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Page 1/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
Statistical Tolerance Analysis
& Scorecards
Week 4
Page 2/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
Six Sigma Tolerance Analysis
Worst case tolerancing
Root sum of squares tolerancing
Statistical tolerancing
- linear applications
- non linear application
Page 3/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
1
Y• Dependent• Output• Effect• Symptom• Monitoring
X1 . . . Xn
• Independent• Input• Cause• Problem• Control
Prevention of defects requires more than just an inspection of “Y”. We need to understand the effect from “X” on “Y” and how to
control the “X”. Than we can avoid the inspection of “Y”.
The Six Sigma Focus
Y = f (x1 + x2 + ... + xn)
Page 4/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
Product Name:
Part DPU
ProcessDPU
Performance DPU
Software DPU
Assembly Current Opp Current Opp Current Opp Current Opp
Totals 0 0 0 0 0 0 0 0First Time Sigma #NUM! #NUM! #NUM! #NUM!DPU/Opp #DIV/0! #DIV/0! #DIV/0! #DIV/0!Sigma/Opp; LT #DIV/0! #DIV/0! #DIV/0! #DIV/0!Sigma/Opp; ST #DIV/0! #DIV/0! #DIV/0! #DIV/0!
6 σ 6 σ 6 σ 6 σ
Scorecards
Sub System A
Sub System B
Firmware
Test Software
Software Worksheet
Performance RequirementsVariable Test Limits
Performance WorksheetSpecificationRequirements
Performance WorksheetContract Requirements
Part A-1 Process Worksheet
Sub-Assembly A ProcessWorksheet
Fab, Assy & Test Process Worksheet
Page 5/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
Co
sts
for
dev
elo
pm
ent
and
man
ufa
ctu
rin
g
SIGMA LEVEL
BEST DESIGN
Optimum
?
...
....
.. ..
Customer Requirements
Detailed Requirements
€ & DPU
Statistical Tolerance Analysis
Page 6/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
Y= 0sy = …
Sub 1 Sub 2
Customer requirements level 1
x1 = s1 =
Y = X1 + X2
Sy2 = S1
2 + S22
Transfer Function
S = ?
x2 = s2 =
Statistical Requirements - „Flow down“
Statistical Tolerance Analysis
0
0 USL
0
Page 7/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
Causes for Product Defects
Deliver
Parts
Process A
Process B
Process C
Process D
Subassembliesor
SystemTest
Buying of subassemblies
Software
Partdefects
Processdefects
Performancedefects
Softwaredefects
Performancedefects
= Test, Inspection
Page 8/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
Bu
yin
g o
f m
ater
ial
Store
Production
Distribution
Acceptanceof a
product family
Bu
yin
g o
fS
ervi
ces
IT
Cus
tom
er
Supplierdefects
Logistical defects
Order fulfillmentdefects
Systemdefect
Supplierdefect
Causes for Defects in Business Processes
Page 9/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
4.976 ± .003
Part
1.240 ± .003
Specification characteristics
Is it ready for manufacturing?
Part 1 Part 2 Part 3
clearance (Gap)
Part 4
Housing
Housing
What is the “worst case” in terms of tolerance stack ?What is the probability of encountering “worst case”?
„Worst Case Analysis“
Page 10/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
… known as Stack-Analysis
Housing Nominal 4.976 Tolerance .003
Part 1 Nominal -1.240 Tolerance .003
Part 2 Nominal -1.240 Tolerance .003
Part 3 Nominal -1.240 Tolerance .003
Part 4 Nominal -1.240 Tolerance .003
Nominal Gap .016 Total Tolerance +/-.015
Minimum Gap .001
Maximum Gap .031
„Worst Case Analysis“
What is the Nominal Gap, the Minimum Gap and the Maximum Gap?
Page 11/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
Traditional Analysis Method
Calculation of the Gap dimension
Q < - -
+ -
N e T em
Σi = 1 N P i + T P i
N e T em
Σi = 1 N P i - T P i < R
NPi = nominal design value of ith PartTPi = tolerance assigned of the ithe nominal parts design valuem = total number of partsT = half of each tolerance value
When using worst-case analysis, the designer seeks to minimize the arithmetic certainty that any given combination of assigned dimensions and tolerances will produce a condition wherein the product can not be assembled. The study of such a simultaneous condition is known as worst-case analysis.
