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Seven QC Tools for ProcessQuality Improvement
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Seven Major Tools1) Flowchart or process mapping
2) Check Sheet
3) Histogram4) Pareto Chart
5) Cause and Effect Diagram
6) Scatter Diagram
7) Control Chart
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Flowcharts or Run chart Used to explore if there is aprocess
A Flow Diagram, also known as a flow chart,is a diagramatic technique to document aprocedure, within a role or department."Structured" flow diagrams are created using
a single entry (with inputs), a single exit (withoutputs), and a combination of three buildingstructures:
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Building structures
sequence- any series of 1-n sequentialsteps can be represented as a singlestep
choice- a decision between two or morepaths (structured subpaths) [e.g., if-then, case/select]
loop- a structured subpath (single entryand single exit) that is executed 0-ntimes
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Check Sheets Also called: defect concentration
diagram
A check sheet is a structured, preparedform for collecting and analyzing data. This
is a generic tool that can be adapted for awide variety of purposes.
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Source:
http://www.hci.com.au/hcisite3/tool
kit/data.htm
Example :
The figure below shows a check sheet used to collect data
on telephone interruptions. The tick marks were added as
data was collected over several weeks.
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Data organizing tools
Once collected, raw data is typicallysummarized (reduced, or compacted)
this can be done in several ways
Histograms
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The Frequency Distributionand HistogramA frequency distribution shows how often each
different value in a set of data occurs.
A histogram is the most commonly used graphto show frequency distributions.
It looks very much like a bar chart, but thereare important differences between them.
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Parts of a HistogramHistogram
100
80
60
40
20
0
0
F
R
E
QU
E
N
CY5 10 15 20 25 30 35 40 45 50 55 60
Days of operation prior to
failure for an HF receiver1
3
2
4
1. Title , 2. Horizontal / X -axis , 3. Bars, 4. Vertical / Y -axis
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Histogram
Recorded are the percentages of code defects for 80 personnel
during development of s/w application.These are the data collected:
EXERCISE 1:
The source of data for the first exercise is the following scenario.A
list of the data collected follows this description
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HistogramEXERCISE 1:
PERCENT defects RECORDED
11 22 15 7 13 20 25 12 16 19
4 14 11 16 18 32 10 16 17 10
8 11 23 14 16 10 5 21 26 10
23 12 10 16 17 24 11 20 9 13
24 10 16 18 22 15 13 19 15 24
11 20 15 13 9 18 22 16 18 9
14 20 11 19 10 17 15 12 17 11
17 11 15 11 15 16 12 28 14 13
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Histogram
Step 1 -Count number of data points ANS : Total - 80
Step2 -Summarize on a tally sheet
Step3 -Compute the range
Largest value = XY Percent defect
Smallest value = XY Percent defect
Range of values = xyz Percent defect
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HistogramEXERCISE 1:
Step 1 Count number of data points
PERCENT Defects RECORDED
11 22 15 7 13 20 25 12 16 19
4 14 11 16 18 32 10 16 17 10
8 11 23 14 16 10 5 21 26 10
23 12 10 16 17 24 11 20 9 13
24 10 16 18 22 15 13 19 15 24
11 20 15 13 9 18 22 16 18 9
14 20 11 19 10 17 15 12 17 11
17 11 15 11 15 16 12 28 14 13
ANS : Total - 80
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EXERCISE 1:
Step 1 Summarize the data on a tally sheet
%Deft No.Of.Pers %Deft No.Of.Pers %Deft No.Of.Pers
0 0 11 9 22 3
1 0 12 4 23 2
2 0 13 5 24 3
3 0 14 4 25 1
4 1 15 7 26 1
5 1 16 8 27 0
6 0 17 5 28 1
7 1 18 4 29 0
8 1 19 3 30 0
9 3 20 4 31 0
10 7 21 1 32 1
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Histogram
Step3 -Compute the range
Largest value = 32 Percent Defects
Smallest value = 4 Percent Defects
Range of values = 28 Percent Defects
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Histogram
