A review of when and how to use the U control chart.

1. Section & Lesson #:
Pre-Requisite Lessons:
Complex Tools + Clear Teaching = Powerful Results
Control Charts: U Chart
Six Sigma-Control – Lesson 7
A review of when and how to use the U control chart.
Six Sigma-Control #03 – Control Charts: Finding the Right
Control Chart
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. o How do you read a control chart?
• Control charts plot the data points (continuous data) over time and define the following:
 Observations – the data points from the dataset that should be pre-sorted in date/time order.
 Mean – the average for all data points.
 LCL – Lower Control Limit defined as 3σ below the mean.
 UCL – Upper Control Limit defined as 3σ above the mean.
 Special Cause Tests – Any of 8 rules can be tested on the data to highlight potential special causes.
• Below is an example of a control chart and its various components:
• Control limits (LCL/UCL) are not the same as Specification limits (LSL/USL).
 Spec limits are tied to the VOC; a process can be “in control” but not meet customer req’ts & vice versa.
Review of Control Charts
2
Mean (average)
of the dataset
Upper Control Limit set
at 3σ above the mean
Lower Control Limit set
at 3σ below the mean
Indicates 20 observations
(data points) in time order
191715131197531
57.5
55.0
52.5
50.0
47.5
45.0
42.5
40.0
Observation
IndividualValue
_
X=48.85
UCL=56.55
LCL=41.15
1
I Chart of Data
Observation #7 failed the test for
data points outside LCL/UCL.
Expected
variation region
(common cause)
Unexpected
variation region
(special cause)

3. U Chart Defined
o What is it?
• It uses a Poisson distribution to measure the proportion
of defectives per unit in a sample.
 A Poisson distribution measures the discrete probability
of the # of events occurring in a fixed timeframe (based on
a known average rate).
– For example, measuring the # of accidents at an intersection, the # of calls to a business, etc.
• It’s ideal when the volume of units (opportunities) vary in each stage (per day, shift, week, etc.).
 Unlike using a raw percentage, it accounts for the variation in the denominator of that percentage.
– For example, two samples yielding a 10% defect rate seem to be the same, but it may make a difference if the 1st sample
was for a weekend with 100 total units (10 defects) and the 2nd sample was for a weekday with 1000 units (100 defects).
• Only the first 4 of 8 special cause tests
are available to run on these charts.
o What are the chart’s requirements?
• The plotted data must be continuous, but
represent discrete values (defective rate).
• Sub-grouping is expected (since it’s discrete
data); a column must identify the groups.
o How do I access the chart in Minitab?
• Go to Stat > Control Charts >
Attribute Charts > U…
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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I-MR chart
What
Type of
Data?
Defects or
Defectives?
What
Sub-Group
size?
X bar-S chart P chart U chart
DiscreteContinuous
DefectivesDefects2+1

4. U Chart Example
o Below is an example of the source data used and the resulting U chart:
• Though the results look the same as the P Chart, the difference is in the control limits.
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
191715131197531
0.14
0.13
0.12
0.11
0.10
0.09
0.08
0.07
0.06
0.05
Sample
SampleCountPerUnit _
U=0.09131
UCL=0.13032
LCL=0.05230
U Chart of Errors
Tests performed with unequal sample sizes
70 errors seem high, but
proportionally it’s “in control”
Period Volume Errors
1 550 50
2 520 49
3 530 47
4 580 51
5 520 47
6 520 48
7 480 39
8 550 52
9 570 49
10 590 48
11 550 50
12 520 51
13 600 70
14 570 48
15 550 52
16 560 50
17 580 51
18 530 49
19 520 48
20 540 49

5. Practical Application
o Identify at least 2 critical metrics used by your organization that are discrete values.
• Acquire some sorted, historical data for each metric that includes at least 20 data points and run
them through U chart.
• Ask yourself the following for each metric:
 Was there any data point that failed the 1st test (falling outside the LCL or UCL)?
– If so, then can you explain what caused this failure? Does it appear to be a special or common cause?
 If any failures were noted, then what actions should be taken to help fix and/or prevent future failures?
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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