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Six Sigma Measure Phase: Process & Data Analysis

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1
Six Sigma-Measure Phase
Measure Phase-part I
•
Measure phase focuses on understanding the current performance of the process and
collecting any necessary data needed for analysis. It also includes assessment of the
measurement system to ensure validity of measurements.
•
Key objective: to establish a process baseline through the development of a clear and
meaningful measurement system
•
Objectives:
Evaluate measurement system
Process
definition
Establish the
process
baseline
Metric
definition
Collect
process data
•
Process definition
•
Clear definition of process under investigation
•
Detailed process mapping
•
Process map examples
Introduction to Six Sigma – INDU 441/INDU 6321
Understand
the process
behavior
2
Six Sigma-Measure Phase
•
Metric definition
•
To define a unit of measurement that provides a way to objectively quantify a process
•
Examples of metrics:
o Services: the percentage of orders filled accurately; the time taken to fill a
customer’s order
o Manufacturing: diameters of machined ball bearings; percentage of fixtures
have surface defects
•
Measures and indicators refer to numerical information that results from
measurement. In other words, they are numerical values associated with a metric.
o Indicator is often used for measurements that are not a direct or exclusive
measure of performance. For instance, the number of complaints or lost
customers are indicators of customer dissatisfaction (which cannot be directly
measured)
•
Types of metrics:
o Discrete metrics: a countable metric such as:
▪
A dimension is either within or out of tolerance
▪
The number of errors in an invoice
▪
An order is complete or incomplete
o Continuous metrics: numerical counts or proportions such as:
▪
Length, time, or weight
Introduction to Six Sigma – INDU 441/INDU 6321
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Six Sigma-Measure Phase
•
A systematic process is required in order to generate useful process performance
measures as follows:
o Identify all customers of the system and determine their requirements (CTQ)
o Define the work process that provides the product or service (detailed process
map)
o Define the value-adding activities and (intermediate) outputs that compose the
process
o Develop specific performance measures or indicators for each key activity
identified in previous step (critical point in the process)
▪
Performance is measured at intermediate checkpoints
▪
Key questions: what factors determine how well the process is
producing according to customer requirements?
o Evaluate the performance measures to ensure their usefulness
•
▪
Are measurements taken at critical points where value-adding
activities occur?
▪
Is it feasible to obtain the data needed for each measure?
▪
Have operational definitions for each measurement been established?
Example of defining metrics for the “pizza ordering and filling process for home
delivery”:
Introduction to Six Sigma – INDU 441/INDU 6321
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Six Sigma-Measure Phase
•
Process measures can be displayed as a KPI tree
•
Operational definitions are developed to provide clear description of each KPI
o KPI name: a consistent terminology must be used throughout the project
o What is the KPI supposed to represent
o Process diagram
o Detailed definition
o Measurement scope
•
Without an operational definition, unreliable data will be collected in different ways.
•
Example-fault repair time KPI
Introduction to Six Sigma – INDU 441/INDU 6321
5
Six Sigma-Measure Phase
•
Collect process data
•
The first step in any data collection effort is to develop operational definitions for all
measures
•
Classification of measurements (data worlds in Six Sigma):
o Attribute data (e.g., accept/reject)
▪
Statistic: percentage
o Variable data
▪
Discrete data (counting things, e.g., number of defects in a sample)
▪
Continuous data (measuring something, e.g., the measurement of PH)
▪
Statistics: average, median, range, standard deviation
Introduction to Six Sigma – INDU 441/INDU 6321
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Six Sigma-Measure Phase
•
Two types of data collection
o In-Process: data collection is integrated into the process and is recorded
automatically
o Manual: data collection system is additional to the process and recorded by text or
typing (e.g., check sheets)
▪
Design the check sheet with a team of people who are going to use it
▪
Keep it clear, easy, and obvious to use
▪
Communicate with people why you are using the check sheet
▪
Record names, dates, serial numbers, etc. for traceability
o Samples of check sheets:
Introduction to Six Sigma – INDU 441/INDU 6321
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Six Sigma-Measure Phase
•
Data collection plan and sampling
o Several factors must be considered for data collection planning:
▪
What is the objective of the study?
▪
What type of sample should be used?
▪
What possible error might result from sampling?