Step 4 -Determine number of intervals
IF YOU HAVE THIS
MANY DATA POINTS
USE THIS NUMBER OF
INTERVALS:
Less than 50 5 to 7 intervals
50 to 99 6 to 10 intervals
100 to 250 7 to 12 intervals
More than 250 10 to 20 intervals
ANS : Select 6 to 10 intervals - 8
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Histogram
Step 5 -Compute interval width
Interval
Width=
Range
Number of Intervals
= 3.5=
Round up to next
whole number
28
8
Use 8 for the number
of intervals
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Histogram
Step6 -Determine the starting point of each interval
Step7 -Count the number of points in each interval
INTERVAL
NUMBER
1
2
3
4
5
6
7
8
STARTING
VALUE
4
8
12
16
20
24
28
32
INTERVAL
WIDTH
+4
+4
+4
+4
+4
+4
+4
+4
ENDING
VALUE
8
12
16
20
24
28
32
36
NUMBER
OF COUNTS
3
20
20
20
10
5
1
1
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Histogram
Step8 -Plot the data
Step9 -Add the title and legend
18
14
10
4
0
0 4 8 12 16 20 24 28 32 36
20
16
12
8
2
6
Critical Defects
PERCENT Defect
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The Frequency Distributionand HistogramFrequency Distribution
Arrangement of data by magnitudeMore compact than a stem-and-leaf
display
Graphs of observed frequencies arecalled histograms.
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Pareto Chart A Pareto chart is a bar graph. The
lengths of the bars represent
frequency or cost (time or money), and
are arranged with longest bars on the
left and the shortest to the right. In this
way the chart visually depicts which
situations are more significant.
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Pareto Chart The Pareto chartis a frequency
distribution (or histogram) of attribute dataarranged by category.
Plot the frequency of occurrence of eachdefect type against the various defect types.
Also called: Pareto diagram, Pareto analysis
Variations: weighted Pareto chart,
comparative Pareto charts
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Why use Pareto chart Breaks big problem into smaller pieces
Identifies most significant factors
Shows where to focus efforts
Allows better use of limited resources
Pareto
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Pareto
Example
Pareto
40
28
1512
838.83
66.0280.58
92.23 100.00
05
1015202530
354045
Documents
Product
Quality
Packages
Delivery
Others
Category of Cost
CostAmoun
t$$
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Cumluative
Cost
Individual category
Cumulative Cost
E l
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ParetoExample
Figure 2 takes the largest category, documents, from Figure 1, breaks it down into
six categories of document-related complaints, and shows cumulative values.
If all complaints cause equal distress to the customer, working on eliminating
document-related complaints would have the most impact, and of those, working onquality certificates should be most fruitful..
Pareto
32
21
15
10837.21
61.63
79.07
90.70100.00
05
10
15
20
25
30
35
ODerrors
PMPerror
not
approved
Version
problem
Training
Category of Cause
Valuesincost
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Cumuvalueof
Costs
Individual cause
Cum cause
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Cause and Effect Diagram A Cause-and-Effect Diagram is a tool that helps
dentify,sort,and display possible causes of a specific problem
or quality characteristic (Viewgraph 1).It graphically illustrates
the relationship between a given outcome and all the factorsthat influence the outcome.
This type of diagram is sometimes called an "Ishikawa
diagram because it was invented by Kaoru Ishikawa,or a
"fishbone diagram"because of the way it looks.
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Cause and Effect Diagram
Variations: cause enumeration diagram, process
fishbone, time-delay fishbone, CEDAC (cause-and-
effect diagram with the addition of cards), desired-
result fishbone, reverse fishbone diagram
The fishbone diagram identifies many possible
causes for an effect or problem. It can be used to
structure a brainstorming session. It immediately
sorts ideas into useful categories.
Cause and Effect
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When should a team use a Cause-And-Effect
Diagram?
