SHOW ALL WORK! ANSWER ALL THE QUESTIONS ASKED IN GREAT DETAIL! Two processes, PP
ID: 352011 • Letter: S
Question
SHOW ALL WORK! ANSWER ALL THE QUESTIONS ASKED IN GREAT DETAIL!
Two processes, PP and Q are used by a supplier to produce the same component, Z which is a critical part of an aircraft engine. The specification for Z calls for a dimension of .24 mm +/- .03 mm. The probabilities of achieving the dimensions for each process, based on their inherent variability, are shown below:
Value
Loss
Process P Probability
Weighted Loss
Process Q Probability
Weighted Loss
0.20
0
0.02
0.21
0.12
0.03
0.22
0.12
0.15
0.23
0.12
0.15
0.24
0.28
0.30
0.25
0.12
0.15
0.26
0.12
0.15
0.27
0.12
0.03
0.28
0
0.02
If the value of k in the Taguchi loss function is 60,000, what is the expected loss for each process and which would be the best process to use based on minimizing the expected loss?
Value
Loss
Process P Probability
Weighted Loss
Process Q Probability
Weighted Loss
0.20
0
0.02
0.21
0.12
0.03
0.22
0.12
0.15
0.23
0.12
0.15
0.24
0.28
0.30
0.25
0.12
0.15
0.26
0.12
0.15
0.27
0.12
0.03
0.28
0
0.02
Explanation / Answer
Specifications are 24 +/- 3 mm
L(x) = 60000 (x - T)2
For a typical calculation:
L(0.21) = 60000 (0.21 - 0.24)2 = $ 54.00
Weighted loss = 0.12 X $54.00 = $ 6.48
The table below uses the above provided formula for inputting the values:
Therefore, Process Q incurs a smaller loss than Process P, even though some output of Q falls outside specifications.
Value Loss ($) Process P Probability Weighted Loss ($) Process Q Probability Weighted Loss ($) 0.2 96 0 0 0.02 1.92 0.21 54 0.12 6.48 0.03 1.62 0.22 24 0.12 2.88 0.15 3.6 0.23 6 0.12 0.72 0.15 0.9 0.24 0 0.28 0 0.3 0 0.25 6 0.12 0.72 0.15 0.9 0.26 24 0.12 2.88 0.15 3.6 0.27 54 0.12 6.48 0.03 1.62 0.28 96 0 0 0.02 1.92 Expected Loss 20.16 16.08Related Questions
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