Statistical Quality Control
OEM 2009
ESI 6321 –Applied Probability Methods in
Engineering
2
Statistical Quality Control
A collection of tools used to monitor and
guide quality improvement activities.
Quality of design:
Quality level (performance, reliability, function)
that is the result of engineering and/or
management decisions
Quality of conformance:
Reduction of variability
Elimination of defects
Goal: all units are identical, and defect-free

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3
Process Variability
Any production process contains
variability.
Chance (common) causes
of variability
Essentially unavoidable, inherent variability in
the process
Assignable (special) causes
of variability
Avoidable variability in the process:
Improperly adjusted machines
Operator errors
Defective raw materials
4
Control Chart
Process is
in control:
Only chance causes of variability are present
Process is
out of control:
Assignable causes of variability are present
The most powerful of all Statistical Quality
Control tools is the
control chart
.
A control chart displays periodic
measurements of some quality
characteristic, and visualizes whether the
process is in or out of control.

5
Control Chart
A control chart consists of a
center line
and two
control limits
for the value of the
quality characteristic that we are
interested in.
If the observed value of the quality
characteristic falls beyond one of the two
control limits, the process is
out of
control
.
This type of control chart is called a
Shewhart control chart
.
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Variables vs. Attributes Control Chart
There are two general types of control
charts:
Variables control charts.
Attributes control charts.
Variable control charts
are used for
quality characteristics that can be
measured on a
continuous
scale.
Attribute control charts
are used for
discrete quality characteristics; for
instance: conforming vs. nonconforming.

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7
Control Chart for Mean
The most widely used variables control
chart monitors the
mean
of a process
parameter.
This mean is then the
quality characteristic
of
interest.
It is often reasonable to assume that the
quality characteristic is
normally
distributed
(when the process is in
control).
We will base our choice of
center line
and
control limits
on this assumption.
In principle, the approach can be generalized
to other population distributions.
8
Designing a Control Chart
Example:
consider the manufacturing of
automobile piston rings.
A critical quality characteristic is the
average realized inside ring diameter.
We know that the process mean inside
ring diameter is 74 mm, and its standard
deviation is 0.01 mm
if the process is in
control
.
Every hour a random sample of 5 rings is
taken, and their average inside ring
diameter is computed and plotted in a
control chart.