Design tolerances using Six Sigma Statistical tolerances

Design tolerances using Six Sigma

1. August 5, 2016

2. August 5,
Page 2

3. Accurate but not precise-On
average, the shots are in the center of
the target but there is a lot of
variability
Precise but not accurate -
The average is not on the center,
but the variability is small
Source: iSixSigma

4. TOTAL Variation
Part to Part Variation
Measurement System Variation
Repeatability:
Variation due to gage
or measurement tool
Reproducibility:
Variation due to people or
operators who are measuring
s
2
Total
= s
2
Part-Part
+ s
2
R&R

5. August 5, 2016 Pa
ge

6. 6
μ
1 μ
2
delta
(δ)
(Between Group Variation)
Within Group Variation
(level of supplier 1)
Total (Overall) VariationX X X X X X X X X

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8. The C
pkindex is a modified C
pindex for mean shift of the process
characteristic.
kranges between <0..1>
The effective standard deviation of the process may then be
estimated as:
August 5, 2016 Pa
ge

9. 9
USLLSL
Voice of the
Customer
Voice of The Process
Voice of the Customer
Voice of the Process
Capability Ratio-compares the capability of a process (voice of the
process) to the specification limits (voice of the customer):
=
USL -LSL
6s
= Cp
Cp = 1:The process is
barely capable (Just fits into
the tolerance window).
Cp = 2:The process is a
six sigma process (The
tolerance window is twice
the process capability).

10. A 3sprocess -because 3 standard
deviations fit between target and
acceptance goalposts
Target Customer
Specification
1s
2s
3s
3s
Before
Target
Customer
Specification
After
1s
6s
6s
Continuous improvement:
By reducing variability
we improve the process
“Design for
Six Sigma”
“Defects ~ 66807 ppm”
“Defects ~ 3.4 ppm”
3s

11. What do we Need?
LSL USL LSL USL
LSL USL
Off-Target, Low Variation
High Potential Defects
Good Cp but Bad Cpk
On Target
High Variation
High Potential Defects
No so good Cp and Cpk
On-Target, Low Variation
Low Potential Defects
Good Cp and Cpk
Variation reduction and process
centering create processes with
less potential for defects.
The concept of defect reduction
applies to ALLprocesses (not just
manufacturing)

12. Page12August 5, 2016
Cp=1.03
Cpk=0.57
Ppk=0.73
What’s the
difference ?
Is this
process
capable long
term?
Supplier Component #1 Capability Analysis

13. For estimating percent nonconforming for a
process, we will substitute the Lower Spec Limit
(LSL) and the Upper Spec Limit (USL) for x
13s
] x-LimitSpec Lower) or [(Upper
=Z s
)x-(x
=Z

14. Z= % Out of
Tolerance Dimension NominalToleranceUSL LSL Failure PointϭUSL - LSLZ-% OUT SPEC
Coefficienct
Friction
0.138 0.01 0.148 0.128 0.116 0.003 0.013.3330.0003%
Hub ID 79 0.05 79.05 78.95 80.15 0.00830.056.0240.0002%
Clutch OD 81.35 0.15 81.5 81.2 80.15 0.03750.154.0000.0250%
Clutch Coil
Turns
5 0.03 5.03 4.97 4.54 0.00820.033.6590.0002%

15. Page15August 5, 2016Probability of SINGLE POINT FAILURE
Dimension
Coefficienct
Friction
Hub ID Clutch OD
Clutch Coil
Turns
X--Nominal 0.138 79 81.35 5
Tolerance 0.01 0.05 0.15 0.03
USL 0.148 79.05 81.5 5.03
LSL 0.128 78.95 81.2 4.97
Failure Point 0.116 80.15 80.15 4.54
(x-Nominal) 0.02 0.05 0.15 0.03
(x-Nominal) sq 0.00 0.00 0.02 0.00
ϭ 0.00 0.01 0.01 0.01
2Ϭ 0.01 0.02 0.02 0.02
e power 0.08 0.15 1.36 0.05
E-power x 1.08 1.16 3.88 1.06
1/2pi 0.16 0.16 0.16 0.16
Probability 0.17 0.19 0.62 0.17
Probability of
FAILURE =
17% 16.8%11.4%

16. The rate of change in the Standard Error approaches zero at about 30 samples.
This is why 30 samples is often recommended when generating summary statistics
such as the Mean and Standard Deviation.
This is also the point at which the t and Z distributions become nearly equivalent.
1
6
3020100
Sample Size
Standard
Error
5

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20. If Total Tolerance Assy= 0.09, calculate WC & RSS required
design tolerance for each part assuming 9 parts of equal
tolerance
WC => Tp= T ASM /9= 0.09/9= +/-0.01
RSS-> Tp= T ASM/√9= 0.09/3= +/-0.03 Which one do you use?
P
a

21. Page21
WC –Tolerance 6 Sigma
Tolerance
Loss of
Function
Out of tol
but
functional

22. August 5,
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Out of spec but
functional part

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