This document provides instruction on assessing the capability of a process that follows a normal distribution. It discusses key metrics like Cp, Cpk, Pp and Ppk which measure process performance relative to customer specifications. The document also explains how to calculate and interpret process capability metrics like DPMO from the output of a process capability analysis in Minitab.

1. Section & Lesson #:
Pre-Requisite Lessons:
Complex Tools + Clear Teaching = Powerful Results
Process Capability: Step 4 (Normal Dist)
Six Sigma-Analyze – Lesson 5
As part of a series about process capability, this lesson shows how to assess
the capability of a process that’s based on a normal distribution.
Six Sigma-Analyze #04 – Process Capability: Steps 1 to 3
Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted by any means
(electronic, mechanical, photographic, photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.

2. Process Capability Review
o What is process capability?
• As the “Voice of the Process” (VOP), it
represents a standard set of metrics
that define how a process is performing
(its capability).
o How do we calculate the process capability?
• This illustration at right shows the
steps and tools you can use to
calculate process capability.
Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted by any means (electronic, mechanical, photographic,
photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.
2
Process Capability
(Voiceof ProcessorVOP)
Customer Requirements
(Voiceof CustomerorVOC)
PerformanceGap
between VOC & VOP
Actual
Process
Performance
Define
(GetVOC)
Measure
(GetVOPData)
Analyze
(AnalyzeGap)
Improve
(Fix Gap)
Control
(Sustain Fix)

3. Capability Analysis (Normal Dist)
o Follow the next set of steps when the following conditions exist in the data:
• Data type = Continuous
• Process = Stable
• Distribution = Normal
o How do I calculate the process capability?
• The example below is run on “MetricA” field in the Minitab 15 Sample Data v1.MPJ file:
 NOTE: Minitab 14 Student Version does not support this process capability calculation. Follow instructions
later on how to manually calculate the process capability.
Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted by any means (electronic, mechanical, photographic,
photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.
3
From Stat > Quality Tools > Capability Analysis > Normal…
Identify the field used for measuring the
process (probably the project Y).
Use “1” for subgroup size. See the Measure
phase lesson on “Rational Sub-Grouping” for
more details.
Type in the customer’s requirements (VOC) in
terms of an upper and/or lower spec limit.

4. An Example from Minitab
o Below is the output from Minitab.
• This output introduces several new HIGHLIGHTED terms & concepts that we’ll begin to explore.
Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted by any means (electronic, mechanical, photographic,
photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.
4
10008006004002000
LSL USL
LSL 50
Target *
USL 1100
Sample Mean 521.646
Sample N 100
StDev (Within) 221.349
StDev (O v erall) 231.974
Process Data
C p 0.79
C PL 0.71
C PU 0.87
C pk 0.71
Pp 0.75
PPL 0.68
PPU 0.83
Ppk 0.68
C pm *
O v erall C apability
Potential (Within) C apability
PPM < LSL 10000.00
PPM > USL 10000.00
PPM Total 20000.00
O bserv ed Performance
PPM < LSL 16553.73
PPM > USL 4489.42
PPM Total 21043.15
Exp. Within Performance
PPM < LSL 21016.93
PPM > USL 6330.14
PPM Total 27347.07
Exp. O v erall Performance
Within
Overall
Process Capability of MetricA
This is the
descriptive
statistics for
your data.
The LSL & USL
(which are the VOC)
are added the graph
PPM stands for “Parts Per
Million” which is used for
calculating DPMO (Defects
per Million Opportunities)
“Observed” is the
calculation for your
actual data.
“Within” is the
SHORT-TERM
calculation for
your data.
“Overall” is the
LONG-TERM
calculation for
your data.
CPK and PPK are the
critical process
capability metrics.