▪
What will the study cost?
o Sampling approaches:
▪
Simple random sampling: every item in the population has an equal
probability of being selected
▪
Stratified sampling: the population is partitioned into groups, or strata,
and a random sample is selected from each stratum
▪
Systematic sampling: every nth (4th, 5th, etc.) item is selected
▪
Cluster sampling: a typical group (e.g., a division of the company) is
selected and a random sample is taken from within the group
▪
Judgment sampling: expert opinion is used to determine the location
and characteristics of a sample group
o The time framework of the study, the size and cost limitation of the sampling
method, accessibility of the population, and the desired accuracy must be
taken into consideration while choosing the sampling approach.
Introduction to Six Sigma – INDU 441/INDU 6321
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Six Sigma-Measure Phase
o Sampling error occurs naturally and results from the fact that a sample may
not always be representative of the population.
o Sampling error is determined based on the sample size and the confidence
level of sampling.
o Sample size
▪
Consider the sample size when using x to provide a point estimate of
the population mean (  ) for variable data. A 100(1 −  ) percent
confidence interval of  is given by x  z /2 / n . Thus (1 −  )
probability exists that the value of the sample mean will provide a
sampling error of z /2 / n or less. If we denote this sampling error
by E and solve E = z /2 / n for n, we obtain the required sample
size for any given value of sampling error (E) at a confidence level of
100(1 −  ) precept as follows:
n = ( z /2 )2  2 / E 2
▪
A similar task is to determine the sample size for estimating a
population proportion for attribute data. A point estimate of the
population proportion (p) is given by the sample proportion ( p ). The
standard error of the proportion is  p =
p (1 − p ) / n . Thus, a
100(1 −  ) percent confidence interval for the population proportion is
p  z /2 p (1 − p ) / n .
The
sampling
error
is
given
by
E = z /2 p(1 − p) / n . Solving the equation for n provides the
following formula for the sample size:
n = ( z /2 )2 p(1 − p) / E 2
•
Understand the process behavior
•
Process capability analysis
o The relationship between the natural variation and specifications is often
quantified by a measure known as the process capability index
o Typical questions that are asked in a process capability study:
▪
Where is the process centered?
▪
How much variability exists in the process?
▪
Is the performance relative to specifications acceptable?
▪
What factors contribute to variability?
Introduction to Six Sigma – INDU 441/INDU 6321
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Six Sigma-Measure Phase
o Process capability metrics
▪
A range of metrics that measure the ability of a process to deliver the
customer’s requirements (to indicate the performance of the process
relative to requirements)
▪
The assessment of how well the process delivers what the customer
wants
▪
Potential capability
▪
▪
•
Cp= width of the specification/width of the histogram
•
Reflects the potential capability of the process
•
Cp must be greater than 1 so that the process is called capable
Capability ratio
•
Cr=1/ Cp
•
Indicates the percentage of the specification spread that is
needed to contain the process range for the production process
to be capable
Actual capability
•
The process natural variability can be smaller than the
specification spread while the process is still generating defects
(the case where process is not centered and only one side of the
specification spread must be compared to the control limits)
•
Cpk=Zmin/3
Introduction to Six Sigma – INDU 441/INDU 6321
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Six Sigma-Measure Phase
•
Reflects the actual capability of the process. It considers only
the nearest specification limit, since this is the limit which is
most likely to be failed
•
Measures how much of the production process really conforms
to the engineered specifications
•
Using the variable control charts
Zmin = min Z L , ZU 
𝑈𝑆𝐿 − 𝑋̿
𝜎̂
𝑋̿ − 𝐿𝑆𝐿
𝑍𝑈 =
𝑍𝐿 =
𝜎̂
𝑅̅
𝜎̂ = 𝑑
2
𝑠̅
𝜎̂ = 𝑐
4
▪
(Range chart method)
(Sigma chart method)
Taguchi capability metric
•
Cpk and Cp take into account the variations within tolerance
(the variations that occur while the process mean fails to meet
the specified target)
•
Taguchi’s approach suggests that any variation from the
engineering target is a source of defect.