Let us say that the minimum and maximum gap constraints are specified as Q and R, respectively. Using worst case methods, one can readily determine whether or not the linear combination of part tolerances is favorable in relation to the gap constraints. This is often called “worst case gap analysis.”.
Ne = nominal design value of the housing (e = Envelope)Te = design tolerance of the housingQ = a specified minimum assembly performance criteriaR = a specified maximum assembly performance criteria
Worst Case Analysis
Page 12/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
At this point, we shall consider several other equations related to the assembly gap. Essentially, the listed equations allows us to compute the nominal assembly gap as well as the maximum and minimum.
S m a x = N e + T e -m
Σi = 1 N P i - T P i
S m in = N e - T e -m
Σi = 1 N P i + T P i
S nom = N e -m
Σi = 1N P i
S nom =m
Σi = 1N i V i B i
B is a "diametrical correction" factor for certain dimensions
V is the algebraic vector associated with the ith nominal dimension within the assembly loop
Worst Case Analysis
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-1σ +1σ +2σ +3σ +4σ +5σ +6σ-2σ-3σ-4σ-5σ-6σ
68.26 %
95.46 %
99.73 %
99.9937 %
99.999943 %
99.9999998 %
+ -µ
. . . Why do we create such a conservative design?
PWC = YFTm = .00275
= .000000000000143
Because of the uncertainties associated with manufacturing?
Limitations of Worst Case AnalysisLet us suppose that each of the parts has a ±3 σ capability This would translate to a first-time yield expectation of .9973 per part. On the other side, we could say the defect probability per part is .0027. With this information, the likelihood of encountering a simultaneous worst case condition could be calculated.
Worst Case Analysis
Page 14/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
Vector Analysis
Gap
Envelope Distribution Part Distribution Part Distribution Part Distribution Part Distributionσ = .001 in.µ = 4.976 in.
σ = .001 in.µ = 1.240 in.
σ = .001 in.µ = 1.240 in.
σ = .001 in.µ = 1.240 in.
σ = .001 in.µ = 1.240 in.
Housing Part 1 Part 2 Part 3 Part 4
Part1
Part2
Part3
Part4
Housing
Assembly gap
How can we include the process capability of the housing and of each component into the gap analysis?
Statistical Tolerance Analysis
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Item 1 Item 2 Item 3 Item 4
F
µ S
PS
Z S = Q - µ S
σS
σ S = Σi = 1
m
= F - µ iΣi = 1
m
Distribution of the assembly gap „S“
µ S σ i2
Q S R S
Note: in this example is , Qs = 0.
QS = lower gap limit
Rs = upper gap limit
Fs represents Qs or Rs
Statistical Tolerance Analysis
Page 16/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
Point of 0 gap ”Q”Point of 0 gap ”Q” µ Gap
Z Q
+ ∞- ∞
σ Gap = σ E2 + σ P1
2 + σ P 22 + σ P 3
2 + σ P42
µ Gap = µ E – (µ P 1 + µ P 2 + µ P 3 + µ P 4
Z Q =
Distribution of the assembly gap
If we know the “typical” mean off-set for the envelope and each of the parts, how could this knowledge be used to make the design robust against such shifts and drifts?
Assignment: Define the probability of a interference fit
)
Statistical Tolerance Analysis
Page 17/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
µ Gap
Z Q
σ Gap = 5 x 0,0012 = 0,00223
µ Gap = 4,976 – 1,24 – 1,24 – 1,24 – 1,24 = 0,016
Z Q =
Statistical Tolerance Analysis
Distribution of the assembly gap
Point of 0 gap ”Q”
Assignment: Define the probability of a interference fit
If we know the “typical” mean off-set for the envelope and each of the parts, how could this knowledge be used to make the design robust against such shifts and drifts?
+ ∞- ∞
Page 18/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
Calculation examples
0,245860,245600,249960.249960.245550.254480.250690.252020.254830.245900,253470,250050.248970.247390.25157
Measurements
Stack 5 = ?
X +/- Y
Minimum rail spacing = ?
Assumption: long term behavior
0.250260.249940.245180.245910.248070.254070.253710.250810.248530.249160.247350.249520.253060.254950.25432
Statistical Tolerance Analysis
Page 19/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
Calculate the mean
Mean of 5 in stack
sigma of 1 part
Sigma of 5 stacked
Six Sigma Design
Minimum Slot
Part Dimension
Stack 5 = ?
