How to analyze tolerances using Excel - ASQ
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. X = A+B
2. X = Sqrt [ Sqr(A) + Sqr(B)]
3. X =ArcTan(B/A)
4. X = ( A - B ) / A
5. 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.
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