This document discusses assessing process capability for binomial or discrete data using binomial analysis or Poisson analysis. It provides an overview of calculating process capability metrics such as defects per million opportunities (DPMO) and Z score. An example is shown applying binomial analysis to a "MetricB" field to analyze defects. Practitioners are asked to identify two discrete metrics from their organization, calculate the DPMO and Z score for each using binomial analysis, and determine if the processes are capable based on the results.

1. Section & Lesson #:
Pre-Requisite Lessons:
Complex Tools + Clear Teaching = Powerful Results
Process Capability: Step 6 (Binomial)
Six Sigma-Analyze – Lesson 7
As part of a series about process capability, this lesson shows how to assess
the capability of a process that’s based on discrete or binomial data.
Six Sigma-Analyze #05 – Process Capability: Step 4 (Normal Dist)
Six Sigma-Analyze #06 – Process Capability: Step 5 (Non-Normal
Dist)
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.
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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. Review of Capability Analysis Metrics
o Below are the metrics previously reviewed when calculating process capability:
• Defects per Million Opportunities (DPMO)
 A count of the number of defects expected to occur for every one million opportunities run in the process.
• Z score or sigma level
 Measures the VOP in relation to the VOC, or the “severity of pain” in the process not meeting the
customer’s requirements.
 If a capable process has at least 3σ between the spec limit and mean, then this process isn’t quite capable.
• Cpk and Ppk
 Measure short-term (Cpk) and long-term (Ppk) process performance (VOP) in relation to the spread (or
total tolerance) between LSL & USL (VOC).
 If Cpk < 1, the process is not capable with the tolerance (LSL & USL).
 The higher Cpk is above 1, the more capable the process is of achieving results within tolerance.
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.
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4. Process Capability (Discrete Data)
o How do you measure process capability for discrete data?
• There are two tools that you can use; the one you use will depend on how your data is setup:
 Binomial Analysis – Uses P chart for measuring the # of defectives out of a total sample.
– For example, measuring unresolved calls, broken products, erroneous bills, etc.
 Poisson Analysis – Uses U chart for measuring the # of defects per unit (DPU).
– For example, measuring # of errors a phone rep made per call, # of errors appearing on each bill, etc.
• The example below is run on “MetricB” field in the Minitab 15 Sample Data v1.MPJ file:
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.
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9181716151413121111
0.15
0.10
0.05
0.00
Sample
Proportion
_
P=0.0700UC L=0.0734LC L=0.0666
100806040200
16
14
12
10
8
Sample
%Defective
Upper C I: 1.4774
%Defectiv e: 7.00
Lower C I: 6.98
Upper C I: 7.02
Target: 0.00
PPM Def: 70002
Lower C I: 69779
Upper C I: 70226
Process Z: 1.4758
Lower C I: 1.4741
(95.0% confidence)
Summary Stats
1000050000
7500
5000
2500
0
Observed Defectives
ExpectedDefectives
1815129630
16
12
8
4
0
%Defective
Frequency
Tar
1
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111
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Binomial Process Capability Analysis of Defects
P Chart
Cumulative %Defective
Binomial Plot
Histogram
MetricB % was
converted to integer
in “Defects” column
Shows change in %
Defective as samples
increase. If it stabilizes,
then you have enough
samples.
From Stat > Quality Tools > Capability Analysis > Binomial…
P Chart shows process
has high variation and is
out of control.
Some process
capability metrics are
listed like PPM (DPMO)
and Process Z.

5. Practical Application
o Identify at least 2 discrete metrics used by your organization.
• Run each metric through the capability analysis for binomial data and answer the following:
 What is the DPMO?
 What is the Z score?
• 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.
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