NG BB 22 Process Measurement
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Transcript of NG BB 22 Process Measurement
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National GuardBlack Belt Training
Module 22
Process Measurement
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CPI Roadmap – Measure
Note: Activities and tools vary by project. Lists provided here are not necessarily all-inclusive.
TOOLS
•Process Mapping
•Process Cycle Efficiency/TOC
•Little’s Law
•Operational Definitions
•Data Collection Plan
•Statistical Sampling
•Measurement System Analysis
•TPM
•Generic Pull
•Setup Reduction
•Control Charts
•Histograms
•Constraint Identification
•Process Capability
ACTIVITIES• Map Current Process / Go & See
• Identify Key Input, Process, Output Metrics
• Develop Operational Definitions
• Develop Data Collection Plan
• Validate Measurement System
• Collect Baseline Data
• Identify Performance Gaps
• Estimate Financial/Operational Benefits
• Determine Process Stability/Capability
• Complete Measure Tollgate
1.Validate the
Problem
4. Determine Root
Cause
3. Set Improvement
Targets
5. Develop Counter-
Measures
6. See Counter-MeasuresThrough
2. IdentifyPerformance
Gaps
7. Confirm Results
& Process
8. StandardizeSuccessfulProcesses
Define Measure Analyze ControlImprove
8-STEP PROCESS
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Learning Objectives
Understand the importance of measurement to process improvement
Apply measures of central tendency and variation to process data
Apply the concepts of common and special cause variation
Apply Sigma Quality Level to processes
Know how to measure the Voice of the Customer and Voice of the Business
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Measurement Fundamentals
Definition: The assignment of numbers to observations according to certain decision rules
Measurement is the beginning of any science or discipline
Without measurements, we do not know where we are going or if we ever got there – we do not even know where we are now!
If it is important to the customer, we should measure it
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Measurement Example
The following data is the number of minutes it took Soldiers to resolve their AKO issues when calling the AKO Helpdesk. Take a few minutes to examine the data:
How should we summarize and present this data to understand the AKO Helpdesk’s overall performance?
Time of Day Minutes To Resolve Issue
0730 000731 110800 060845 140903 110925 580940 471006 161120 091145 481158 431205 531214 491310 091400 10
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Calculating the Mean
An easy way of summarizing data is to calculate the arithmetic average (or “mean”) of the column of numbers
Mathematically, we can express this as follows:
n
XX
n
i i 1
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Mean Example
Lets go back to our AKO Helpdesk data:
0, 11, 6, 14, 11, 58, 47, 16, 9, 48, 43, 53, 49, 9, 10
What is the mean value?
X-bar = (0 + 11 + 6 + 14 + 11 + 58 + 47 + 16 + 9 + 48 + 43 + 53 + 49 + 9 + 10) / 15 = 25.6 minutes
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Measures of Central Tendency
The Mean is a measurement of central tendency, that is, where the “center” of most of the data is. Another measure of central tendency is the Median.
The Median is calculated by listing the data in ascending order and then finding the value that is in the middle of the list
If we re-order our AKO Helpdesk data in ascending order, we get the following list:
0, 6, 9, 9, 10, 11, 11, 14, 16, 43, 47, 48, 49, 53, 58
The value which occurs in the middle of the list is 14 minutes –this is the Median
The Median can be a fraction or decimal even if the data is all integers. If we had fourteen instead of fifteen data points (no 58) the median would have been (11 + 14) / 2 = 12.5 minutes
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Central Tendency – The Whole Story?
While it is important to know where the “center” of our data is, does it tell the whole story?
What does this tell us about the AKO Helpdesk’s performance? What does is not tell us?
Why is there a difference between the mean and median in our example?
