NG BB 26 Control Charts
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Transcript of NG BB 26 Control Charts
National GuardBlack Belt Training
National GuardBlack Belt Training
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Module 26
Control Charts
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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
Control chart fundamentals
Use of control charts to identify Common Cause and Special Cause variation
Factors to consider in constructing control charts
Variables control charts
Attribute control charts
Understand the interpretation and application of these charts
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Observation
Indi
vidu
al V
alue
30272421181512963
20
15
10
5
_X=10.58
UC L=18.48
LC L=2.67
Observation
Mov
ing
Ran
ge
30272421181512963
10.0
7.5
5.0
2.5
0.0
__MR=2.97
UC L=9.71
LC L=0
1
I-MR Chart of Pizza Preparation Time
Control Chart Terms
Control Chart = a time plot showing process performance, mean (average), and control limits
The Voice of the Process !!!
Control charts measure the “health” of the process
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Control Chart Terms
Control Limits = statistically calculated boundaries within which a process in control should operate
These boundaries result from the process itself and are NOT customer specifications
Observation
Indi
vidu
al V
alue
30272421181512963
20
15
10
5
_X=10.58
UC L=18.48
LC L=2.67
Observation
Mov
ing
Ran
ge
30272421181512963
10.0
7.5
5.0
2.5
0.0
__MR=2.97
UC L=9.71
LC L=0
1
I-MR Chart of Pizza Preparation Time
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Common vs. Special Cause
Measurements display variation
Variation is either:
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 harder 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 easier to eliminate
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Process Control
When a process is “in control”
This implies a stable, predictable amount of variation (common cause variation)
This does not mean a "good" or desirable amount of variation
When a process is “out-of-control”
This implies an unstable, unpredictable amount of variation
It is subject to both common AND special causes of variation
A process can be in statistical control and not capable of consistently producing good output within specification limits
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Types of Control Charts
The Control Chart family can be broken into two groups based on the type of data we are charting:
Continuous/Variable
Attribute/Discrete
Since we “prefer” Continuous data we will study this group of Control Charts first
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Continuous Data Control Charts
The theory of all Control Charts can be learned by studying the Xbar (Average) and R (Range) chart for continuous data
We will then explore the I-MR (Individuals - Moving Range) Chart
Xbar-R Charts allow us to study:
Variation “within each subgroup” (precision) on the R chart
Variation “between each subgroup” (accuracy) on the Xbar chart
Note: Look at the R chart first, if it is in control, then look at the Xbar chart
Examples of continuous data: width, diameter, temperature, weight, cycle times, etc.
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Control Chart Assumptions
Normally Distributed Data
Control limits approximate +/- 3 sigma from the mean
These control limits are based upon a normal distribution
If the distribution of the data is non-normal, you must use one of the x-bar charts, because the x-bars are likely to be normally distributed due to the effects of the Central Limit Theorem
Rule of thumb for x-bar charts is subgroups of at least 4. Rarely is the underlying distribution so far from normal to require larger subgroups to achieve normality in the x-bars.
Independent Data Points
“Independence” means the value of any given data point is not influenced by the value of any other data point (it is random)
Violation of this assumption means the probability of any given data value occurring is not determined by its distance from the mean, but by its place in the sequence in a data series or pattern
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Continuous Data Control Charts
Subgroup Size of 1
I-MR
Subgroup Size < 3-9
Xbar-R
Subgroup Size > 9
Xbar-S
Measurement(Continuous/Variable Data)
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Continuous Data Control Charts
Utilize probabilities and knowledge of the normal distribution
I-MR chart is used:
When you are learning about a process with few data points
When sampling is very expensive
When the sampling is by destructive testing and
When you are building data to begin another chart type
Xbar-R Chart is used with a sampling plan to monitor repetitive processes. The sub-group sizes are from 3 to 9 items. Frequently practitioners will choose subgroups of 5. All of the theory of Control Charts can be applied with these charts
Xbar-S Chart is used with larger sample groups of 10 or more items. Statisticians sometimes state that the standard deviation is only robust when the subgroup size is greater than 9 (These charts are similar to the Xbar-R Chart)
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Introduction to Xbar-R
Xbar-R Charts are a way of displaying variable data
Examples of variable data: width, diameter, temperature, weight, time, etc.
R Chart: a look at “Precision”
Displays changes in the „within‟ subgroup dispersion of the process. Often called “Short-Term Variation.”
Asks "Is the variation in the measurements „within‟ subgroups consistent?”
