" 7 2.95" 0.58" 13 3.11"
0.80" 19 3.41" 1.66" 2 3.10 1.18 8 2.75 1.08 14...
MEAN CI x-bar (Grand Mean) LCL x-bar (CI-A2*R-bar) UCL x-bar (CI+A2*R-bar) Sample Range (Max-Min) R-bar (Mean)...
MEAN
CI
x-bar
(Grand Mean)
LCL
x-bar
(CI-A2*R-bar)
UCL
x-bar
(CI+A2*R-bar)
Sample
Range
(Max-Min)
R-bar
(Mean)
UCL
R
(R-bar*D4)
1
68.51
68.46
68.54
68.34
68.46
68.46
2
68.94
68.2
68.54
68.56
68.7
68.7
3
68.66
68.44
68.55
68.77
68.7
68.64
4
68.49
68.94
68.56
68.62
68.69
68.56
5
68.64
68.63
68.62
68.32
68.34
68.24
6
68.34
68.42
68.99
68.02
68.03
68.47
7
68.99
68.94
68.95
68.95
68.94
68.97
8
68.92
68.91
68.97
68.93
68.96
68.95
GRAND MEAN
n=
A2=
D4=
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