Statistical Process Control. Variables Data. Click Here 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. SPC. Introduction. Variability. Normal Variability : - PowerPoint PPT Presentation
Statistical Process Control
Variables DataStatistical Process ControlClick Here to Begin
Introduce Statistical Process Control
Understand the process of creating an X bar R Chart
Understand the methods used in monitoring SPC charts
Objectives:
IntroductionSPC
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
Variability
Per Jurans Quality Handbook, the basic procedure for developing
X Charts is as follows:1.) Select the measurable characteristic to
be studied2.) 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 laterDeveloping 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 process6.)
Periodically assess the effectiveness of the chart, revising it as
needed or discontinuing it
Developing X Charts:
Xbar R ChartSPC
UCL = Ave + (3*Sigma)LCL = Ave (3*Sigma)Vs.UCL = Ave +
(A2*Rbar)LCL = Ave (A2*Rbar)
(A2*Rbar) = (3*Sigma)Equations:
Control Chart Factors
Xbar & R Chart
Average of AveragesConstant
Average Range
Example: Variable Data
Determine Average(s) for dataTo find the average take the sum
and divide it by the number being added together.
Example: Variable DataNext determine the range(s) of dataTo 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 DataNow calculate the UCL:To calculate the UCL
first find the sum of all sample averages:
= Sum = 8.36Then take the sum and divide it by the number of
numbers added together:8.36/16 = 0.52Average of Averages (X double
bar) = 0.52
0.660.290.610.390.290.480.570.480.630.540.470.400.770.580.280.90
Example: Variable DataNow calculate the UCL:To calculate the UCL
next find the sum of all sample ranges:
= Sum = 9.44Then take the sum and divide it by the number of
numbers added together:9.44/16 = 0.59Average range (R bar) =
0.590.600.560.590.960.370.750.650.840.490.760.670.480.280.670.600.19
Example: Variable DataNow 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 DataNow we will find A2. A2 is a constant
found on the following table:
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)
Example: Variable DataUCL = 0.86
Calculate the LCL:Now calculate the LCL using the formula:
LCL = X double bar - (A2*R bar)LCL = 0.52 - (0.577 * 0.59)
Example: Variable DataLCL = 0.18
The UCL and LCL have been calculated and were found to
equal:
UCL = 0.86LCL = 0.18
What does this mean?
Example Recap: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:
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)R Chart:
We have already found R bar to be = 0.59-so-UCL = 2.114*0.59LCL
= 0*0.59
UCL = 1.25LCL = 0Now complete the R Chart:
Now complete the R Chart:
Monitoring Control ChartsSPC
Completed X bar R Charts:
Look for Special Causes, which are suspect when:1.) One or more
points are above the UCL or below the LCL2.) Seven or more
consecutive points are above or below the centerline3.) One in
twenty plotted points is in the 1/3 outer edge of the chart4.)
Movements of five or more consecutive points are either up or
downControl Chart Interpretation Rules:
Completed X bar R Charts:
Special Cause
If special causes are identified, the process is considered to
be unstableRemoving special causes when they are harmful (which is
most of the time) is an important part of process
improvementTracking down special causes often relies heavily on
peoples (operators, supervisors, etc.) memories of what made that
occurrence differentSpecial Cause Variation
When you spot a special cause:
Control any damage or problems with immediate (short term)
fixOnce a quick fix is in place, search for the causeOnce you
determine the special cause, develop a longer-term remedySpecial
Cause Variation
Variables DataThe EndStatistical Process Control