C pm =
USL − LSL
6 ˆ 2 + (  − T )2
Introduction to Six Sigma – INDU 441/INDU 6321
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Six Sigma-Measure Phase
▪
Part per million (PPM) metric (or dpmo)
PPM = PPM L + PPM U
USL − 
PPM U = 106  [1 −  (
)]
ˆ
LSL − 
PPM L = 106   (
)
ˆ
o Critical to schedule (CTS) metrics (Lean metrics)
▪
Lean metrics measure the levels of waste generated by the process
▪
The elimination of waste is done through the identification of the
activities that do not add value to the customer
▪
Workers capacity
•
The amount of time needed for one worker to produce a unit of
product
•
Takt time is defined as the maximum amount of time that the
producer is allowed to take in order to produce and deliver
customer orders on time
Takt time= net available production time/units requested by
customer
▪
Cycle time
•
Total elapsed time for the process from start to completion
•
It does not consider the customer current orders
•
It only considers the capabilities of available resources
Cycle time=net production time/number of units produced
•
▪
Process cycle efficiency
•
▪
The production process must be designed in a way that the
cycle time does not exceed the takt time
Is calculated by dividing the value-added time associated with a
process by the total lead time of the process
Process lead time
•
Is calculated by dividing the number of items in process by the
completions per hour
•
Example:
Introduction to Six Sigma – INDU 441/INDU 6321
12
Six Sigma-Measure Phase
It takes 2 hours on average to complete each purchase order,
then there are 0.5 completion per hour. If there are 10 purchase
orders waiting in queue, the process lead time is 20 hours.
▪
Overall equipment effectiveness (OEE)
OEE = A (Availability) x P (Performance) x Q (Quality)
A = actual operating time/planned time
P = net operating rate x operating speed rate
Operating speed rate= specified cycle time/actual cycle time
Net operating rate= actual processing time/operating time
Q = acceptable output / total output
•
The OEE availability is calculated as the actual time the
process is producing product or service divided by the amount
of time that is planned for production.
o Planned time excludes all scheduled shutdowns when
equipment is not operational (including lunches, breaks,
plant shutdowns for holidays, etc.)
o The remaining portion of the planned time includes the
available time for production, and the downtime.
o Downtime is loss in production time due to shift
changeovers, part changeovers, waiting for material,
equipment failures and so on
•
The OEE enables us to determine how efficiently the
equipment is used
o It accounts for process inefficiencies due to poor quality
materials,
operator
inefficiencies,
equipment
shutdowns, etc.
o A 100% performance implies the process is running at
maximum velocity.
•
The OEE quality is the percent of the total output that meets the
requirement without need for any repair or rework
o 100% quality means the process is producing no errors
Example- based on the information summarized in the following table, find the
OEE.
Introduction to Six Sigma – INDU 441/INDU 6321
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Six Sigma-Measure Phase
Work hours
Breaks
Meeting
Unexpected downtime
Machine’s manual spec
Actual machine performance
Number of units processed
Quality rate
8
30 min
15 min
35 min
1 unit per min
1.05 min per unit
405
0.97
Availability=
time
(operating
–
down
time)/operating
time=
(8  60) − (30 + 15) − 35 400
=
= 0.92
(8  60) − (30 + 15)
435
Equipment performance efficiency=net operating rate x operating speed rate
Net
operating
rate=actual
processing
time/operating
1.05  405
425.25
=
= 0.978
(8  60) − (30 + 15)
435
Operating speed rate=specified cycle time/actual cycle time=
Equipment performance efficiency= 0.978  0.952 = 0.931
OEE= 0.978  0.952  0.97 = 0.831
Introduction to Six Sigma – INDU 441/INDU 6321
1
= 0.952
1.05
time=
14
Six Sigma-Measure Phase
•
Process baseline must be estimated by means of meaningful statistics in order to have
a credible evidence of sustainable improvements
o Example of inappropriate statistics for process baselines estimation:
•
Enumerative statistical study (Deming, 1975): a study in which action will be taken
on the universe (the sample being studied)
o ANOVA, t-test, confidence intervals
o Proceed from predetermined hypothesis
•
Analytic statistical study (Deming, 1975): a study in which action will be taken on a
process or cause-system that produced the sample being studied. The aim is to
improve the process in the future
o Provide operational guidelines rather than precise calculation of probability
o Generate new hypothesis
o Statistical process control (SPC) charts
•
Some appropriate analytic statistics questions:
o Is the process central tendency stable over time?
o Is the process dispersion stable over time?
o Is the process distribution consistent over time?
•
If the answer to any of the above questions is no, the cause of the instability must be
found
Introduction to Six Sigma – INDU 441/INDU 6321
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Six Sigma-Measure Phase
•
Analytic methods will be needed to validate the conclusions developed with the use of
enumerative methods, to ensure their relevance to the process under study
•
Statistical process control (SPC) charts are used in the measure phase to define the
process baseline
o If the process is statistically stable (evidenced by SPC charts), the process
capability and Sigma level are valid
o If the process is not statistically stable, then the cause of variation must be sought
o SPC charts enable the producer to determine if his production process is stable
and in control
o If the process is yielding products that are consistent and in a manner that makes it
possible for the producer to make a prediction on future trends
o If the variations in the output of the process are contained within the control limits
in a random manner, then the process is stable and in control.
