Transcript “out of control”? - Rose

Statistical Process Control
Using Control Charts to Monitor
“Quality”
Walter Shewhart
Developer of Control Charts in the late 1920’s
www.york.ac.uk/.../ histstat/people/welcome.htm
Statistical Process Control
• SPC does not refer to a particular
technique, algorithm or procedure
• SPC is an optimisation philosophy
concerned with continuous process
improvements, using a collection of
(statistical) tools for
– data and process analysis
– making inferences about process behaviour
– decision making
http://lorien.ncl.ac.uk/ming/spc/spc1.htm
Ultimately, SPC seeks to
maximize profit by:
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improving product quality
improving productivity
streamlining process
reducing wastage
reducing emissions
improving customer service, etc.
http://lorien.ncl.ac.uk/ming/spc/spc1.htm
Control Charts
• Control charts are particularly useful for
monitoring quality and giving early warnings
that a process may be going “Out of Control”
and on its way to producing defective parts.
http://www.pqsystems.com/products/SPC/CHARTrunner/CHARTrunnerChartingExample1.php
Objectives
• Be able to explain how control charts
relate to assigned dimension and
tolerance
• State what value you get from control
charts
• Be able to name several ways that control
charts indicate that a process is “out of
control”
Reminder:
Normal Distribution
Defined by two parameters:
mean and standard deviation
http://www.campbell.berry.edu/faculty/jgrout/spclecture.ppt
Example:
Suppose we specify a dimension
and tolerance as shown.
2.500.05
Questions:
- What does the X control chart look like?
- How does control chart relate to the tolerances?
Control charts are normal distributions
with an added time dimension
http://lorien.ncl.ac.uk/ming/spc/spc8.htm#interpretation
Control charts provide a graphical means
for testing hypotheses about the data
being monitored. Consider the commonly
used Shewhart Chart as an example.
http://lorien.ncl.ac.uk/ming/spc/spc8.htm#interpretation
What does the X control chart look like?
- First we measure a number of parts as they come off the line.
- For example we might measure 4 parts per hour for 20 hours.
- Those 80 parts would give us an overall mean and standard deviation
that would define the control chart.
- The average of the size of the four parts would give us
the y values for each hour (plotted on the x-axis)
+3

-3
Time
How does the control
chart relate to the tolerances?
Assigned Tolerances
2.45
-3
2.55
+3
Measured Variation
Value of Control Charts
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Defect Prevention through “Early Warning”
Prevent “Over-Tweaking” of Process
Assures that Process is Working
Provides Information on “Process
Capability”
Defect Prevention
• When you see signs that the process is
“out of control” you can look for and fix the
causes before you make bad parts.
• The control chart can help you distinguish
between “common cause” and “special
cause” problems.
Q - How do you know a process is “out of control”?
A – When the data aren’t “normal”
“Out of Control” cues include
- Points outside of control limits (3σ)
- 8 consecutive points on one side of center line
- 2 of 3 consecutive points outside the 2 limits
- 4 of 5 points outside the 1  limits
- 7 consecutive points trending up or down
Screen Dump from MiniTab
Prevent “Over-Tweaking”
• Without understanding of the statistics you
can chase your tail trying to get rid of
variation
Process Capability
• Comparing the control chart information
with the tolerance specification tells you
about the process capability.
The capability index is defined as:
Cp = (allowable range)/6s = (USL - LSL)/6s
LSL
LCL
USL (Upper Specification Limit)
UCL (Upper Control Limit)
http://lorien.ncl.ac.uk/ming/spc/spc9.htm
The process performance index
takes account of the mean (m) and
is defined as:
Cpk = min[ (USL - m)/3s, (m - LSL)/3ss ]
LSL
LCL
USL (Upper Specification Limit)
UCL (Upper Control Limit)
http://lorien.ncl.ac.uk/ming/spc/spc9.htm
Process Capability
2.45
Assigned Tolerances
2.55
Good
CPK>1
-3
+3
Measured Variation
Poor
CPK<1
-3
+3
Tolerance Stackups
Tolerance Stack-up for an O-Ring
www.afmusa.com/doc_ generator.asp?doc_id=1238
How to calculate Stack-up
• WC – Worst Case (add all the tolerances
at full value)
• RSS – Root Sum Squared (add the
tolerances statistically)
• Monte Carlo (use part distribution data to
predict the distribution of the added
tolerances)