# Statistical Process Control

Pages: 93 (13394 words) Published: April 7, 2013
Process Capability Assessment
Control Charts for Individual Measurements
Cumulative-Sum control charts
Control Charts for Large Sample

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Statistical Process Control - Part II
IE 330, Spring 2013,
Instructor: Yu-Ching Lee

March 14, 2013

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Process Capability Assessment
Control Charts for Individual Measurements
Cumulative-Sum control charts
Control Charts for Large Sample

Use of the histogram
Process Capability Indices
Statistical Assignment of Tolerances
Loss Function Approach

. Process Capability
Recall that we compared the two diﬀerent ideas—Product
conformance v.s. Control of the process—in our previous
lecture slides.
Product conformance issue is also referred to as the process capability.
One should never place the engineering speciﬁcations on a
control chart, since such would wrongly suggest that
tracking a quality characteristic is related to the engineering speciﬁcations.
Although the two issues are completely diﬀerent, they are
linked in the sense that it is impossible to assess process
capability without being reasonably assured of having good
statistical control.
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Process Capability Assessment
Control Charts for Individual Measurements
Cumulative-Sum control charts
Control Charts for Large Sample

Use of the histogram
Process Capability Indices
Statistical Assignment of Tolerances
Loss Function Approach

. Process Capability

If a process is in statistical control but not capable of
meeting the speciﬁcations, the problem may be one of the
following:
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1 The process is oﬀ-center from the nominal.
. The process variability is too large relative to the
tolerance/speciﬁcation.
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3 Both of the above.
2

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Process Capability Assessment
Control Charts for Individual Measurements
Cumulative-Sum control charts
Control Charts for Large Sample

Use of the histogram
Process Capability Indices
Statistical Assignment of Tolerances
Loss Function Approach

. Statistical Assessment of Process Capability
Correct order of inspection:
1: Checking for statistical control
2: Assessing process capability
We now revisit the example of cylinder boring process in
ﬁle
’Cylinder Boring Process Data ChartConstructed.xlsx’.
Step 1: This process, given that the samples 1, 6, 11
and 16 have been deleted, is in-control.
Step 2: We can proceed to evaluate the process with
respect to its conformance to speciﬁcations, given that
the nominal value is 199, LSL is 195, and USL is 203.
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Process Capability Assessment
Control Charts for Individual Measurements
Cumulative-Sum control charts
Control Charts for Large Sample

Use of the histogram
Process Capability Indices
Statistical Assignment of Tolerances
Loss Function Approach

. Statistical Assessment of Process Capability
For this statistical control process, we have
X = 199.95 and R = 6.84.
The good control of the R chart indicates that our estimate
of the process variation,
σX =
ˆ

R
6.84
=
= 2.9401
d2
2.326

is a valid estimate of common-cause variation.
To get a clear picture of the statistical nature of the data from an individual measurements point of view, a frequency
histogram was plotted.
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Process Capability Assessment
Control Charts for Individual Measurements
Cumulative-Sum control charts
Control Charts for Large Sample

Use of the histogram
Process Capability Indices
Statistical Assignment of Tolerances
Loss Function Approach

. Statistical Assessment of Process Capability
(continued)

The histogram seems to exhibit the shape of the normal
distribution, but the mean appears to be a little higher than the nominal value of 199.
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Process Capability Assessment
Control Charts for Individual Measurements
Cumulative-Sum control charts
Control Charts for Large Sample

Use of the histogram
Process Capability Indices
Statistical Assignment of Tolerances
Loss Function Approach

. Statistical...

References: N. L. Johnson and F. C. Leone generalized the cusum charts
to Poisson and binomial random variables as well as for
testing for shifts in variance and range.
N. L. Johnson and F. C. Leone, Cumulative Sum
Control Charts: Mathematical Principles Applied to
Their Construction and Use, Parts I, II and III,
Industrial Quality Control, Vol. 18, No. 12, Vol. 19,
No. 1, and Vol. 19, No.2, 1962.
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