X +/- Y
Minimum rail spacing = ?
The calculation
µ = 0.250
5 ∗ µ = 1.250
σ = 0.00312
sqrt (5 ∗ σ^2) = 0.007
1.250 +/- 0.042
1.292
0.250 +/- 0.01872
Statistical Tolerance Analysis
Page 20/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
Example 1: Statistical Tolerance Analysis
A practical application
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Assembly Housing Pads
Cylinder
Piston
Rotor group
LC of the spindle
Example 1: Statistical Tolerance Analysis
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Pads
.750 ± .015
.062 ±.005
Cylinder
PistonHousing
Seals
Cylinder cover
3.700±.02
1.55±.01
Rotor
.750±.035
CylinderPiston
Caliper Assembly Pads
.95±.005
Example 1: Statistical Tolerance Analysis
Page 23/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
3.700.950 .950
1.551.55
.062 .062
.750 .750.750
Gap
CoverHousing
piston
Cover
Rotor
Loop Diagram
PositiveDesignVector
NegativeDesignVector
piston
Tolerance Vector Analysis
PadsBacking plate
Example 1: Statistical Tolerance Analysis
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Statistical Design Analysis Spreadsheet
Response Description: Order to Ship Cycle for MTO; Replineshment Cycle for MTI_________ Analyst: _____________________ Date: 22. Feb 05
Analysis Table
Variable Information Tolerance Dist. Type
Factor Short or % or Normal or Sensitivity
Description Mean Long Term Std Dev Lower Upper Actual Uniform Coef. DPU ZST
L A N
Mean Response→Response Upper Spec Limit
Response Lower Spec Limit
Summary TableResponse Components
Worst Case LimitsMean Std Dev DPU ZST Lower Upper DPU ZST
Rev 2.0a
© Dr. Maurice L. Berryman, 1996. All rights reserved.
Calc Sensitivities
Clear Sensitivities
Hide Rows
Unhide Rows
Example 1: Statistical Tolerance Analysis
Page 25/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
Statistical Design Analysis Spreadsheet
Response Description: Automotiv Break Disk________________________________________ Analyst: _____________________ Date: 22. Feb 05
Analysis TableVariable Information Tolerance Dist. Type
Factor Short or % or Normal or Sensitivity
Description Mean Long Term Std Dev Lower Upper Actual Uniform Coef. DPU ZST
cover 0,95 L 0,0017 0,005 0,005 A N 1 2,102E-02 3,53housing 3,7 L 0,0667 0,2 0,2 A N 1 2,700E-03 4,28cover 0,95 L 0,0017 0,005 0,005 A N 1 2,700E-03 4,28piston 1,55 L 0,0333 0,1 0,1 A N -1 2,700E-03 4,28bp 0,062 L 0,0017 0,005 0,005 A N -1 2,700E-03 4,28pad 0,75 L 0,0050 0,015 0,015 A N -1 2,700E-03 4,28rotor 0,75 L 0,0117 0,035 0,035 A N -1 2,700E-03 4,28pad 0,75 L 0,0050 0,015 0,015 A N -1 2,700E-03 4,28pb 0,062 L 0,0017 0,005 0,005 A N -1 2,700E-03 4,28piston 1,55 L 0,0333 0,1 0,1 A N -1 2,700E-03 4,28
Mean Response→ 0,126Response Upper Spec Limit Response Lower Spec Limit 0
Summary TableResponse Components
Worst Case LimitsMean Std Dev DPU ZST Lower Upper DPU ZST
0,126 0,08286 6,418E-02 3,02 -0,359 0,611 4,531E-02 4,11 Rev 2.0a
© Dr. Maurice L. Berryman, 1996. All rights reserved.
Example 1: Statistical Tolerance Analysis
Page 26/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
Gap
Outer leg (72.8 +/- .20)Seal (3.60 +/- .10)
piston (53.2 +/- .90)
Rotor (25 +/- .12)
Inner shoe (6.4 +/- .30)Outer shoe (6.4 +/- .30)
-A-
-A- to seal (11.9 +/- ..25)
Example 2: Statistical Tolerance Analysis
Page 27/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
-A-
+
-
53.2
6.4
25
Nom. Gap
6.4
72.8
11.9
3.6
Note: The gap should always be positive unless you are working with interference fits!
