As part of a series about process capability, this lesson shows how to assess the capability of a process that’s based on a non-normal distribution.

1. Section & Lesson #:
Pre-Requisite Lessons:
Complex Tools + Clear Teaching = Powerful Results
Process Capability: Step 5 (Non-Normal Dist)
Six Sigma-Analyze – Lesson 6
As part of a series about process capability, this lesson shows how to assess
the capability of a process that’s based on a non-normal distribution.
Six Sigma-Analyze #05 – Process Capability: Step 4 (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. Capability Analysis (Non-Normal Dist)
o How do you measure process capability for non-normal data?
• Use the same process capability tool in Minitab, but transform the data first.
 A Box-Cox transformation will raise the data to the power λ (lambda) – a number between -5 and 5.
 This method will “normalize” the non-normal data in order to calculate the process capability metrics.
• In the “Capability Analysis (Normal Distribution)” box, click the “Box-Cox…” button.
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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1.050.900.750.600.450.300.15
transformed data
LSL* USL*
USL* 0.974679
Sample Mean* 0.547926
StDev (Within)* 0.178648
StDev (O v erall)* 0.22427
LSL 0.02
Target *
USL 0.95
Sample Mean 0.350017
Sample N 100
StDev (Within) 0.191106
StDev (O v erall) 0.250974
LSL* 0.141421
Target* *
A fter Transformation
Process Data
C p 0.78
C PL 0.76
C PU 0.80
C pk 0.76
Pp 0.62
PPL 0.60
PPU 0.63
Ppk 0.60
C pm *
O v erall C apability
Potential (Within) C apability
PPM < LSL 20000.00
PPM > USL 0.00
PPM Total 20000.00
O bserv ed Performance
PPM < LSL* 11439.49
PPM > USL* 8452.00
PPM Total 19891.49
Exp. Within Performance
PPM < LSL* 34949.08
PPM > USL* 28529.82
PPM Total 63478.90
Exp. O v erall Performance
Within
O v erall
Process Capability of MetricB
Using Box-Cox Transformation With Lambda = 0.5
This option will
transform the
data into this…
All of the process
capability metrics can
be interpreted as
previously described.
From Stat > Quality Tools > Capability Analysis > Normal…

5. 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 non-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 non-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.
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