Statistical Process Control Using Control Charts to Monitor “Quality”
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Transcript of Statistical Process Control Using Control Charts to Monitor “Quality”
Statistical Process Control
Using Control Charts to Monitor “Quality”
Walter Shewhart
www.york.ac.uk/.../ histstat/people/welcome.htm
Developer of Control Charts in the late 1920’s
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:
• 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”
Normal Distribution Defined by two parameters:
mean and standard deviation
http://www.campbell.berry.edu/faculty/jgrout/spclecture.ppt
Reminder:
2.500.05
Example:Suppose we specify a dimension and tolerance as shown.
Questions: - What does the control chart look like?
- How does control chart relate to the tolerances?
X
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 control chart look like?X
- 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
+3-3
2.552.45
Assigned Tolerances
Measured Variation
How does the control chart relate to the tolerances?
Value of Control Charts
• 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
USL (Upper Specification Limit)LSL
LCL 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 ]
USL (Upper Specification Limit)LSL
LCL UCL (Upper Control Limit)
http://lorien.ncl.ac.uk/ming/spc/spc9.htm
+3-3
2.552.45
Assigned Tolerances
Measured Variation
-3 +3
Process Capability
Good
Poor
CPK>1
CPK<1
Tolerance Stackups
www.afmusa.com/doc_ generator.asp?doc_id=1238
Tolerance Stack-up for an O-Ring
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)