5. Process Capability (DPMO)
o What is DPMO?
• It’s a count of the number of defects expected to occur
for every one million opportunities run in the process.
 It’s essentially like a percent defective or p(d) that’s
carried out to the 4th decimal place.
o How is it calculated?
• The equation for DPMO is as follows:
o How is it interpreted? (using the Minitab example)
Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted by any means (electronic, mechanical, photographic,
photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.
5
10008006004002000
LSL USL
LSL 50
Target *
USL 1100
Sample Mean 521.646
Sample N 100
StDev (Within) 221.349
StDev (O v erall) 231.974
Process Data
C p 0.79
C PL 0.71
C PU 0.87
C pk 0.71
Pp 0.75
PPL 0.68
PPU 0.83
Ppk 0.68
C pm *
O v erall C apability
Potential (Within) C apability
PPM < LSL 10000.00
PPM > USL 10000.00
PPM Total 20000.00
O bserv ed Performance
PPM < LSL 16553.73
PPM > USL 4489.42
PPM Total 21043.15
Exp. Within Performance
PPM < LSL 21016.93
PPM > USL 6330.14
PPM Total 27347.07
Exp. O v erall Performance
Within
Overall
Process Capability of MetricA
10008006004002000
LSL USL
LSL 50
Target *
USL 1100
Sample Mean 521.646
Sample N 100
StDev (Within) 221.349
StDev (O v erall) 231.974
Process Data
C p 0.79
C PL 0.71
C PU 0.87
C pk 0.71
Pp 0.75
PPL 0.68
PPU 0.83
Ppk 0.68
C pm *
O v erall C apability
Potential (Within) C apability
PPM < LSL 10000.00
PPM > USL 10000.00
PPM Total 20000.00
O bserv ed Performance
PPM < LSL 16553.73
PPM > USL 4489.42
PPM Total 21043.15
Exp. Within Performance
PPM < LSL 21016.93
PPM > USL 6330.14
PPM Total 27347.07
Exp. O v erall Performance
Within
Overall
Process Capability of MetricA
In the actual dataset that was “observed”,
1% (or 10,000 out of 1,000,000) of the data
points each fell below the LSL and above
the USL; together 2% (or 20,000 out of
1,000,000) of the data points are defects
By calculating for the short-term,
1.66% of the data points would fall
below the LSL and only 0.45% would
lie above the USL leaving a total p(d)
of 2.1% (or 97.9% success).
By calculating for the long-term,
2.1% of the data points would fall
below the LSL and only 0.63% would
lie above the USL leaving a total p(d)
of 2.73% (or 97.27% success).
What can we conclude from this? Based on the short & long term calculations, it
appears the process is more likely to fail (create defects) that fall below the LSL.

6. Process Capability (Z score or sigma level)
o What is a Z Score (a.k.a. sigma level)?
• Practically, Z score measures the VOP in relation to the
VOC. In a sense, it measures the “severity of pain” in
the process not meeting the customer’s requirements.
• Technically, Z score measures the number of standard
deviations (σ) a data point (like USL) is from the mean.
o How is it calculated?
• The equation for Z score is as follows (“X” is generally an observation like USL)
o How is it interpreted?
• From the Minitab example, use USL as “X”:
• What can we conclude from this?
 If a capable process has at least 3 σ between the spec
limit and mean, then this process is not quite capable.
• How is short vs. long term data accounted for in the Z score?
 If the data is short term (Zst) and you want to calculate long term capability (Zlt) then subtract 1.5σ from Z.
 If the data is long term (Zlt) and you want to calculate short term capability (Zst) then add 1.5σ to Z.
 Therefore, a formula we can derive from this is: Zlt = Zst – Zshift (or 1.5)
Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted by any means (electronic, mechanical, photographic,
photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.
6
10008006004002000
LSL USL
LSL 50
Target *
USL 1100
Sample Mean 521.646
Sample N 100
StDev (Within) 221.349
StDev (O v erall) 231.974
Process Data
C p 0.79
C PL 0.71
C PU 0.87
C pk 0.71
Pp 0.75
PPL 0.68
PPU 0.83
Ppk 0.68
C pm *
O v erall C apability
Potential (Within) C apability
PPM < LSL 10000.00
PPM > USL 10000.00
PPM Total 20000.00
O bserv ed Performance
PPM < LSL 16553.73
PPM > USL 4489.42
PPM Total 21043.15
Exp. Within Performance
PPM < LSL 21016.93
PPM > USL 6330.14
PPM Total 27347.07
Exp. O v erall Performance
Within
Overall
Process Capability of MetricA
10008006004002000
LSL USL
LSL 50
Target *
USL 1100
Sample Mean 521.646
Sample N 100
StDev (Within) 221.349
StDev (O v erall) 231.974
Process Data
Pot
PPM < LSL 10000.00
PPM > USL 10000.00
PPM Total 20000.00
O bserv ed Performance
PPM < LSL 16553.73
PPM > USL 4489.42
PPM Total 21043.15
Exp. Within Performance
PPM < LSL 21016.93
PPM > USL 6330.14
PPM Total 27347.07
Exp. O v erall Performance
Process Capability of MetricA

7. 10008006004002000
LSL USL
LSL 50
Target *
USL 1100
Sample Mean 521.646
Sample N 100
StDev (Within) 221.349
StDev (O v erall) 231.974
Process Data
C
C
C
C
Pp
PP
PP
Pp
C
O v er
Potential (
PPM < LSL 10000.00
PPM > USL 10000.00
PPM Total 20000.00
O bserv ed Performance
PPM < LSL 16553.73
PPM > USL 4489.42
PPM Total 21043.15
Exp. Within Performance
PPM < LSL 21016.93
PPM > USL 6330.14
PPM Total 27347.07
Exp. O v erall Performance
Wi
Ov
Process Capability of MetricA
Process Capability (Convert Z to Probability)
o What is cumulative probability?
• It refers to the portion of your distribution (area
under the curve) derived by your Z score.
• It’s a calculation converting the Z score into a p(d),
which is used for calculating the DPMO.
 For example, having the short term Z scores (sigma levels)
shown at right, then the DPMO can be determined.
o How is it calculated?
Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted by any means (electronic, mechanical, photographic,
photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.
7
0.4
0.3
0.2
0.1
0.0
X
Density
-2.61286 0
0.00449
Distribution Plot
Normal, Mean=0, StDev=1
SigmaST % Success DPMO
1σ 30.9% 691,462
2σ 69.1% 308,538
3σ 93.3% 66,807
4σ 99.38% 6,210
5σ 99.977% 233
6σ 99.9997% 3.4
From Calc > Probability Distributions > Normal…
A negative Z
score will calculate
the p(d)…
…which matches the PPM (DPMO)