o It does not say whether the products generated by this process meets customer
expectations
o Process capabilities indices are used to determine how effective the process is at
meeting customer expectations
•
Distributions
o They show the way in which the probabilities are associated with the numbers
being studied
o Sampling distributions are used in Six Sigma projects involving enumerative
statistics
▪
The empirical distribution assigns the probability 1/n to each Xi in the
sample
▪
Some sample statistics
▪
•
Sample mean
•
Unbiased sample standard deviation
•
Standard error of the mean
Binomial distribution
Introduction to Six Sigma – INDU 441/INDU 6321
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Six Sigma-Measure Phase
•
Assume that a process is producing some proportion of
nonconforming units (p) (p: the number of nonconforming
units in the sample by the number of items sampled). The
probability of getting x defectives in sample of n units is:
❖ Example: 1% of products in a manufacturing line do not
conform to specifications. Calculate the probability that in a
sample of 30 units of the product, no more than 1 defective
item is detected?
p( x  1) = p( x = 0) + p( x = 1)
( )
( )
= 30 (0.01)0 (0.99)30 + 30 (0.01)1 (0.99)29
0
1
30!
30!
(0.01)0 (0.99)30 +
(0.01)1 (0.99)29
0!30!
1!29!
= 96.38%
=
▪
Poisson distribution
•
When we are concerned with the number of non-conformances.
The probability of counts of nonconformity:
❖ Example: the number of welding defects per unit in a circuit
board follows a Poisson distribution with  = 4 . Calculate the
probability that a circuit board has more than 2 defectives.
4x e−4
p( x  2) = 1 − p( x  2) =1 − 
x!
x =0
= 1 − (0.238) = 0.762
2
▪
Normal distribution
•
Sometimes the process itself produces an approximately normal
distribution, other times a normal distribution can be obtained
by using averages or other mathematical transformation on data
Introduction to Six Sigma – INDU 441/INDU 6321
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Six Sigma-Measure Phase
▪
Exponential distribution
•
•
Useful in analyzing the system reliability
Statistical process control charts
o Central Limit Theorem (CLT) - The basis of statistical process control tools
▪
The distribution of average values of samples drawn from any
population will tend toward a normal distribution as the sample size
grows without bound
▪
By this rule, averages of small samples can be used to evaluate any
process using the normal distribution
o Common and special causes of variation
▪
Common (chance) cause: any unknown and unavoidable random cause
of variation
•
▪
If the influence of any particular chance is very small, and if
the number of common causes of variation is very large and
relatively constant, we have a situation where variation is
predictable within limits (a controlled system)
Special (assignable) causes of variation: At times, the variation is
caused by a source of variation that is not part of the constant system.
These sources of variation are called special causes of variation
(Deming)
•
Example: large variations related to machines, materials,
operators, etc.
▪
Statistically controlled system: any system exhibiting only commoncause variation
▪
The goal of SPC is reduction or elimination of variability in the
process by identification of special causes of variation
o Statistical process control
▪
The use of valid analytical statistical methods to identify the existence
of special causes of variation in a process
▪
The basic rule of statistical process control: variation from commoncause systems should be left to chance, but special causes of variation
should be identified and eliminated
Introduction to Six Sigma – INDU 441/INDU 6321
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Six Sigma-Measure Phase
▪
We look for long-term process improvements to address commoncauses variation
▪
Variation between “control limits” in SPC charts: variation from
common cause; any variability beyond control limits: special cause of
variation
▪
Out-of-control situations:
•
At least one point plots beyond the control charts
•
The points behave a systematic or non-random manner
•
Run tests (Similar to Western Electric Handbook rules)
▪
Control charts are used in Six Sigma to monitor mean, range, and
standard deviation (Sigma)
▪
The basis of control charts is the rational subgroup
•
Items produced under essentially the same conditions
•
The average, range, and Sigma are computed for each subgroup
and then plotted on the control chart
▪
All control limits are set at plus and minus three standard deviations
from the center line of the chart (Shewhart charts)
▪
Control chart selection decision tree
Introduction to Six Sigma – INDU 441/INDU 6321
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Six Sigma-Measure Phase
▪
Control limit equations for ranges charts
▪
Control limit equations for averages using ranges charts
ˆ =
R
d2
ˆ = x
▪
Control limit equations for Sigma charts
Introduction to Six Sigma – INDU 441/INDU 6321
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Six Sigma-Measure Phase
▪
Control limit equations for averages using sigma charts
ˆ =
s
c4
ˆ = x
▪
Example of average and sigma control charts
Introduction to Six Sigma – INDU 441/INDU 6321
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Six Sigma-Measure Phase
Introduction to Six Sigma – INDU 441/INDU 6321
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Six Sigma-Measure Phase
▪
Control limit equations for individual measurements (X charts)
•
When it is not feasible to use averages for process control
•
Expensive observations (destructive testing), output too
homogeneous (chemical processes), etc.