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Measures of Central Tendency
Mean, Median and Mode
Mode - most frequently occurring data point
A histogram shows data by frequency of occurrence. It also shows the “distribution” and “spread” and of the data
6050403020100
Median
Mean
5040302010
1st Q uartile 9.000
Median 14.000
3rd Q uartile 48.000
Maximum 58.000
14.043 37.157
9.374 47.626
15.279 32.914
A -Squared 1.29
P-V alue < 0.005
Mean 25.600
StDev 20.870
V ariance 435.543
Skewness 0.43325
Kurtosis -1.78559
N 15
Minimum 0.000
A nderson-Darling Normality Test
95% C onfidence Interv al for Mean
95% C onfidence Interv al for Median
95% C onfidence Interv al for StDev
95% Confidence Intervals
Summary for Minutes
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Measuring Variation
Another important way of summarizing our data is by measuring the average “spread” or variation between each data point and the mean
While the center of our process is important, knowing the spread is particularly important in service because each user is an individual and deserves to be provided with acceptable service
Do you care that the average wait is 26 minutes if you are the one who had to wait 58 minutes?
A commonly used term in statistics for measuring this variation is the standard deviation
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Calculating the Standard Deviation
The standard deviation gives us a feel for the overall consistency of our data set
Mathematically, it is calculated as follows:
1
)(1
2
n
XX
s
n
i
i
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Standard Deviation Example
From the previous example we know that the sample mean, x-bar, is 25.6 minutes
Find the sample standard deviation:( 0 - 25.6)2 = 655.36(11 - 25.6)2 = 213.16( 6 – 25.6)2 = 384.16(14 – 25.6)2 = 134.56(11 – 25.6)2 = 213.16(58 – 25.6)2 =1049.76 (47 – 25.6)2 = 457.96(16 – 25.6)2 = 92.16( 9 – 25.6)2 = 275.56(48 – 25.6)2 = 501.76(43 – 25.6)2 = 302.76(53 – 25.6)2 = 750.76(49 – 25.6)2 = 547.56( 9 – 25.6)2 = 275.56(10 – 25.6)2 =243.36
Subtotal = 6097.60
Subtotal (Sum of Squares) = 6097.60Divided by (n-1) = 14
Variance = 435.54 min2
Standard Deviation = 20.86 min(Square Root of Variance)
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Variance
If we square the standard deviation, we get the Variance
The Variance of a Data Sample is defined as follows:
The Variance of the Population from which the sample is drawn is defined as:
The Variance is useful since we cannot add Standard Deviations together, but we can add Variances (more on this in future modules)
Sample
Variance
2s=
2Population
Variance
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Min, Max, and Range
A simple way of measuring the amount of consistency in a data set is by calculating Min, Max, and Range
The Min is the smallest value in our data set; the Max is the largest value
The Range is the difference between the Max and Min and gives us a feel for the “spread” in our data
Using our AKO Helpdesk data, the Min = 0 minutes, the Max = 58 minutes, the Range is 58 - 0 = 58 minutes
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Central Tendency and Variation
A key concept in Lean Six Sigma is understanding how central tendency and variation work together to describe a process by summarizing its data:
Central Tendency is where the “middle” of the process is – this is where we would expect most of the data points to be
Variation tells us how much “spread” there is in the data – the smaller the variation, the more consistent the process
Both a measure of central tendency and variation are necessary to describe a data set
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Understanding Variation
There will always be some variation present in all processes:
Nature – Shape/size of leaves, snowflakes, etc.
Human – Handwriting, tone of voice, speed of walk, etc.
Mechanical – Weight/size/shape of product, etc.
We can tolerate this variation if:
The process is on target
The variation is small compared to the process specifications
The process is stable over time
We need to recognize that sources of variation (especially Special Cause variation) should be minimized or, if possible, eliminated
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Variation – Its Impact on Business
Variation is the Enemy of Improvement Efforts
In the 1998 GE annual report, Chief Executive Jack Welch clearly articulated a concern that had been troubling other CEOs:
“We have tended to use all our energy and Six Sigma
science to “move the mean”… The problem is, as has
been said, “the mean never happens,” and the
customer is still seeing variances in when the deliveries
actually occur – a heroic 4-day delivery time on one
order, with an awful 20-day delay on another, and no
real consistency… Variation is Evil.”
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Types of Variation
Common Cause Variation
This is the consistent, stable, random variability within the process
We will have to make a fundamental improvement to reduce common cause variation
Is usually hard to reduce
Special Cause Variation
This is due to a specific cause that we can isolate
Special cause variation can be detected by spotting outliers or patterns in the data
Usually easy to eliminate
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Exercise: Your Signature
First, write your name 5 times
Next, write your name 5 times with the other hand
Is the variability common or special cause?