8. Process Capability (Cpk & Ppk)
o What is Cpk & Ppk?
• These measure short-term (Cpk) and long-term (Ppk)
process performance (VOP) in relation to the spread
(or total tolerance) between LSL & USL (VOC).
o How is it calculated?
• The equation for Cpk is as follows (Ppk is similar):
o How is it interpreted? (using the Minitab example)
• Cp represents the process potential while Cpk is the process performance.
• If Cpk < 1, the process is not capable within the tolerance (LSL & USL).
• The higher Cpk is above 1, the more capable the process is of achieving results within tolerance.
• If Cp is much greater than Cpk, then the process mean is missing the target.
 If they are both <1, then it may be better to focus on shifting the mean before
reducing variation in order to get faster improvements.
• Ppk will always be lower than Cpk. But if it’s significantly lower, then it’s
driven by the long term variation (mean shift) between sub-groups.
 In these cases, focus on reducing that sub-group variation knowing that the long-
term process capability (Ppk) has the potential of improving closer to the Cpk.
Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted by any means (electronic, mechanical, photographic,
photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.
8
10008006004002000
LSL USL
LSL 50
Target *
USL 1100
Sample Mean 521.646
Sample N 100
StDev (Within) 221.349
StDev (O v erall) 231.974
Process Data
C p 0.79
C PL 0.71
C PU 0.87
C pk 0.71
Pp 0.75
PPL 0.68
PPU 0.83
Ppk 0.68
C pm *
O v erall C apability
Potential (Within) C apability
PPM < LSL 10000.00
PPM > USL 10000.00
PPM Total 20000.00
O bserv ed Performance
PPM < LSL 16553.73
PPM > USL 4489.42
PPM Total 21043.15
Exp. Within Performance
PPM < LSL 21016.93
PPM > USL 6330.14
PPM Total 27347.07
Exp. O v erall Performance
Within
Overall
Process Capability of MetricA
10008006004002000
LSL USL
LSL 50
Target *
USL 1100
Sample Mean 521.646
Sample N 100
StDev (Within) 221.349
StDev (O v erall) 231.974
Process Data
C p 0.79
C PL 0.71
C PU 0.87
C pk 0.71
Pp 0.75
PPL 0.68
PPU 0.83
Ppk 0.68
C pm *
O v erall C apability
Potential (Within) C apability
Within
Overall
Process Capability of MetricA

9. Process Capability (Sixpack)
o Minitab combines the tests for stability, normality & process capability into one chart.
• Go to Stat > Quality Tools > Capability Sixpack > Normal…
 NOTE: Minitab 14 Student Version does not support this process capability tool.
Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted by any means (electronic, mechanical, photographic,
photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.
9
9181716151413121111
1000
500
0
IndividualValue
_
X=522
UCL=1186
LCL=-142
9181716151413121111
800
400
0
MovingRange
__
MR=249.7
UCL=815.8
LCL=0
10095908580
1000
750
500
Observation
Values
10008006004002000
LSL USL
LSL 50
USL 1100
Specifications
150010005000
Within
O v erall
Specs
StDev 221.349
C p 0.79
C pk 0.71
Within
StDev 231.974
Pp 0.75
Ppk 0.68
C pm *
O v erall
Process Capability Sixpack of MetricA
I Chart
Moving Range Chart
Last 25 Observations
Capability Histogram
Normal Prob Plot
A D: 0.500, P: 0.204
Capability Plot
This is the I-MR
chart for testing
stability.
This is the
histogram with
the LSL & USL.
This is the
probability plot to
test normality
(with Anderson-
Darling test).
Cpk & Ppk are included. PPM (or DPMO)
is not included since Cpk & Ppk are
stronger measures of process capability.

10. Practical Application
o Refer to the 2 continuous metrics identified in the first lesson about process capability.
• For each metric, answer the following:
 Was the metric a continuous value, from a stable process having a normal distribution?
– These attributes are based on the first 3 steps of the process capability calculation method.
 If so, then run a capability analysis for a normal distribution and answer the following:
– What is the DPMO?
– What is the Z score?
– What is the cumulative probability or p(d)?
– What are the Cpk and Ppk?
 Based on the above findings, is the process capable?
Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted by any means (electronic, mechanical, photographic,
photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.
10