•
Range charts (moving range charts) are applicable
•
Example:
Introduction to Six Sigma – INDU 441/INDU 6321
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Six Sigma-Measure Phase
R=Largest in subgroup – Smallest in subgroup,
where the subgroup is a consecutive pair of successive
measurement
▪
Control charts for attribute data
▪
Control limit equations for proportion defective (p chart)
•
Analysis of p chart patterns between the control limits become
extremely complicated if the sample size varies because the
distribution of p varies with the sample size
•
Example
Introduction to Six Sigma – INDU 441/INDU 6321
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Six Sigma-Measure Phase
Introduction to Six Sigma – INDU 441/INDU 6321
25
Six Sigma-Measure Phase
▪
Control limit equations for count of defective (np chart)
▪
Example
Introduction to Six Sigma – INDU 441/INDU 6321
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Six Sigma-Measure Phase
▪
Control limit equations for average occurrences-per-unit (u charts)
•
Can be applied to any variable where the appropriate
performance measure is a count of how often a particular event
occurs
•
Unlike p and np charts, u charts do not necessarily involve
counting physical items. Rather, they involve counting of
events
Introduction to Six Sigma – INDU 441/INDU 6321
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Six Sigma-Measure Phase
where n is the subgroup size in units. If the subgroup size
varies, the control limits will also vary.
•
Example
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Six Sigma-Measure Phase
▪
Control limit equations for counts of occurrences-per-unit (c charts)
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Six Sigma-Measure Phase
▪
Example
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Six Sigma-Measure Phase
▪
Control chart interpretation
•
Probing the patterns in control charts to identify the underlying
system of causes at work
•
Freak patterns
o Causes that have a large effect but occur infrequently
o Look at cause-and-effect diagram for items that meet
this criteria
o The key to identifying freak patterns are timelines in
collecting and recording the data
o Try sampling more frequently if you have difficulty to
identify freak patterns
•
Drift patterns
o The current process value is partly determined by the
previous process state
o Tool ware, plating bath
Introduction to Six Sigma – INDU 441/INDU 6321
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Six Sigma-Measure Phase
o Whenever economically possible, the drift should be
eliminated, e.g., by installing an automatic chemical
dispenser for the plating bath, or make automatic
compensating adjustments to correct the tool wear
o When drift elimination is not possible, the control charts
can be modified in one of the two ways:
•
▪
Makes the slop of the center line and control
limits match the natural process drift
▪
Plot deviations from the natural drift
Cycles
o Due to the nature of the process (e.g., hour of the day,
day of the week, etc.)
o Caused by modifying the process inputs or methods
according to a regular schedule
o The action to eliminate cycles
▪
The control chart can be adjusted by plotting the
control measure against a variable base
▪
If a day-of-the-week cycle exists for shipping
errors because of the workload, you can plot
errors per 100 orders instead of error per day
Introduction to Six Sigma – INDU 441/INDU 6321
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Six Sigma-Measure Phase
•
Run tests (special causes)
o If the process is stable, the distribution of subgroup
averages will be approximately normal
o We can analyze the patterns on the control charts to see
if they might be attributed to a special cause of variation
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Six Sigma-Measure Phase
o The patterns on the control charts can be used as an aid
in trouble shouting
•
Estimating process baseline using process capability analysis
o Collect samples from 25 or more subgroups of consecutively produced units
o Plot the results on the appropriate control chart. If all groups are in statistical
control go to step 3. Otherwise, attempt to identify special cause of variation
by observing the conditions or time periods under which they occur
o Using the control limits from the previous step. Once you are satisfied that
sufficient time has passed for most special causes to have been identified and
eliminated, got to step 4.
o Estimate process capability. The initial error rates estimated in the “Define”
phase can then be revised by the right values.
o Estimate process Sigma level based on the dpmo metric
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Six Sigma-Measure Phase
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Six Sigma-Measure Phase
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Six Sigma-Measure Phase
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Six Sigma-Measure Phase
Introduction to Six Sigma – INDU 441/INDU 6321
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