1) The document discusses process capability and sigma metrics, which are used to measure process performance and defect rates. It provides examples of how defect rates decrease significantly as sigma levels increase from 1 to 6. 2) It explains key process capability ratios like Cp, Cpk, and how they are calculated. Cp measures how close the process is to the specification limits, while Cpk also considers whether the process is centered between the limits. 3) The document provides examples of how a process shift can decrease Cpk and increase defect rates, even if the process remains within specifications. Maintaining low variation and centering are important to minimize defects.

1. Process Capability
Julian Kalac, P.Eng
Lean Six Sigma Master Black Belt

2. 2
Normal Distribution
-6s -5s -4s -3s -2s -1s 0 1s 2s 3s 4s 5s 6s
One Standard
Deviation (s)
This is a Normal distribution where:
Mean = 0
Standard Deviation = 1

4. Process Capability & “Sigma”
Cp Sigma* Defect Rate
0.67 ± 2σ 31%
1.0 ± 3σ 6.7%
1.33 ± 4σ 0.6%
1.66 ± 5σ 0.02%
2.0 ± 6σ 0.003%

5. Sigma vs. Defect Rate
• 1 sigma – 690,000 DPMO – 31%
• 2 sigma – 308,537 DPMO – 69.14%
• 3 sigma – 66807 DPMO – 93.32%
• 4 sigma – 6210 DPMO – 99.38%
• 5 sigma – 233 DPMO – 99.97%
• 6 sigma – 3.4 DPMO – 99.99%
When is good is good enough?
6.7% rejects
69% rejects
31% rejects

6. 6
Cp
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).

7. 7
C Min(
X-LSL
3
USL-X
3
pk =
s s
, )
C
X-LSL
3
pL =
s
USL-X
3s
CpU =
Cpk accounts for process centering and spread.
Process Capability Ratios

8. 8
Cp & Cpk for an Off-Center Process
Cp= 1.3
Cpk = 1.3
Cp= 1.3
Cpk = 0.8
Cp= 1.3
Cpk = 0.0

9. Process Capability & “Sigma” & Defect Per Mil
Cp Sigma* Defect/Mil
0.67 ± 2σ 308,537
1.0 ± 3σ 66807
1.33 ± 4σ 6210
1.66 ± 5σ 233
2.0 ± 6σ 3.4

10. 10
Cpk
4.5
3.0
2.0
1.67
1.33
1.0
0.9
0.8
0.67
0.5
TARGET USL UCLLCL LSL
Z (Sigma) Value
6.0
5.0
4.0
3.0
2.0
PPM
<<1 PPBillion
.0018
< 1
230
2,700
6,210
16,400
66,800
308,000
3.4 PPM
Yield ST
99.99966 %
99.977%
99. 379%
≈ 99%
≈ 95 %
Process Variation Shifts over time
What are some of the ways that we can easily indicate the dispersion
(spread) characteristic of the population?
Three measures that have historically been used:
range, variance and standard deviation

11. -6s -5s -4s -3s -2s -1s 0 1s 2s 3s 4s 5s 6s
Process Capability Cpk=2 Process Shift
Cpk= 1.33 after 1.5s Process shift
USLLSL
LCL UCLCpk = 2 before 1.5Ϭ shift
Cpk = 1.33 after 1.5Ϭ shift,
within spec

12. -6s -5s -4s -3s -2s -1s 0 1s 2s 3s 4s 5s 6s
Process Capability Cpk =1 6.7% Out of Spec
Process Shift 1.5 Out of spec= 52%
Control LimitsCpk= 1 -> 3s Process
LSL USL
LCL UCL

13. -6s -5s -4s -3s -2s -1s 0 1s 2s 3s 4s 5s 6s
Process Capability Cpk =2—38% Out of Spec
Control LimitsCpk= 0.67 -> 2s Process
LSL USL
LCL UCL

14. 14
Accuracy and Precision
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

15. Variation and Mean Shift
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 ALL processes (not just
manufacturing)