Identify the possible root causes ,the basic
reasons,for a specific effect, problem,or condition.
Sort out and relate some of the interactions among
the factors affecting a particular process or effect.
Analyze existing problems so that corrective action
can be taken.
Cause and Effect
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Why should we use a Cause-and-Effect
Diagram?
Helps determine the root causes of a problem or quality
characteristic using a structured approach.
Encourages group participation and utilizes group
knowledge of the process.
Uses an orderly,easy-to-read format to diagram cause-and-
effect relationships.
Indicates possible causes of variation in a process.
Increases knowledge of the process by helping everyone tolearn more about the factors at work and how they relate.
Identifies areas where data should be collected for further
study.
Cause and Effect
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Benefits of Using a Cause-and-Effect
Diagram
Helps determine root causes
Encourages group participation
Uses an orderly,easy-to-read format
Indicates possible causes of variation
Increases process knowledge Identifies areas for collecting data
Cause and Effect
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Step 1 Identify and Define the Effect Decide on the effect to examine
Use Operational Definitions
Phrase effect as
>positive (an objective)or
>negative (a problem)
Cause and Effect
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Step 21. Brainstorm the major categories of causes of the
problem. If this is difficult use generic headings:
Methods Machines (equipment)
People (manpower)
Materials
Measurement
Environment
Cause and Effect
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Step 31. Write the categories of causes as branches from the main
arrow.
Cause and Effect
EFFORT
CAUSE B CAUSE D
CAUSE A CAUSE C
Library-functionI/O and fileHardwareComputational
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ExceptionFailure
Standard libraries
not available
Standard libraries
modified
Incorrect return code
from external function
Incorrect parameters
passed to external
function
problem
File does not exist
File permissions
incorrect
File corrupted
problems
File moved
Invalid
filename
File locked by
another
program
Output file
already exists
Insufficient disk
space
Power outage
Spurious
interrupts
problems
Disconnected /
dismounted
Timeout
Transient errors
Corrupt memory
Crash
Divide by zero
Uninitialized
variable
Square root of a
negative number
problem
Type mismatch
Insufficient
precision
Over flow /
underflow
Null pointer and
memory problems
External user /
client problem
Return-value problem
function/procedure call
Data-input
problem
Incorrect delimiters
Non-numeric in
numeric field
Non-ASCII
Extraneous data
Missing data
Empty data file
Data values outside
of range
Missing end of File
Values of arguments
invalid
Wrong number of
argument
Failure to handle
error return code
Wrong type of
arguments
Erroneous
response to
prompt
Later response
to prompt
Incorrect
command line
arguments
No response to
prompt
Buffer overflow
Corrupt memory
Non- allocated
memory accessed
Insufficient memory
Memory allocation error
Illegal access
Array boundary violation
Invalid pointer dereferenced
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Scatter Diagram The scatter diagramis a plot of two variables that can be
used to identify any potential relationship between thevariables
The shape of the scatter diagram often indicates what typeof relationship may exist
The scatter diagram graphs pairs of numerical data, with one
variable on each axis, to look for a relationship betweenthem. If the variables are correlated, the points will fall alonga line or curve. The better the correlation, the tighter thepoints will hug the line.
Also called: scatter plot, X
Y graph
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ScatterScatter plot for relationship between apartment
size and its rent (n=25)
500700
900
1100
1300
1500
1700
1900
2100
2300
2500
500 700 900 1100 1300 1500 1700 1900 2100
Size
Rent
Scatter plot suggests that there is a positive, linear relationship between Rent and Size
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Example
If there are 24 data points.
To test for a relationship, they calculate:A = points in upper left + points in lower right = 8 + 9 = 17
B = points in upper right + points in lower left = 4 + 3 = 7Q = the smaller of A and B = the smaller of 7 and 17 = 7N = A + B = 7 + 17 = 24
Then they look up the limit for N on the trend test table. For N =24, the limit is 6.