Must be “in control” before we can build or use the Xbar chart
Xbar Chart: a look at “Accuracy”
Shows changes in the average value of the process and is a visualization of the “Longer-Term Variation”
Asks "Is the variation „between‟ the averages of the subgroups more than that predicted by the variation within the subgroups?“
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Mechanics of an Xbar-R Chart
Control charts track processes by plotting data over time in the form:
Center Line (X)
Upper Control Limit
Upper Control Limit Averages
Chart = X Double Bar + A2 R Bar
Center Line Averages Chart =
Average of the Subgroup Averages
Lower Control Limit Averages
Chart = X Double Bar - A2 R Bar
X Chart
Lower Control LimitCenter Line (R)
Upper Control Limit
Upper Control Limit
Range Chart = D4Rbar
Center Line Range Chart =
Average of the Subgroup Ranges
Lower Control Limit
Range Chart = D3Rbar
Range Chart
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Example: Xbar-R Chart
Stat > Control Charts > Variables Charts for Subgroups > Xbar-R
Open the worksheet data file called ORDER TAKING.MTW
In this file, orders are taken by order entry clerks. The data is the average hold time a customer waits before speaking with a person to take their order.
The delays are a problem, as many customers give up and we have a dropped call and lost order
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Example: Xbar-R Chart
Double click on C-1 Ave Hold TimeThis places it in the
Variables box5
Type in 5 for yourSubgroup size
Our response is Ave. Hold Time and we choose 5 cells to represent our Subgroup size
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How Do We Interpret This Chart?
Always Look at the R Chart first ! Only if it is in control, is the Xbar chart usable !
Sample
Sa
mp
le M
ea
n
54321
16
14
12
10
8
__X=10.88
UC L=14.97
LC L=6.79
Sample
Sa
mp
le R
an
ge
54321
16
12
8
4
0
_R=7.10
UC L=15.01
LC L=0
1
Xbar-R Chart of Ave. Hold Time
Xbar Chart
R Chart
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Control Chart Data Requirements
Data requirements for control chart applications:
Must be in time series order
Minimum of 25 consecutive (no time gaps) subgroups or
Minimum of 100 consecutive observations
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I-MR Chart
The Individuals and Moving Range chart is also for continuous data
It can be used for many transactional applications:
Revenue or cost tracking
Customer satisfaction
Call times
System response times
Wait times
Most common continuous measures – time and money!
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Individuals and Moving Range (I-MR) Chart
The top chart is a plot of individual pizza preparation times
The bottom chart is the Moving Range, in this case, the Range of two adjacent pizza preparation times
Observation
Indi
vidu
al V
alue
30272421181512963
20
15
10
5
_X=10.58
UC L=18.48
LC L=2.67
Observation
Mov
ing
Ran
ge
30272421181512963
10.0
7.5
5.0
2.5
0.0
__MR=2.97
UC L=9.71
LC L=0
1
I-MR Chart of Pizza Preparation Time
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Control Limit Calculation
The UCL (Upper Control Limit) and the LCL (Lower Control Limit) are calculated by Minitab using the sample/process data
The control limits approximate +/- 3 standard deviations (99+% of the data)
Here, 99+% of the pizzas are prepared between 2.6 and 18.7 minutes
Be careful not to confuse control limits and specification limits! If a data point appears outside of the control limits, there is less than a 1% chance that this was part of the normal process. Since it is very unlikely that this value occurred by chance, it is called “Special Cause” variation.
Observation
Individ
ual V
alue
30272421181512963
20
15
10
5
_X=10.58
UCL=18.48
LCL=2.67
1
I Chart of Pizza Preparation Time
UCL
X
LCL
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Control Limit Interpretation
Another type of Special Cause variation occurs when there is a predictable pattern in the data
The predictable pattern of the data means the data is not random and that there is an underlying reason for this pattern – a Special Cause
The Western Electric rules are helpful in identifying patterns in the data (these are in the appendix)
Observation
Indiv
idual
Value
272421181512963
20.0
17.5
15.0
12.5
10.0
7.5
5.0
_X=9.87
UCL=15.29
LCL=4.453
3
3
3
3
3
1
3
3
3
1
I Chart of Pizza Prep Time 2
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Exercise: Begin Building an I-MR Chart
Let‟s begin building an I-MR chart for a Pizza Preparation process. Begin by using the 5 Pizza Preparation Time measurements below to start the calculations for a Control Chart on a flip-chart.
