Variables Data
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to Begin
Objectives:
• Introduce Statistical Process Control
• Understand the process of creating an X
bar R Chart
• Understand the methods used in
monitoring SPC charts
Introduction
Variability
Normal Variability:
-Normal variability is the inherent variability within a
process (It is the best the process can do in terms of
variability)
-If you want to reduce normal, or inherent, variability you
will usually have to redesign the process
Non-Normal Variability:
-Non-normal variability is a result of special causes
-The objective of the SPC chart is to determine when
special causes are present
Developing X Charts:
Per Juran’s Quality Handbook, the basic
procedure for developing X Charts is as follows:
• 1.) Select the measurable characteristic to be studied
• 2.) Collect enough observations (20 or more) for a trial
study (The observations should be far enough apart to
allow the process to potentially be able to shift)
• 3.) Calculate control limits and the centerline for the
trial study using the formulas given later
Developing X Charts:
• 4.) Set up the trial control chart using the centerline
and limits, and plot the observations obtained in step 2
(If all points are within the control limits and there are
no unnatural patterns, extend the limits for future
control)
• 5.) Revise the control limits and centerline as needed
(by removing out-of-control points by observing trends,
etc.) to assist in improving the process
• 6.) Periodically assess the effectiveness of the chart,
revising it as needed or discontinuing it
Xbar R Chart
Equations:
UCL = Ave + (3*Sigma)
LCL = Ave – (3*Sigma)
Vs.
UCL = Ave + (A2*Rbar)
LCL = Ave – (A2*Rbar)
(A2*Rbar) = (3*Sigma)
Control Chart Factors
Xbar & R Chart
Average of
Averages
Constant
Average
Range
Example: Variable Data
Determine Average(s)
for data
To find the average take
the sum and divide it by
the number being added
together.
Example: Variable Data
Next determine the
range(s) of data
To find the range list the
numbers under consideration
from lowest to highest value,
then subtract the lowest value
from the highest value
Example: Variable Data
Example: Variable Data
Now calculate the UCL:
To calculate the UCL first find the sum of all
sample averages:
0.66
0.29
0.61
0.39
0.29
0.48
0.57
0.48
0.63
0.54
0.47
0.40
0.77
0.58
0.28
= Sum = 8.36
Then take the sum and divide it by the number of
numbers added together:
8.36/16 = 0.52
Average of Averages (X double bar) = 0.52
0.90
Example: Variable Data
Now calculate the UCL:
To calculate the UCL next find the sum of all
sample ranges:
0.60
0.56
0.59
0.96
0.37
0.75
0.65
0.84
0.49
0.76
0.67
0.48
0.28
0.67
0.60
= Sum = 9.44
Then take the sum and divide it by the number of
numbers added together:
9.44/16 = 0.59
Average range (R bar) = 0.59
0.19
Example: Variable Data
Now calculate the UCL:
Recall the formula for the UCL is:
UCL = Average of Averages + (A2*Average Range)
-or-
UCL = X double bar + (A2*R bar)
Thus far we have calculated the average of the averages
and the average range, so the formula becomes:
UCL = 0.52 + (A2*0.59)
Example: Variable Data
Now we will find A2. A2 is a constant found on the
following table:
Example: Variable Data
Example: Variable Data
To finish the calculation of UCL we
simply plug the values into the
formula:
UCL = X double bar + (A2*R bar)
UCL = 0.52 + (0.577 * 0.59)
UCL = 0.86
Example: Variable Data
Calculate the LCL:
Now calculate the LCL using the
formula:
LCL = X double bar - (A2*R bar)
LCL = 0.52 - (0.577 * 0.59)
LCL = 0.18
Example Recap:
The UCL and LCL have been calculated
and were found to equal:
UCL = 0.86
LCL = 0.18
What does this mean?
One would expect 99.73% of
sample averages (n = 5) to lie
within the range of the UCL
and LCL due to normal
variation. . . In other words,
one could expect 99.73% of all
sample averages to lie
between 0.86 and 0.18
Now complete the Xbar Chart:
R Chart:
The next steps are to calculate the upper and lower
control limits for the Range Chart
--The objective of the Range chart is to detect changes in
variability
Recall:
UCL = (D4*R bar)
LCL = (D3*R bar)
Now complete the R Chart:
We have already found R bar to be = 0.59
-soUCL = 2.114*0.59
LCL = 0*0.59
UCL = 1.25
LCL = 0
Now complete the R Chart:
Monitoring Control Charts
Completed X bar R Charts:
Control Chart Interpretation Rules:
Look for Special Causes, which are suspect when:
1.) One or more points are above the UCL or below the
LCL
2.) Seven or more consecutive points are above or
below the centerline
3.) One in twenty plotted points is in the 1/3 outer edge
of the chart
4.) Movements of five or more consecutive points are
either up or down
Completed X bar R Charts:
Special Cause
Special Cause Variation
• If special causes are identified, the process is
considered to be ‘unstable’
• Removing special causes when they are
harmful (which is most of the time) is an
important part of process improvement
• Tracking down special causes often relies
heavily on people’s (operators, supervisors, etc.)
memories of what made that occurrence
different
Special Cause Variation
When you spot a special cause:
1. Control any damage or problems with
immediate (short term) fix
2. Once a ‘quick fix’ is in place, search for the
cause
3. Once you determine the special cause, develop
a longer-term remedy
Variables Data—The End