Q is greater than the limit. Therefore, the pattern could haveoccurred from random chance, and no relationship is demonstrated.
Scatter
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Control Chart The control chart is a graph used to study how a process changes
over time. Data are plotted in time order. A control chart always hasa central line for the average, an upper line for the upper controllimit and a lower line for the lower control limit. These lines are
determined from historical data. By comparing current data to theselines, you can draw conclusions about whether the process variationis consistent (in control) or is unpredictable (out of control, affectedby special causes of variation).
Control charts for variable data are used in pairs. The top chartmonitors the average, or the centering of the distribution of datafrom the process. The bottom chart monitors the range, or thewidth of the distribution. If your data were shots in target practice,the average is where the shots are clustering, and the range is howtightly they are clustered. Control charts for attribute data are used
singly.
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What is control chartA statistical tool used to distinguish
between process variation resulting
from common causes and variation
resulting from special causes.
Control Chart
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Analyzing Process Performance
Why Control Charts?
Notice what the control charts dothey seek to identify if
the process is behaving one way or another. This, in
effect, is the same as asking if the process exists as awell-defined entity, where the past can be used to predict
the future, or if the process is so ill-defined and
unpredictable that the past gives little clue to the future.
Donald J. Wheeler, 1995
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Variations Different types of control charts can be used, depending upon the
type of data. The two broadest groupings are for variable data andattribute data.
Variable dataare measured on a continuous scale. Forexample: time, weight, distance or temperature can bemeasured in fractions or decimals. The possibility ofmeasuring to greater precision defines variable data.
Attribute dataare counted and cannot have fractions ordecimals. Attribute data arise when you are determining onlythe presence or absence of something: success or failure,accept or reject, correct or not correct. For example, areport can have four errors or five errors, but it cannot havefour and a half errors.
Control Chart
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Variables charts X and R chart (also called averages and range chart)
X and s chart
chart of individuals (also called X chart, X-R chart, IX-
MR chart, Xm R chart, moving range chart) moving averagemoving range chart (also called MA
MR chart)
target charts (also called difference charts, deviationcharts and nominal charts)
CUSUM (also called cumulative sum chart) EWMA (also called exponentially weighted moving
average chart)
multivariate chart (also called Hotelling T2)
Control Chart
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Attributes charts p chart (also called proportion chart)
np chart
c chart (also called count chart)
u chart
Control Chart
Charts for either kind of data
short run charts (also called stabilized chartsor Z charts)
group charts (also called multiplecharacteristic charts)
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Why should teams use Control
Charts? Monitor process variation over time.
Differentiate between special cause
and common cause variation.
Assess the effectiveness of changes
to improve a process.
Communicate how a processperformed during a specific period.
Control Chart
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Why to use Monitor process variation over time
Differentiate between special cause and common cause variation
Assess effectiveness of changes
Communicate process performance
When controlling ongoing processes by finding and correcting problems asthey occur.
When predicting the expected range of outcomes from a process.
When determining whether a process is stable (in statistical control).
When analyzing patterns of process variation from special causes (non-routine events) or common causes (built into the process).
When determining whether your quality improvement project should aim toprevent specific problems or to make fundamental changes to the process
Control Chart
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What are the types of Control Charts?
There are two main categories of Control Charts,those that
display attribute data ,and those that display variables
data .
While these two categories encompass a number of different types of Control
Charts,
there are three types that will work for the majority of the data analysis cases
you will encounter.In this module,we will study the construction and application in these three
types of Control Charts:
X-Bar and R Chart
Individual X and Moving Range Chart for Variables Data
Individual X and Moving Range Chart for Attribute Data
Control Chart
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Chart types studied in this module:
X-Bar and R Chart
Individual X and Moving Range Chart
-For Variables Data
-For Attribute Data
Other Control Chart types:
X-Bar and S Chart u Chart
Median X and R Chart p Chart
c Chart np Chart
Control Chart
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Analyzing Process Performance
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Analyzing Process Performance
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Analyzing Process Performance
Detecting Signals
The simplest rule for detecting a signal (possible
assignable cause): a point outside the 3-sigma control
limits.