Individuals Chart
Plot each individual time measurement
Calculate the Centerline
The centerline on an Individuals chart is the overall average
Verify that the average is 9.6
The control limits will be calculated by a formula in Minitab. They approximate +/- 3 standard deviations of the pizza prep times
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Pizza Exercise
Moving Range Chart
Calculate the ranges
The first range is between points 1 and 2
Range = Max - Min
12 - 7 = 5
The next range is between points 2 and 3
Range = Max - Min
11 - 7 = 4
Continue for the next 2 ranges
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Pizza Exercise (Cont.)
Moving Range Chart
Calculate the Centerline
The centerline is the average of the moving ranges, called R
For these 5 points (4 range calculations), verify that R = 3
The Control Limits will be calculated in Minitab. In this case they approximate +/- 3 standard deviations of the range values.
We expect the Control Limits to be tighter for the Moving Range chart than for the Individuals chart
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Build I-MR Chart in Minitab
Let‟s continue with our exercise:
1. Open the exercise Exercise9.mtw
2. Choose: Stat> Control Charts> Variables Charts for Individuals> I-MR
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I-MR Input Window
3. Double click on C1 Pizza PreparationTime. This places it in the Variables box.
4. Click OK
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Individual and Moving Range (I-MR) Chart
Is our Pizza Prep process in statistical control?Is the process likely to be acceptable to our customers?
Observation
In
div
idu
al
Va
lue
30272421181512963
20
15
10
5
_X=10.58
UC L=18.48
LC L=2.67
Observation
Mo
vin
g R
an
ge
30272421181512963
10.0
7.5
5.0
2.5
0.0
__MR=2.97
UC L=9.71
LC L=0
1
I-MR Chart of Pizza Preparation Time
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Remember the tests that we used in Run Charts? These are used in Control Charts as well.
The additional tests are called the “Western Electric Rules”
They can be found under Stat>Control Charts>Variables Charts for Individuals>I-MR>I-MR Options>Tests
Western Electric Rules
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Point outside of the limit:Control limits are calculated to measure the natural variability of a process. Any point on, or outside, the limit is consideredabnormal and requires investigation.
Run:A “run” is a series of points occurringcontinually on one side of the center line. A “run” of seven points is considered abnormal. Also considered abnormal: 10 out of 11,12 of 14, or 16 of 20 points on oneside of the center line.
Trending:Seven points in a continuous upward or downward direction.
Upper Control Limit
Lower Control Limit
Center Line
Upper Control Limit
Lower Control Limit
Center Line
Upper Control Limit
Lower Control Limit
Center Line
Control Chart Tests
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Approaching the center line (hugging):When most points lie within the center line and 1.5s it is not a controlled state and usually means the mixing of data from different populations. This makes the control limits too wide and stratification of data is usually necessary.
Cycling (periodicity):Any repeated up and down trend is abnormal and requires investigation.
Approaching control limits:2 of 3 points lying outside the2s line is considered abnormal.
Upper Control Limit
Lower Control Limit
CL
Upper Control Limit
Lower Control Limit
CL
LCL
UCL
CL
Control Chart Tests
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Special Causes Are Clues to the Process
A control chart is a guide to improving your process
Take advantage of every clue
Identify and investigate all special causes – they teach us how things affect the process
Some special causes are good!
For example, in our pizza delivery case, a delivery time out of control on the low side would be good. We could investigate this case to try to discover a new best practice.
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Process for Identifying Special Causes
Check all the W.E. rules each time you plot a point
Look across the entire chart
Circle all special causes
Investigate immediately – this is especially important. Do not lose the opportunity to learn as much as possible about the conditions that caused this special cause variability.
Take notes on the investigation
You must investigate and eliminate the special cause!
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Next Steps
Identify assignable causes
Establish that the data are normally distributed without the special cause data points
Circle the special causes
Eliminate special causes from the control limit calculation
Recalculate control limits
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Observation
In
div
idu
al
Va
lue
30272421181512963
20
15
10
5
0
_X=10.69
UC L=18.86
LC L=2.52
Observation
Mo
vin
g R
an
ge
30272421181512963
10.0
7.5
5.0
2.5
0.0
__MR=3.07
UC L=10.04
LC L=0
1
1
1
I-MR Chart of Pizza Preparation Time
New Control Limits
If you can investigateand determine what
caused these „Out of Control‟
points, you can then delete them and recalculate your
control chart limits
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Attribute Control Charts
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Attribute Data Charts
Two categories of attribute data:
Count data (outcomes: 0, 1, 2, 3, 4, 5, etc.)
