Hi, could you please answer this question by using excle with full details and s
ID: 380939 • Letter: H
Question
Hi, could you please answer this question by using excle with full details and showin formulas please. thank u
You're measuring the voltage drop across a resistor circuit and the engineers have indicated that the specification limits are 120V +/- 2.5 V. If the voltage exceeds those specifications, the circuit must be scrapped at a cost of $500.00 per circuit. You've collected the following samples.
a. compute the value of k in the Taguchi loss function
b. Based on the data provided, what is the expected loss from this process?
measurements 124.0 120.0 117.0 120.0 118.0 117.0 122.0 119.0 119.0 118.0 120.0 116.0 116.0 122.0 117.0 122.0 118.0 116.0 122.0 119.0 123.0 120.0 120.0 119.0 123.0 120.0 120.0 118.0 119.0 119.0 118.0 119.0 116.0 121.0 121.0 118.0 121.0 119.0 119.0 123.0 119.0 116.0 119.0 117.0 122.0 117.0 120.0 120.0 118.0 121.0 117.0 121.0 122.0 122.0 120.0 123.0 119.0 119.0 120.0 119.0 116.0 119.0 122.0 117.0 123.0Explanation / Answer
Taguchi loss function
a. compute the value of k in the Taguchi loss function
K=80
b. Based on the data provided, what is the expected loss from this process?
=$23903.36
measurements, n=65
x
x-P.M
(x-P.M)^2
1
124
4.52
20.4304
2
117
-2.48
6.1504
3
120
0.52
0.2704
4
122
2.52
6.3504
5
123
3.52
12.3904
6
120
0.52
0.2704
7
118
-1.48
2.1904
8
118
-1.48
2.1904
9
119
-0.48
0.2304
10
117
-2.48
6.1504
11
117
-2.48
6.1504
12
123
3.52
12.3904
13
116
-3.48
12.1104
14
120
0.52
0.2704
15
122
2.52
6.3504
16
116
-3.48
12.1104
17
118
-1.48
2.1904
18
120
0.52
0.2704
19
120
0.52
0.2704
20
119
-0.48
0.2304
21
121
1.52
2.3104
22
116
-3.48
12.1104
23
120
0.52
0.2704
24
121
1.52
2.3104
25
119
-0.48
0.2304
26
119
-0.48
0.2304
27
117
-2.48
6.1504
28
119
-0.48
0.2304
29
116
-3.48
12.1104
30
116
-3.48
12.1104
31
120
0.52
0.2704
32
118
-1.48
2.1904
33
116
-3.48
12.1104
34
119
-0.48
0.2304
35
119
-0.48
0.2304
36
120
0.52
0.2704
37
122
2.52
6.3504
38
119
-0.48
0.2304
39
122
2.52
6.3504
40
120
0.52
0.2704
41
119
-0.48
0.2304
42
122
2.52
6.3504
43
122
2.52
6.3504
44
119
-0.48
0.2304
45
119
-0.48
0.2304
46
121
1.52
2.3104
47
119
-0.48
0.2304
48
117
-2.48
6.1504
49
118
-1.48
2.1904
50
122
2.52
6.3504
51
120
0.52
0.2704
52
117
-2.48
6.1504
53
118
-1.48
2.1904
54
118
-1.48
2.1904
55
117
-2.48
6.1504
56
119
-0.48
0.2304
57
123
3.52
12.3904
58
119
-0.48
0.2304
59
121
1.52
2.3104
60
123
3.52
12.3904
61
122
2.52
6.3504
62
121
1.52
2.3104
63
120
0.52
0.2704
64
119
-0.48
0.2304
65
123
3.52
12.3904
S(x-process mean)2
282.22
SUM
7766
S.D
PROCESS MEAN =sum/n=
119.48
2.08
PROCESS MEAN
=sum/n
=7766/65
=119.48
S.D
=Sqrt ( S (x-process mean)2 / n )
= Sqrt ( 282.22 / 65 )
=2.08
65 samples (constituting a single sample set or a process) are collected from the resistor circuit
T=120V
X=120+ 2.5 V =122.5 V
The average of the points or samples, PM= 119.48
Standard deviation =2.08
Find k
If the voltage exceeds those specifications in any of the sample, the circuit must be scrapped at a cost of $500.00 per circuit.
Loss at a point /loss if a sample exceeds the specification limit:
L(x) = k*(x-t) ^2
Where,
k = loss coefficient
x = measured value
t = target value
If the circuit voltage exceeds the specification limit, then it has to be scrapped for $500
$500.00= k*(122.5- 120)2
K=80
Average Loss of a sample set/ process:
L = k*(s2 + (pm - t)2)
Where,
s = standard deviation of sample
PM= process mean
L = 80 * (2.082 + (119.48- 120)2) = $367.74
So, the average loss per sample in this set is $8.73.For the loss of the total 30 parts produced
Expected loss from the process
Total Loss form the process
= Avg. Loss * number of samples
=$367.74 * 65
=$23903.36
measurements, n=65
x
x-P.M
(x-P.M)^2
1
124
4.52
20.4304
2
117
-2.48
6.1504
3
120
0.52
0.2704
4
122
2.52
6.3504
5
123
3.52
12.3904
6
120
0.52
0.2704
7
118
-1.48
2.1904
8
118
-1.48
2.1904
9
119
-0.48
0.2304
10
117
-2.48
6.1504
11
117
-2.48
6.1504
12
123
3.52
12.3904
13
116
-3.48
12.1104
14
120
0.52
0.2704
15
122
2.52
6.3504
16
116
-3.48
12.1104
17
118
-1.48
2.1904
18
120
0.52
0.2704
19
120
0.52
0.2704
20
119
-0.48
0.2304
21
121
1.52
2.3104
22
116
-3.48
12.1104
23
120
0.52
0.2704
24
121
1.52
2.3104
25
119
-0.48
0.2304
26
119
-0.48
0.2304
27
117
-2.48
6.1504
28
119
-0.48
0.2304
29
116
-3.48
12.1104
30
116
-3.48
12.1104
31
120
0.52
0.2704
32
118
-1.48
2.1904
33
116
-3.48
12.1104
34
119
-0.48
0.2304
35
119
-0.48
0.2304
36
120
0.52
0.2704
37
122
2.52
6.3504
38
119
-0.48
0.2304
39
122
2.52
6.3504
40
120
0.52
0.2704
41
119
-0.48
0.2304
42
122
2.52
6.3504
43
122
2.52
6.3504
44
119
-0.48
0.2304
45
119
-0.48
0.2304
46
121
1.52
2.3104
47
119
-0.48
0.2304
48
117
-2.48
6.1504
49
118
-1.48
2.1904
50
122
2.52
6.3504
51
120
0.52
0.2704
52
117
-2.48
6.1504
53
118
-1.48
2.1904
54
118
-1.48
2.1904
55
117
-2.48
6.1504
56
119
-0.48
0.2304
57
123
3.52
12.3904
58
119
-0.48
0.2304
59
121
1.52
2.3104
60
123
3.52
12.3904
61
122
2.52
6.3504
62
121
1.52
2.3104
63
120
0.52
0.2704
64
119
-0.48
0.2304
65
123
3.52
12.3904
S(x-process mean)2
282.22
SUM
7766
S.D
PROCESS MEAN =sum/n=
119.48
2.08
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