Loop Diagram
Example 2: Statistical Tolerance Analysis
Page 28/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
Statistical Design Analysis Spreadsheet
Response Description: Break Assembly, example 2___________________________________ Analyst: _____________________ Date: 22. Feb 05
Analysis TableVariable Information Tolerance Dist. Type
Factor Short or % or Normal or Sensitivity
Description Mean Long Term Std Dev Lower Upper Actual Uniform Coef. DPU ZST
Outer leg 72,8 S 0,0667 0,2 0,2 A N -1 2,102E-02 3,53A to seal 11,9 S 0,0833 0,25 0,25 A N -1 2,102E-02 3,53Seal 3,6 S 0,0333 0,1 0,1 A N -1 2,102E-02 3,53Outer shoe 6,4 S 0,1000 0,3 0,3 A N 1 2,102E-02 3,53Rotor 25 S 0,0400 0,12 0,12 A N 1 2,102E-02 3,53Inner shoe 6,4 S 0,1000 0,3 0,3 A N 1 2,102E-02 3,53Piston 53,2 S 0,3000 0,9 0,9 A N 1 2,102E-02 3,53
Mean Response→ 2,7Response Upper Spec Limit
Response Lower Spec Limit 0
Summary TableResponse Components
Worst Case LimitsMean Std Dev DPU ZST Lower Upper DPU ZST
2,7 0,457962 2,286E-09 7,36 0,53 4,87 1,471E-01 3,53 Rev 2.0a
© Dr. Maurice L. Berryman, 1996. All rights reserved.
Example 2: Statistical Tolerance Analysis
Page 29/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
Example: Order Cycle Time
How good is the fulfilment for 2,7 days (65h)?
Order entry2 +/- 1h
Raw supply28 +/-16 h
Process2 +/- 1 h
Waiting10 +/- 1h
Turn around4+/- 0,5 h
Turn around4+/- 0,5 h
QC + Packaging1 +/- 0,5 h
Order to Delivery = Order entry + Raw supply + Turn around + Waiting + Processing + Waiting + Turn around + QC + Packaging
Waiting10 +/- 1h
Page 30/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
Hypothetical Data Baseline
Example: Order Cycle Time
Statistical Design Analysis Spreadsheet
Response Description: Auftragslaufzeit für Prozess XY__________________________________ Analyst: _____________________ Date: 08. Sep 05
Analysis TableVariable Information Tolerance Dist. Type
Factor Short or % or Normal or Sensitivity
Description Mean Long Term Std Dev Lower Upper Actual Uniform Coef. DPU ZST
Order entry + scheduling 2 L 0,3333 1 1 A N 1 2,700E-03 4,28Raw supply 28 L 5,3333 16 16 A N 1 2,700E-03 4,28Waiting 10 L 0,3333 1 1 A N 2 2,700E-03 4,28Turn around 4 L 0,1667 0,5 0,5 A N 1 2,700E-03 4,28Process 2 L 0,3333 1 1 A N 1 2,700E-03 4,28Turn around 4 L 0,1667 0,5 0,5 A N 1 2,700E-03 4,28Waiting 10 L 0,3333 1 1 A N 1 2,700E-03 4,28QC + packaging 1 L 0,1667 0,5 0,5 A N 1 2,700E-03 4,28
Mean Response→ 61Response Upper Spec Limit 65Response Lower Spec Limit 0
Summary TableResponse Components
Worst Case LimitsMean Std Dev DPU ZST Lower Upper DPU ZST
61 5,4134606 2,300E-01 2,24 38,5 83,5 2,160E-02 4,28 Rev 2.0a
© Dr. Maurice L. Berryman, 1996. All rights reserved.
