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)