Good/bad product data (only 2 possible outcomes)
Four common attribute charts:
C and U charts are used for count data of
Errors in the process, either a step in the process or the overall process, or
Defects in the process‟ or steps‟ deliverables
NP and P charts are used for good/bad process, service, or product data (items or process steps that are defective or flawed)
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Which Chart to Use?
C Chart “defect count“
U Chart, “defects / unit”
NP Chart, “no. defective”
P Chart, “proportion ”
Count or Classification(Discrete/Attribute Data)
Defects
Fixedsample sizes
Variablesample sizes
Defective Units
Fixedsample sizes
Variablesample sizes
Discrete/Attribute DataTo select an attribute chart, first choose between plotting defects or defective units. Then decide between fixed or variable opportunity. The variable opportunity charts are used more frequently.
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Deeper into Attribute Charts
Many transactional processes and manufacturing processes only record data as to the service or the products being either bad or good, defective or not defective
There are two sub-families in the Attribute control charts:
If we count defects (usually with any item having more than one opportunity for a defect) we use the C or Ucharts
If the sample size is always the same, use a C-chart. If the sample size varies, use a U-chart.
If we count defective units instead of defects, we use the NP or P charts
If the sample size is always the same, use a NP-chart. If the sample size varies, use a P-chart.
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Charts for Attribute Data
Most of the Attribute Control Charts are identical in interpretation and very similar to create in Minitab
The equations used are slightly different, but still based on the theory we learned with the Xbar Chart
One of the most commonly used attribute charts is the P-Chart which plots Proportion Defective
If you calculated Proportion Defective as your baseline capability metric – this chart is for you!
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P-Chart
P-Charts should be used whenever we are monitoring proportion defective (percentage defective is just another proportion)
Some uses of the P-Chart in transactional applications would be:
Billing errors (proportion of total bills that had errors)
Defective loan applications
Proportion of invoices with errors
Proportion of missing reservations
Defective room service orders
Missing items
Proportion of customers who were dissatisfied with service
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P-Chart Pizza Exercise
Anthony's Pizza wishes to monitor defective pizzas
Each day for a month the cook keeps a count of the number of defective pizzas for that day and also the total number of pizzas that day
Let‟s use the first 5 days data below to start the P-Chart on a flipchart
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P-Chart Pizza Exercise (Cont.)
Calculate the proportion defective
Recall the formula for proportion defective:
In this example:
For the first day:
Calculate the proportion defective for days 2-5
UnitsTotal
UnitsDefectiveofNumberDefectiveProportion
PizzasTotal
PizzasDefectiveofNumberDefectiveProportion
0.021420
9DefectiveProportion
Note: Percentage Defective, in this case, would be 2.1% defective
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P-Chart Pizza Exercise (Cont.)
Next, calculate the center line
The center line is the proportion of Total Defectives (for all samples) to Total Units (for all samples)
Verify that this is 0.019
The Control Limits are calculated in Minitab
The equations are slightly different, but the Control Limits are still calculated from the actual values, predicting the range of 99% of the data
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Minitab - Attributes Control Charts
1. Open worksheet: Exercise9.mtw
2. Choose Stat>Control Charts>Attributes Charts>P
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P-Chart Input Window
3. Double click on C-4 Defective Pizzas. This places it in the Variables box.
4. Place cursor in the Subgroups sizes box and then double click on C-5 Number of Pizzasto move it there
5. Click OK
Note: Minitab calculates the proportion defective for us. We enter the defective units in the Variable box. Then we enter the total units over
that time period in the Subgroup sizes box.
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P-Chart
Note: Minitab recalculates the control limits every time the subgroup size changes.
To get a straight line, you can enter a constant value under “Subgroup size.”
In this example, the best constant would be the average of the “Number of Pizzas.”
What are your thoughts around our defective pizzas?
Sample
Pro
po
rtio
n
30272421181512963
0.05
0.04
0.03
0.02
0.01
0.00
_P=0.01932
UCL=0.03689
LCL=0.00174
1
P Chart of Defective Pizzas
Tests performed with unequal sample sizes
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Exercise: Create a Control Chart
Now Anthony's Pizza wants to investigate sales history and billing errors for the same month
In teams, continue with Exercise9.mtw. Use an I-MR Chart to monitor sales for the month.
Use a P-Chart to observe the proportion of defective bills
Prepare to teach back to the class on your findings
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Quick Review - Control Chart Reminders
There are several types of control charts:
Determine type of data: continuous or attribute
Be clear on the purpose and value you wish to gain from the chart
Control limits are derived from process data
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Control Chart Uses and Benefits
Demonstrate stability and predictability of a process over time
Range of variation within the “control limits”
Distinguish between common vs. special cause variation
Provides more information than Run Charts
Can be used to demonstrate changes in performance
Provide a common language for process performance
Offer early warning of problems
BUT…..