Page 31/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
Statistical Design Analysis Spreadsheet
Response Description: Auftragslaufzeit für Prozess XY__________________________________ Analyst: _____________________ Date: 08. Sep 05
Analysis TableVariable Information Tolerance Dist. Type
Factor Short or % or Normal or Sensitivity
Description Mean Long Term Std Dev Lower Upper Actual Uniform Coef. DPU ZST
Order entry + scheduling 2 L 0,3333 1 1 A N 1 2,700E-03 4,28Raw supply 25 L 3,3333 10 10 A N 1 2,700E-03 4,28Waiting 5 L 0,3333 1 1 A N 1 2,700E-03 4,28Turn around 4 L 0,1667 0,5 0,5 A N 1 2,700E-03 4,28Process 2 L 0,3333 1 1 A N 1 2,700E-03 4,28Turn around 4 L 0,1667 0,5 0,5 A N 1 2,700E-03 4,28Waiting 5 L 0,3333 1 1 A N 1 2,700E-03 4,28QC + packaging 1 L 0,1667 0,5 0,5 A N 1 2,700E-03 4,28
Mean Response→ 48Response Upper Spec Limit 65Response Lower Spec Limit 0
Summary TableResponse Components
Worst Case LimitsMean Std Dev DPU ZST Lower Upper DPU ZST
48 3,4115816 3,273E-07 6,47 32,5 63,5 2,160E-02 4,28 Rev 2.0a
© Dr. Maurice L. Berryman, 1996. All rights reserved.
Hypothetical Data Future alternative
Example: Order Cycle Time
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1. Enter the information and data for each variable
2. Enter the Std Dev. optional input; if a value is entered here, the tolerance field is not used. If no value is entered, this is a calculated field based on the tolerance field entries described below.
3. Enter the tolerance information for each variable
4. Selection of the probability distribution based of the toleranceassumption
5. Entry of the equation in the equation field (mean response)
6. Use the “ calc sensitivities” button for calculation
7. Analysis of the area results and components
8. If a new equation has to be used push „clear sensitivities“ and enter new equation for new analysis with the use of the „calculate sensitivities“ button.
Statistical Analysis Spreadsheet, procedure - short cut
Statistical Tolerance Analysis
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1. Designed to analyze tolerance stack-ups on linear and non-linear transfer functions (1-dimensional or multi-dimensional tolerance analysis)
2. Can be used for limited optimization based on sensitivity analysis and tolerancing
3. User Entries are highlighted in color (Both required and optional inputs)
4. Calculated Cells are write protected (Formulas hidden)
5. The analysis spreadsheet can handle up to 20 different variables in a statistical analysis.
6. If more than 20, terms can be combined on lower level analysis spreadsheets
7. Top Section is all user inputs
8. Bottom Section (Summary Box) is response results section
Statistical Analysis Spreadsheet, general information
Statistical Tolerance Analysis
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1 Define the Problem
2
Statistical Tolerance Analysis
Identify Important Terms for Analysis: (Dimensions and properties of material)
Dimensions of the beam
tensile stress in beam (s)
max bending moment in beam
moment of inertia
distance to where beam is analyzed
yield strength of material (S)
load
performance requirement > 0: P = (S - s)
Page 35/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
t
h
w
P
L1
LT
WP
F
Statistical Tolerance Analysis
Structural Design A Sensitivity Study
Page 36/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
σ t
FA
Fht wt t
= =+ −2 2 4 2
( )( )( )
σ
σ
b
bP T P
McI
ch
hPW L L W
wh w t h t
=
=
=− −
− − −
23 2 2
2 21
3 3
Statistical Tolerance Analysis
Tensile Stress:
Bending Stress:
Maximum Stress:It will be a combination of tensile stress and bending stress
Page 37/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
( )( )( )33
P1TP
2s
bts
t2ht2wwhWL2L2hPW3
t4wt2ht2F
−−−−−
+−+
=σ
σ+σ=σ
Statistical Tolerance Analysis
Total stress will be the sum of bending and tension stress
If the yield strength, Sy of the material is known, the design margin is equal to the difference between the maximum stress and the yield strength, or Sy-ss
Page 38/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
( )( )( )33
P1TP
2y t2ht2wwhWL2L2hPW3
t4wt2ht2F
S.Diff−−−−−
+−+
−=
Statistical Tolerance Analysis
The equation above will be programmed into
the Statistical Design Analysis Spreadsheet
for analysis and optimization
All specifications are entered in the spreadsheet Struc.xls.
Assume all dimensions are 3 sigma long term.
Adjust specifications to achieve 6 sigma design margin.
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Appendix:
Procedure for the Spreadsheet
Acronyms
Page 40/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
• User Inputs
1) Variable Information:
– Description: Description of the variables in the stack-up
– Name: Name of the variables
– Mean: Mean value of the variable
– Std Dev: This is an optional input; if a value is entered here, the tolerance field is not used. If no value is entered, this is a calculated field based on the tolerance field entries described below. Once a value is typed into this field, it replaces the formula which is used when data is entered into the tolerance fields.
