HW 14
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Auburn University *
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Course
5720
Subject
Industrial Engineering
Date
Dec 6, 2023
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doc
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2
Uploaded by ChancellorFlagFinch34
7-26 Light bulbs are tested for their luminance, with the intensity of brightness
desired to be within a certain range. Random samples of five bulbs are chosen
from the output, and the luminance is measured. The sample mean X and the
standard deviation s are found. After 30 samples, the following summary
information is obtained:
The specifications are 90 ±15 lumens.
(a) Find the control limits for the X- and s-charts.
X^-=2550/30=85
S^-=195/30=6.5
USL=105, LSL=75
B3=0, B4=2.089, A3=1.427, C4=9400
Control limit for X^- charts:
UCL=X^-+A3*S^-=94.276
LCL= X^--A3*S^-=75.725
Control limit for S chart:
UCL=B4*S^-=13.579
LCL=B3*S^-=0
(b) Assuming that the process is in control, estimate the process mean and
process standard deviation.
Process mean=85
Estimate standard deviation=S^-/C4=6.9149
(c) Comment on the ability of the process to meet specifications. What
proportion of the output is nonconforming?
Proportion of output will be nonconforming=P(z<-1.45) +P(x>2.89) =0.07546
Proportion of output will be nonconforming is 0.07546
(d) If the process mean is moved to 90 lumens, what proportion of output will be
nonconforming? What suggestions would you make to improve the performance
of the process?
µ=90
Proportion of output will be nonconforming=p(z<-2.17) +P(z>2.17) =0.03001
Proportion of outcome will be nonconforming is 0.03001
7-30 In a gasoline-blending plant, the quality of the output as indicated by its
octane rating is measured for a sample taken from each batch. The observations
from 20 such samples are shown in Table 7-26. Construct a chart for the moving
range of two successive observations and a chart for individuals.
Sampl
e
Octane
Rating
Sampl
e
Octane
Rating
Sampl
e
Octane
Rating
Sampl
e
Octane
Rating
1
89.2
6
87.5
11
85.4
16
90.3
2
86.5
7
92.6
12
91.6
17
85.6
3
88.4
8
87.0
13
87.7
18
90.9
4
91.8
9
89.8
14
85.5
19
82.1
5
90.3
10
92.2
15
91.5
20
85.8
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