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Special Cause Variation
Sample
Sa
mp
le M
ea
n
2018161412108642
603
602
601
600
599
598
__X=600.23
UCL=602.474
LCL=597.986
11
Xbar Chart of Supp2
Control Chart showing Special Cause variation
Examples of Special Cause variation are:
Uncommon occurrence or circumstance
Soldiers out for training holiday or flu epidemic
Convoy vehicle flat tire
Procedure change
Base-wide electricalpower outage
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Common Cause Variation
Sample
Sa
mp
le M
ea
n
2018161412108642
600.5
600.0
599.5
599.0
__X=599.548
UCL=600.321
LCL=598.775
Xbar Chart of Supp1
Control Chart showing variation due only to
Common Cause
Some examples of Common Cause variation are:
Experience of individual Soldiers
Internet server speed fluctuations
Soldier out on sick-call
Day to day unit issues
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Understanding Accuracy and Precision
If the pictures to the right represent weapons training by two recruits, which one is better?
Green?
Blue?
Which one is more accurate(better average)?
Which one is more precise(more consistency)?
(Green)
(Blue)
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Weapons Training Example
On average, the green target is centered on the bulls-eye, therefore more accurate
Accuracy is a measure of “average distance from the target”
However, the blue target is more consistent, therefore more precise
Precision is a measure of “average distance from each other”
(Green)
(Blue)
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Weapons Training Example
How could the recruit using the green target improve performance?
How could the recruit using the blue target improve performance?
Which recruit do you think has a better chance of becoming an expert shooter?
Typically, it is easier to shift the mean than to reduce variation
(Green)
(Blue)
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ReduceSpread
CenterProcess
Too Much Spread Off Center
Centered On-Target
Goal: Shift the Mean / Reduce Variation
Result: Improved Customer Satisfaction and Reduced Costs
(Green) (Blue)
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Introducing The Distribution
Up to now, we have been using the mean and standard deviation to summarize the data generated from a process
Another way we can summarize the data is by showing its distribution
The distribution shows us the number of times (“frequency count”) a particular data value appears in our data set
The “peak” of the distribution shows its central tendency; the “spread” of the distribution tells us about the degree of variation present in the data
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The Distribution
By examining the distribution, we can see patterns that are difficult to see in a simple table of numbers
Different processes and phenomena will generate different distribution patterns
Both common and special cause variation will be present in the distribution
The examples shown are different types of distributions
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Histogram
A common graphical tool used to portray the distribution is the histogram
The histogram is constructed by taking the difference between the min and max observation and dividing it up into evenly spaced intervals
The number of observations in each interval are then counted and their frequency plotted as the height of each bar
The histogram is, in essence, a simplified view of the distribution that generated the plotted data
#
Histogram
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Exercise: Build a Histogram
Note the height in inches of the tallest and shortest students in the class
Divide this range into 5 equally sized intervals
Make a bar to show the number of students in class who’s height falls within each interval
The resulting chart is a histogram
How would you describe the shape of our histogram?
How much variation is present in our data? Common or Special Cause?
Height(Inches)
Frequency
56 60 6864 7672
2
6
4
10
8
12
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Interpreting Histogram Data
If the variation is common cause, it reflects the natural variation inherent in the process and will show higher frequencies around the central tendency and taper off toward the edges of the distribution. The underlying process generating the data is stable, and the value of each data point is random and consistent with the rest of the distribution.
If the variation is special cause, an observation will not “fit” the rest of the distribution (i.e, it is an outlier), or there will be a “pattern” in our data. In other words, there is an identifiablereason for why this variation exists.
Common Cause Variation
Special Cause - Bimodal
Special Cause - Outlier
Outlier
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Exercise: Minitab
Let’s use Minitab to help us analyze some data
Open the Minitab data set called Red Beads Data.mtw
Four teams of four people each sampled 50 beads from the same bead box
Each team member drew 10 samples of 50
The samples were randomly drawn and the beads randomly replaced after drawn
The data collected was the number of “red” beads counted out of the fifty beads sampled
What do you think the histogram of this data will look like?
