Download How to analyze tolerances using Excel

How to Analyze Tolerances Using Excel
The examples provided are tolerance analysis for 2, 4 and 5 random
variables. Each example can be taken as a template to be modified for
the user's own application. The examples in TolAnal2.xls are as follows:
1.
2.
3.
4.
5.
X = A+B
X = Sqrt [ Sqr(A) + Sqr(B)]
X =ArcTan(B/A)
X=(A-B)/A
V = Pi * L * R*R
The example in TolAnal4.xls is
6.
IL (amps) = (VZ - VBE ) * (  - 1)
R2

and
TolAnal5.xls example is an extension of the TolAnal4.xls
7.
PL(watts) = IL2 * RL
EXCEL spreadsheet “Circuit A,B,C,D,E” is used in example 7 and it is
described in detail as follows:
Data Enter:
EXCEL
EXCEL
Variable Aim / Mean Col &Row Sigma Col & Row
Vz
4.7
A 257
0.05
C 257
VBE
0.64
B 257 0.01
D 257
R2
380
G 257 17
I 257
Beta
35
H 257
5
J 257
RL
1000
K 257 40
L 257
Working columns:
A = Vz B= VBE C = R2 D = Beta E = RL
Power Amp equation in column G for estimating treatment
combination
=(( ((A2-B2)/C2)* ((D2-1)/D2) )*(((A2-B2)/C2)*((D2-1)/D2))*E2)
The entries of the Mean and the modified standard deviation or sigma
are as follows:
3 1 = 3 Column A: Vz
Row 2: Mean minus Sqrt 3 times sigma
3: Mean
4: Mean plus Sqrt 3 times sigma
Repeat the cycle until row 244
3 2 = 9 Column B: VBE
Row 2: Mean minus Sqrt 3 times sigma.
3:
“
“
“
“
“
4:
“
“
“
“
“
5: Mean
6:
“
7:
“
8: Mean plus Sqrt 3 times sigma
9: “
“
“
“
“
10: “
“
“
“
“
Repeat the cycle until row 244
3 3 = 27 Column G: R2
Row 2: Mean minus Sqrt 3 times sigma
3:
…
28: “
“
“
“
3 4 = 81 Column H: Beta
Row 2: Mean minus Sqrt 3 times sigma
3:
…
82: “
“
“
“
3 5 = 243 Column K: RL
Row 2: Mean minus Sqrt 3 times sigma
3:
…
243: “
“
“
“
Appropriate weights of 1/6 or 4/6 are assigned in columns H – L
The Response variable taken together with the corresponding weights
for each moment are in columns N - Q
Sensitive analysis is easily performed through a copy of the initial
spreadsheet. To estimate the contribution of error for a variable of
interest we proceed as follows:
1. The associated sensitivity spreadsheets are used to estimate the
percent variation, when a random variable is held constant. A value of
0.0 is entered for sigma in the copied spreadsheet, which will
automatically estimate the 2nd moment for the response variable. See
Tab “Circuit A, B, C, D, E Sens A” for the Zener diode variable.
2. Create 4 additional copies of the initial spread sheet and name the
tabs for the variable whose sensitivity we estimate, i.e. B or C… E.
3. A summary worksheet is provided that graphically portrays the
amount of contribution of error from each random variable, as
computed in the sensitivity worksheets.
4. A tolerance is computed for the response variable that was estimated
from the given functional equation. Typically, tolerance is taken as plus
or minus 3 times the standard deviation of the response variable.