# Statistical Process Control

**Topics:**Control chart, Process capability, Standard deviation

**Pages:**93 (13394 words)

**Published:**April 7, 2013

Control Charts for Individual Measurements

Cumulative-Sum control charts

Control Charts for Large Sample

.

.

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:

.

1 The process is oﬀ-center from the nominal.

. The process variability is too large relative to the

tolerance/speciﬁcation.

.

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.

4 / 127

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.

5 / 127

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.

6 / 127

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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