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1. Let’s make a histogram of the data
Select: Stat>
Basic Statistics>
Display Descriptive Statistics
Exercise: Minitab
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Exercise: Minitab
2. Double click (select) C3 Red Beads to place it in the Variables box
3. Click on Graphs
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Exercise: Minitab
4. Check the box for Histogram of Data
5. Click OK
6. Click OK
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Exercise: Minitab
This is a frequency histogram that shows us, for the entire 160 samples run, how many red beads remained in the paddle each time
For example, 22 times out of 160, there were 11 red beads in the paddle
What type of variation is present? Common or Special Cause?
22
11
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Descriptive Statistics: Red Beads
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3
Red Beads 160 0 10.684 0.239 3.029 4.000 8.026 11.000 13.000
Variable Maximum
Red Beads 19.000
Exercise: Minitab
Notice that the Data in Session Window gives us information on both Central Tendency and Variation
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Other Information from Minitab
Standard Error of the Mean (SEMEAN)
Gives the standard error of the mean. It is calculated as .
Quartiles
Every group of data has four quartiles. If you sort the data from smallest to largest, the first 25% of the data is less than or equal to the first quartile. The second quartile takes all the data up to the median. The first 75% of the data is less than or equal to the third quartile and 25% of the data is greater than or equal to the third quartile – the fourth quartile.
The Inter Quartile Range equals Q3 - Q1, spanning 50% of the data
n
s
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Exercise: Minitab
1. Let’s make a Box Plot of the data
Select: Stat>Basic Statistics>Display Descriptive Statistics
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Exercise: Minitab
2. When this dialog box comes up, double click on C3-Red Beadsto place it in the Variables box. Then double click on C1-Teams to place it in the By Variables box.Finally, click on Graphs.
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Exercise: Minitab
3. Select Boxplot of Data,click on OK and thenclick on OK again
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Displayed are 4 boxplots, one for each team
One way of interpreting a box plot is “looking down at the top of a histogram”
This is a good way to see how spread and centering differ from one team to another
Exercise: Minitab
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Notice also that team 4 has a slightly wider spread (i.e., larger standard deviation) than team 1 with a narrower spread (i.e., smaller std. deviation)
Exercise: Minitab
Notice that Team 1has 2 Outliers
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Descriptive Statistics: Red Beads
Variable Team N N* Mean SE Mean StDev Minimum Q1 Median
Red Beads 1 40 0 11.325 0.426 2.693 6.000 10.000 11.000
2 40 0 10.200 0.482 3.048 4.000 8.000 10.000
3 40 0 10.700 0.495 3.131 5.000 8.000 11.000
4 40 0 10.511 0.509 3.220 5.185 7.307 10.802
Variable Team Q3 Maximum
Red Beads 1 13.000 19.000
2 12.750 17.000
3 13.000 16.0004 12.987 16.573
Exercise: Minitab
As before, the session window gives us all the numbers
As we would have figured from the box plot, team 4 has a slightly larger standard deviation than team 1
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1. Now let’s make a Dotplot of the data
Select Graph> Dotplot
Exercise: Minitab
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Exercise: Minitab
2. Next select One Y and With Groups, since we have only one Y variable but four teams.Then click on OK.
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Exercise: Minitab
3. Double click on C3-Red Beads to place it in the Graph Variables box
4. Double click on C1-Team to place it in the Categorical Variables box. Then click on OK.
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Displayed are the Four Dotplots, one for each team
This is a good way to see how spread and centering differ from one team to another. Also, the scale remains the same.