Spreadsheet Field Descriptions
Statistical Tolerance Analysis
Page 41/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
• User Inputs
2) Tolerance Field inputs:
– Upper and Lower Tolerance: The user can enter the upper and lower tolerances of the variable.
– % or actual: When a % sign is typed into it recognizes the lowerand upper tolerance as a percent of Mean value. When an “A” is typed in for “Actual” the lower and upper are recognized as the actual value of the upper and lower limit.
– Tolerance Field Inputs (cont):
– Distribution Type: Enter “N” for normal and “U” for Uniform distributions. If N, then the std dev is calculated as the (tolerance range) / 6. If U, then the std dev is calculated as the (tolerance range) / SQRT(12).
Statistical Tolerance Analysis
Spreadsheet Field Descriptions
Page 42/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
Spreadsheet Field Descriptions
• User Inputs
3) Enter Equation:
– The equation for the relationship between the response and variables is entered here. The entry must be in terms of the cell locations of the means of the variables (e.g... = (C9 +C10); this says the response is the sum of the variables whose mean values show up in C9 and C10).
– Upper and Lower Response Spec Limits: the upper and lower specs for the response is entered here. This can be a one sidedspec if necessary.
Statistical Tolerance Analysis
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• Calculations for Top Section:– Sens: This is the sensitivity of that variable based on the partial
derivative of the transfer function loaded into the equation box.
– DPU: Probability of bad parts based on their tolerance range and mean and standard deviations. DPU is the probability that parts will be produced outside the tolerance range.
– On parts with a uniform distribution this probability is shown to be zero, with truncation outside the tolerance range.
– Sigma: “Sigma” of the individual variables based on their capability relative to the specification. This is a long term Sigma where 3.4 defects/mil = 6 Sigma.
– The calculations for the top section are completed as the data is entered into the variable and tolerance fields.
– These calculations do not change when calculate sensitivity is pushed.
Statistical Tolerance Analysis
Spreadsheet Field Descriptions
Page 44/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
Statistical Tolerance Analysis
Spreadsheet Field Descriptions
• Calculations of the Summary Section:1) Response Section:
– Mean: Mean value of the response based on the individual variable means and transfer function
– Std Dev: Standard deviation of the response based on individual variable standard deviations and sensitivities from the differentiation of the transfer function
– DPU & Sigma: These are based on the responses long term capability. The limits of the Sigma number are -1.5 to 28. Outside of these values will still produce the same numbers.
– Worst Case Upper and Lower Limit: These are for the response based on the worst combination of the individual variables at their worst case values and their effect on the response.
2) Components Section:
– DPU: The sum of all DPUs for the individual components
– Sigma: Based on the total Component DPU with the number of opportunities being the total number of components
Page 45/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
• BOM - Bill of Materials
• DFA - Design for Assembly
• DFM - Design for Manufacturability
• DOE - Design of Experiments
• DPMO - Defects per million opportunities
• DPU - Defects Per Unit
• DPU sub - DPU submitted
• DPU obs - DPU observed
• DPU esc - DPU escaping
• DV - Dependent Variable
Statistical Tolerance Analysis
Acronyms
Page 46/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
• EE - Electrical Engineering
• FEA - Finite Element Analysis
• FMEA - Failure Modes and effects analysis
• GR&R - gauge repeatability & reproducibility
• H/W - Hardware
• I & T - Integration & Test Phase of a Program
• IV - Independent Variable
• LSL - Lower Specification Limit
• ME - Mechanical Engineering
• mil. - million
• oppor - opportunity
Statistical Tolerance Analysis
Acronyms
Page 47/4705b BB W4 Tolerancing 05, D. Szemkus/H. Winkler
• PCB - Printed Circuit Board• PCD - Process Capability Database• PCM - Process Capability Models• QFD - Quality Function Deployment • RSS - Root Sum Squares• SDM - Statistical Design Methods• SE - Systems Engineering• S/W - Software• USL - Upper Specification Limit• Tol - Tolerance• WC - Worst Case• 1-d - one dimensional linear stack-up
Statistical Tolerance Analysis
Acronyms
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