Many other sets of detection rules proposed.
makes the control chart more sensitive to signals
also leads to more false alarms decision on detection
rules should be based on economic trade-offs
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Analyzing Process Performance
Stability Concepts
Stable process = Process In Statistical
Control
= Sources of Variability
Due to CommonCauses only
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Analyzing Process Performance
Control Charts
Two broad classes of control charts
variable data, which is continuous
attribute data, which is discrete
Choice of what control chart to use should be based on
knowing the right assumptions!
Use the correct formulas for the kind of control
chart selected!
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Analyzing Process Performance
The Distinction Between Variables Data and Attributes
Data
Variables data (sometimes called measu rement data)
are usual ly measurements of cont inuous phenomena.
Examples: measurements of length, weight, height,
volume, voltage, horsepower, torque, efficiency,
speed, and viscosity.
Software examples: elapsed time, effort expended,
years of experience, memory utilization, CPU
utilization, and cost of rework.
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Analyzing Process Performance
The Distinction Between Variables Data and Attributes Data
Attributes data occur when information is recorded only
about whether an item conforms or fails to conform to a
specified criterion or set of criteria.
Attributes data almost always originate as counts.
Examples: the number of defects found, the number of
defective items found, the number of source statements ofa given type, the number of lines of comments in a module
of n lines, the number of people with certain skills or
experience on a project or team, and the percent of
projects using formal code inspections.
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Analyzing Process Performance
Average - Range Control Charts
where X =X
number of samples
R =R
number of sample
D R and D R3 4
Control Limits for Mean:X A R2
Control Limits for Range:
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Sample
Size d2 A 2 D3 D4------------------------------------------------------------------
2 1.128 1.880 0 3.267
3 1.693 1.023 0 2.575
4 2.059 0.729 0 2.2825 2.326 0.577 0 2.116
6 2.534 0.483 0 2.004
10 3.078 0.308 0.233 1.777
15 3.472 0.223 0.348 1.65220 3.735 0.180 0.414 1.586
25 3.931 0.153 0.459 1.541
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0 1 2 3 4 5 6 7 8 9 10
Sample Number
MEAN
S
R
ANGES
UCL
CL
LCL
UCL
CL
LCL
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Analyzing Process Performance
Detecting Instabilities and Out-of-Control Situations
To test for instabilities in processes, we examine
control charts for instances and patterns that signalnonrandom behavior.
Values falling outside the control limits and unusual
patterns within the running record suggest thatassignable causes exist.
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Analyzing Process Performance
Detecting Instabilities and Out-of-Control SituationsTest 1: A single point falls outside the 3-sigma control
limits.
Test 2: At least two of three successive values fall on thesame side of, and more than two sigma units away from,
the center line.
Test 3: At least four out of five successive values fall on
the same side of, and more than one sigma unit awayfrom, the center line.
Test 4: At least eight successive values fall on the same
side of the center line.
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Useful Control Charts
Most likely to be of value for software processes
u-chart
XmR chart
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XmR Chart
When measurements are spaced widely in time orwhen each measurement is used by itself to
evaluate or control a process, a time-sequenced
plot of individual values, rather than averages,
may be all that is possible.
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XmR Chart
Control limits for Individuals Chart:
X-bar 3(MR-bar/d2)
Upper limit for Moving Range Chart:
D4MR-bar
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Week
First Quarter
Second Quarter
Third quarter
19 27 20 16 18 25 22 24 17 25 15 17
20 22 19 16 22 19 25 22 18 20 16 17
20 15 27 25 17 19 28
1 2 3 4 5 6 7 8 9 10 11 12
Each week, a system test organization reports the
number of critical problems that remain unresolved.
There is concern that week 31 value of 28 is higher than
would have been expected.
A control chart is constructed to investigate this possibility.
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