Exercise: Minitab
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Introducing the Normal Distribution
In our Red Bead example, you may have noticed that the data in our histogram took on the shape of a bell shaped curve
If we measure process performance over time, many processes tend to follow a Normal Distribution or bell shaped curve:
The Normal distribution is important in statistics because of the relationship between the shape of the curve and the standard deviation ()
ƒ(x) = Y
Variation
Average
x
Fre
quen
cy
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Properties of the Normal Distribution
One way of demonstrating the relationship between the standard deviationsigma () and the shape of the curve is to use sigma as a “measuring rod” to describe how far we are away from the mean
The special properties of the normal distribution allow us to calculate the area underneath the curve based upon how many sigmas (or standard deviations) we are away from the mean:
-3 -2 -1 +1 +2 +3
+/-3 =99.73%
+/-2 =95.45%
+/-1 =68.27%
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Properties of the Normal Distribution Another property of the normal distribution is the area under the curve gives
us the probability of a data point being drawn from this portion of the distribution
This special property enables us to predict process performance over time
Essentially all of the area (99.73%) of the normal distribution is contained between -3 sigma and +3 sigma from the mean. Only 0.27% of the data falls outside 3 standard deviations from the mean:
-3 -2 -1 +1 +2 +3
+/-3 = 99.7%
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Process Performance
There are two aspects to process performance:
Efficiency – Time and cost associated with executing the process
Cycle time (processing time, on-time delivery, responsiveness, etc.)
Cost (number of resources required, capital equipment, etc.)
Effectiveness – Quality of the output of the process
Level of output (calls answered, orders processed, etc.)
Defects (accuracy, mistakes, errors, etc.)
Customer Satisfaction
Improving both the efficiency and effectiveness of process performance will enable us to reduce costs and better satisfy customers
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Process Capability
Process capability measures whether or not a process is capable of meeting customer requirements
It is a quantifiable comparison of a process’ performance (Voice of the Process) vs. the customer requirements or “specifications” (Voice of the Customer)
Most measures have some desired value (“target”) and some acceptable limit of variation around the desired value
The extent to which the “expected” values fall within these limits determines how capable the process is of meeting its requirements
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Understanding Acceptable Performance
“Acceptable Performance” by definition is that which is acceptable to the customer:
Target – The desired or nominal value of a characteristic
Tolerance – An allowable deviation from the target value where performance is still acceptable to the customer
Specifications – Boundaries where performance outside of these limits is not acceptable to the customer
LSL = Lower Spec Limit
USL = Upper Spec Limit
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Co
st
Correct View
LSL USLTarget USL
Traditional View
Tolerance
Co
st
LSL USLTarget
A Graphical View of Process Performance
• Target• Pass/Fail
• Target• Service Break Points
– Less than 1: Delighted– 1 to 2: Very Satisfied– 2 to 3: Satisfied
1 1 22 33
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Satisfying Customer Requirements
Specification Limits establish the boundaries for acceptable process performance. Performance outside these boundaries is “unacceptable.” They are “defects.”
They are typically described by an Upper Specification Limit (USL) and Lower Specification Limit (LSL)
For example, what are the spec limits for the temperature of this room?
How LOW can the temperature get before you become uncomfortable or dissatisfied? This is the LSL.
How HIGH can the temperature get before you become uncomfortable or dissatisfied? This is the USL.
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Current process has 3 standard deviations between target and USL
Improved process (reduced variation) has 6 standard deviations
between target and USL
What Reduced Variation Looks Like
USLLSL
1 Standard Deviation
Target
Process
Center
3
USLLSL
Target
Process
Center
1 Standard Deviation
3
6
3
SQL = 3.0 SQL = 6.0
NOTE: Illustrations do not include the 1.5 Sigma Shift, the discussion of which is beyond the scope of this lesson
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Sigma is a Greek letter and a statistical unit of measurement that describes the variability or spread of data (the standard deviation of a population)
Six Sigma refers to a methodology of continuous improvement where the goal is to improve process performance to meet customers’ requirements
Sigma Quality Level is a measure of process performance with respect to customer requirements
Note: Another approach to measuring process capability, Cp and Cpk, is shown in the Appendix and will be discussed
in a future module.
Process Capability Is Sigma Quality Level
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Sigma Quality Level and Process Capability
If we measure the performance of a process…
Mean
Standard Deviation
…and know the customer’s Specification Limits, then:
We can calculate Sigma Quality Level…which tells us how many “defects” we can expect over time (process capability)
Understanding process capability will help us:
Establish a baseline of current performance
Measure on-going performance to determine level of improvement and then monitor and control performance to maintain the gain
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SQL DPMO
2
3
4
5
6
308,537
66,807
6,210
233
3.4
69.2%
93.32%
99.379%
99.977%
99.9997%
Yield
A 3 SQL process will fail to meet customer requirements 7% of the time
Sigma Quality Level (SQL) and Defects per Million Opportunities (DPMO)
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Process Capability: Invoice Example
Errors made in preparing customer invoices has led to unacceptable delays in receiving customer payments
A review of the last 100 prepared invoices revealedthat 15 of them required correctionsbefore they could be sent to customers
However, there were three types of errors associatedwith the invoices and several invoices had more thanone error:
Incorrect address
Wrong amount
Mismatch of account number
In total, there were 19 different defects on the 15 faulty invoices
What is the Sigma Quality Level?