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Control Chart Challenges
Must use correct type of chart for the data
Must meet normality and independence assumptions
Non-normal, continuous data must use x-bar chart to meet normality requirement
Control limits vs. customer requirements
Remember that the control limits are providing the Voice of the Process
We need to look at specification limits to see the Voice of the Customer
A process “in control” may be ineffective, inefficient, or both!
Control charts require effective, ongoing data collection. To be effective for determining root causes of special cause variation, they must be reacted to immediately!
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Steps in Control Charting
Select process characteristic to control, the key x or Y
Collect data and calculate appropriate statistics
Assess data distribution normality
Construct preliminary control charts
Establish control (find and eliminate special causes)
Construct final control charts
Establish stability (find and reduce common causes)
Use for ongoing control purposes
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What Do Control Charts Tell Us?
When the process mean has shifted
When process variability has changed
When special causes are present
Process is not predictable
Opportunity to learn about the process
When no special causes are present
Process is predictable
No clues to improvement available; may need to introduce a special cause in order to understand cause and effect, and then to effect a change
Control charts tell you when, not why!!
Observation
In
div
idu
al
Va
lue
30272421181512963
20
15
10
5
0
_X=10.69
UC L=18.86
LC L=2.52
Observation
Mo
vin
g R
an
ge
30272421181512963
10.0
7.5
5.0
2.5
0.0
__MR=3.07
UC L=10.04
LC L=0
1
1
1
I-MR Chart of Pizza Preparation Time
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Process Control Chart Template
The current baseline delivery time is stable over time with both the Moving Range (3.22 days) and Individual Average (29.13 days) experiencing common cause variation
255 data points collected with zero subgroups, thus the I&MR control chart selected
Observation
In
div
idu
al
Va
lue
2442171901631361098255281
40
35
30
25
20
_X=29.13
UC L=37.70
LC L=20.56
Observation
Mo
vin
g R
an
ge
2442171901631361098255281
10.0
7.5
5.0
2.5
0.0
__MR=3.22
UC L=10.53
LC L=0
I-MR Chart of Delivery Time
Required As Applicable- Example -
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Exercise: Prepare a Control Chart
Objective
Create control charts for the GGA's Budget Department
Instructions
Identify Primary Y metric
Determine best control charts to use
Run proper control chart for that data
Time = 15 Minutes
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Takeaways
Control limits are calculated from a time series of the characteristic we are measuring
Different formulas are available, depending on the type of data
Control limits should not be recalculated each time data are collected
The control limits are a function of the sampling and subgrouping plan
Variation due to "assignable cause" is often the easiest variation to reduce/eliminate
Control limits are not related to standards! Nor are they specifications! Control limits are a measure of what the process is doing/has done. It is the present/past tense, not the future (what we want the process to do or what it has the potential to do)
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What other comments or questions
do you have?
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References
Wheeler, Donald J. & Chambers, David S., Understanding Statistical Process Control, Second Edition, SPC Press, Knoxville Tennessee, 1992
Pruit, James M. & Snyder, Helmut, Essentials of SPC in the Process Industries, Instrument Society of America, 1996
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APPENDIX
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Western Electric Rules
1. One point beyond Zone A
Detects a shift in the mean, an increase in the standard deviation, or a single aberration in the process. For interpreting Test 1, the R chart can be used to rule out increases in variation.
2. Nine points in a row in Zone C or beyond
Detects a shift in the process mean
3. Six points in a row steadily increasing or decreasing
Detects a trend or drift in the process mean. Small trends will be signaled by this test before Test 1.
UNCLASSIFIED / FOUO
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61
Western Electric Rules (Cont.)
4. Fourteen points in a row alternating up and down
Detects systematic effects, such as two alternately used machines, vendors, or operators
5. Two out of three points in a row in Zone A or beyond
Detects a shift in the process average or increase in the standard deviation. Any two out of three points provide a positive test.
6. Four out of five points in Zone B or beyond
Detects a shift in the process mean. Any four out of five points provide a positive test.
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62
Western Electric Rules (Cont.)
7. Fifteen points in a row in Zone C, above and below the center line
Detects stratification of subgroups when the observations in a single subgroup come from various sources with different means
8. Eight points in a row on both sides of the center line with none in Zone C
Detects stratification of subgroups when the observations in one subgroup come from a single source, but subgroups come from different sources with different means