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Process Capability: Invoice Example
There are two ways to determine Sigma Quality Level (SQL), depending on the type of data measured:
Continuous or Variable Data – Data that can take on any value (e.g., average cycle time of a process or room temperature)
We calculate SQL using mean, standard deviation, and specification limits
Discrete or Attribute Data – Data that typically can result in one of two possible outcomes (e.g., pass/fail, defective/acceptable)
For this Invoice Example case, we calculate Defects Per Million Opportunities
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1. Determine number of defect or error opportunities per unit
2. Determine number of units processed
3. Determine total number of defects made
4. Calculate Defects per Opportunity
5. Calculate DPMO
6. Look up the S.Q.L. in the Table (see next slide)
O =
N =
D =
DPO =D
N x O
DPMO = DPO x 1,000,000 =
Sigma Quality Level =
=
Calculating Sigma Quality Level Based on Defects Per Million Opportunities (DPMO)
3
100
19
0.063
63,333
~ 3
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Yield DPMO Sigma
6.6% 934,000 0
8.0% 920,000 0.1
10.0% 900,000 0.2
12.0% 880,000 0.3
14.0% 860,000 0.4
16.0% 840,000 0.5
19.0% 810,000 0.6
22.0% 780,000 0.7
25.0% 750,000 0.8
28.0% 720,000 0.9
31.0% 690,000 1
35.0% 650,000 1.1
39.0% 610,000 1.2
43.0% 570,000 1.3
46.0% 540,000 1.4
50.0% 500,000 1.5
54.0% 460,000 1.6
58.0% 420,000 1.7
61.8% 382,000 1.8
65.6% 344,000 1.9
Yield DPMO SQL Yield DPMO Sigma
69.2% 308,000 2
72.6% 274,000 2.1
75.8% 242,000 2.2
78.8% 212,000 2.3
81.6% 184,000 2.4
84.2% 158,000 2.5
86.5% 135,000 2.6
88.5% 115,000 2.7
90.3% 96,800 2.8
91.9% 80,800 2.9
93.3% 66,800 3
94.5% 54,800 3.1
95.5% 44,600 3.2
96.4% 35,900 3.3
97.1% 28,700 3.4
97.7% 22,700 3.5
98.2% 17,800 3.6
98.6% 13,900 3.7
98.9% 10,700 3.8
99.2% 8,190 3.9
Yield DPMO SQL Yield DPMO Sigma
99.4% 6,210 4
99.5% 4,660 4.1
99.7% 3,460 4.2
99.75% 2,550 4.3
99.81% 1,860 4.4
99.87% 1,350 4.5
99.90% 960 4.6
99.93% 680 4.7
99.95% 480 4.8
99.97% 330 4.9
99.977% 230 5
99.985% 150 5.1
99.990% 100 5.2
99.993% 70 5.3
99.996% 40 5.4
99.997% 30 5.5
99.9980% 20 5.6
99.9990% 10 5.7
99.9992% 8 5.8
99.9995% 5 5.9
99.99966% 3.4 6
Yield DPMO SQL
Sigma Quality Level (SQL) Conversion Table
UNCLASSIFIED / FOUO
UNCLASSIFIED / FOUO
65
How Do We Improve a Process?
Let's say that you have this situation
How do you go about improving it?
Desired
Current
USLLSL
Desired
Current
USLLSL
UNCLASSIFIED / FOUO
UNCLASSIFIED / FOUO
66
Lean Six Sigma Reduces Process Cycle Time, Improving
On- Time Delivery Performance for Tier One Auto Supplier (Average Reduced from 14 Days to 2 Days, Variance from 2 Days to 4 Hours)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
0 2 4 6 8 10 12 14 16 18 20
Lead-Time (days)
% D
istr
ibu
tio
n
Mean Delivery Time Reduced
Time Variation Reduced
Shift Mean and Reduce Variability CPI Improvements Reduce Process Cycle Time and Improve
Consistency(Average Cycle Time Reduced from 14 days to 2 days,
Variation Reduced from 2 days to 4 hours)
Distribution
UNCLASSIFIED / FOUO
UNCLASSIFIED / FOUO
“As Is” Baseline Statistics Template
The current process has a non-normal distribution with the P-Value < 0.05
Mean = 44 days
Median = 22 days
Std Dev = 61 days
Range = 365 days
Required Deliverable
360300240180120600
Median
Mean
6050403020
1st Q uartile 12.000
Median 22.000
3rd Q uartile 52.000
Maximum 365.000
33.647 55.981
17.000 29.123
54.308 70.246
A -Squared 12.65
P-V alue < 0.005
Mean 44.814
StDev 61.251
V ariance 3751.674
Skewness 2.87329
Kurtosis 9.54577
N 118
Minimum 1.000
A nderson-Darling Normality Test
95% C onfidence Interv al for Mean
95% C onfidence Interv al for Median
95% C onfidence Interv al for StDev95% Confidence Intervals
Summary for Workdays
- Example -
UNCLASSIFIED / FOUO
UNCLASSIFIED / FOUO
68
Takeaways
Now you should be able to:
Explain the importance of measurement to process improvement
Given process data, calculate a measure of central tendency and variation and describe what they tell us
Identify and contrast special cause and common cause variation
Given process data, calculate a Sigma Quality Level and describe what it tells us
Explain what is meant by VOC and VOP
UNCLASSIFIED / FOUO
UNCLASSIFIED / FOUO
What other comments or questions
do you have?
UNCLASSIFIED / FOUO
UNCLASSIFIED / FOUO
UNCLASSIFIED / FOUO
UNCLASSIFIED / FOUO
National GuardBlack Belt Training
APPENDIX
UNCLASSIFIED / FOUO
UNCLASSIFIED / FOUO
71
If Cp < 1 then the variability of the processis greater than the specification limits.
Process Capability Ratio – Cp
Process Capability Ratio (Cp) is the ratio of total variation allowed by the specification to the total variation actually measured from the process
Use Cp when:
The mean can easily be adjusted (i.e., in many transactional processes the resource level(s) can easily be adjusted with no/minor impact on quality), AND
The mean is monitored (so operators will know when adjustment is necessary – doing control charting is one way of monitoring)
Typical goals for Cp are greater than 1.33 (or 1.67 for high risk or high liability items)
UNCLASSIFIED / FOUO
UNCLASSIFIED / FOUO
72
+3-3
Process Width
TLSL USL
or
99.7% of values
Where is “within”
rather than pooled
Process Capability Ratio – Cp (Cont.)
Cp = Allowed variation (Specification)Normal variation of the Process 6
Cp = USL – LSL
UNCLASSIFIED / FOUO
UNCLASSIFIED / FOUO
73
This index accounts for the dynamic mean shift in the process – the amount that the process is off target
Calculate both values and report the smaller number
Notice how this equation is similar to the Z-statistic
3
ZCpk
σ
LSLxor
σ
xUSLMinC pk
33
Where is “within” rather than pooled
Process Capability Ratio – Cpk
s
xxZ
UNCLASSIFIED / FOUO
UNCLASSIFIED / FOUO
74
n - 1
Process Capability Ratio – Cpk (Cont.)
Ratio of 1/2 total variation allowed by spec. to ½ the actual variation, with only the portion closest to a spec. limit being counted
Use when the mean cannot be easily adjusted (i.e., in transactional processes where there is little flexibility, that is, where certain skill/expertise is not readily adjusted)
Typical goals for Cpk are greater than 1.33 (or 1.67 if safety related)
For sigma estimates use:
R/d2 [short term] (calculated from X-bar and R chart)
s = S (xi – x)2 [long term] (calculated from all data points)
Long term: When the data has been collected over a time period and over enough different sources of variation that over 80% of the variation is likely to be included
