Transcript Introduction to Statistical Quality Control, 5th edition

IES 331 Quality Control
Chapter 7
Process and Measurement System Capability Analysis
Week 10
August 9–11, 2005
Dr. Karndee Prichanont
IES331 1/2005
Process Capability

Uniformity of the process

A uniformity of output

Natural tolerance limits are defined
as follows:
Process Capability
Analysis: Quantifying
variability relative to
product requirements or
specifications
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Dr. Karndee Prichanont
IES331 1/2005
Process Capability Analysis

Process Capability Analysis:

In the form of probability distribution having…

a specified shape,

center (mean), and

spread (standard deviation)

A percentage outside of specifications

However, specifications are not necessary to process
capability analysis
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Dr. Karndee Prichanont
IES331 1/2005
Major Uses of Process Capability Analysis
1.
Predicting how well the process will hold the tolerances
2.
Assisting product developers/designers in selecting or
modifying a process
3.
Assisting in establishing an interval between sampling
process
4.
Specifying performance requirements for new equipment
5.
Selecting suppliers
6.
Planning the sequence of production processes
7.
Reducing the variability in a manufacturing process
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Dr. Karndee Prichanont
IES331 1/2005
Reasons for Poor Process Capability
Process may have
good potential
capability
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Dr. Karndee Prichanont
IES331 1/2005
Process Capability Analysis using a
Histogram or a Probability Plot


If use Histogram, there should be at least 100 or
more observations
Data collection Steps
1.
Choose machines or machines. Try to isolate the headto-head variability in multiple machines
2.
Select the process operating conditions
3.
Select representative operator
4.
Monitor data collection process
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Dr. Karndee Prichanont
IES331 1/2005
Exercise 7-11: page 377
The weights of nominal 1-kg
containers of a
concentrated chemical
ingredient are shown
here. Prepare a normal
probability plot of the
data and estimate process
capability
0.9475
0.9705
0.9770
0.9775
0.9860
0.9960
0.9965
0.9975
1.0050
1.0075
1.0100
1.0175
1.0180
1.0200
1.0250
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Dr. Karndee Prichanont
IES331 1/2005
Exercise 7-11: page 377 (cont)
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Dr. Karndee Prichanont
IES331 1/2005
Process Capability Ratios


Process capability ratio (PCR Cp)
introduced in Chapter 5
Percentage of the specification
band used up by the process
Exercise 7-7: A Process is in statistical
control with CL(x-bar) = 39.7 and
R-bar = 2.5. The control chart uses
sample size of 2. Specification are
at 40+/-5. The quality
characteristic is normally
distributed. Find Cp and P
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Dr. Karndee Prichanont
IES331 1/2005
One-Sided PCR
Exercise 7-7: A Process is in statistical control with
CL(x-bar) = 39.7 and R-bar = 2.5. The control chart
uses sample size of 2. Specification are at 40+/-5. The
quality characteristic is normally distributed.
Find C
pu
and Cpl
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Dr. Karndee Prichanont
IES331 1/2005
Interpretation
of the PCR
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Dr. Karndee Prichanont
IES331 1/2005
Assumptions for Interpretation of
Numbers in Table 7-2
1.
The quality characteristic has a normal
distribution
2.
The process is in statistical control
3.
In the case of two-sided specifications, the
process mean is centered between the lower and
upper specification
Violation of these assumptions can lead to big
trouble in using the data in Table 7-2.
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Dr. Karndee Prichanont
IES331 1/2005
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Dr. Karndee Prichanont
IES331 1/2005
• Cp does not take
process centering into
account
• It is a measure of
potential capability, not
actual capability
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Dr. Karndee Prichanont
IES331 1/2005
A Measure of Actual Capability
Cpk = minimum (Cpu, Cpl)


Measure the one-sided PCR for the specification
limit nearest to the process average.
If Cp = Cpk, the process is centered at the
midpoint of the specifications,

If Cpk < Cp , the process is off-center

Cp measures potential capability,

Cpk measures actual capability
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Dr. Karndee Prichanont
IES331 1/2005
Normality and Process Capability Ratios


The assumption of normality is critical to the
usual interpretation of these ratios (such as
Table 7-2)
For non-normal data, options are
1.
Transform non-normal data to normal
2.
Extend the usual definitions of PCRs to handle nonnormal data
3.
Modify the definitions of PCRs for general families of
distributions
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Dr. Karndee Prichanont
IES331 1/2005
Confidence Interval and Tests of
Process Capability Ratios
Confidence intervals are an important way to
express the information in a PCR
Exercise 7-20: Suppose that a quality characteristic has a normal
distribution with specification limits at USL = 100 and LSL = 90. A
random sample of 30 parts results in average of 97 and standard
deviation of 1.6
•Calculate a point estimate of Cpk
•Find a 95% confidence interval on Cpk
•How can we decrease the width of confidence interval on Cpk?
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Dr. Karndee Prichanont
IES331 1/2005
Process Capability Analysis Using
a Control Chart


Process must be in an in-control state to
produce a reliable estimates of process
capability
When process is out of control, we must find and
eliminate the assignable causes to bring the
process into an in-control state
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Dr. Karndee Prichanont
IES331 1/2005
Gauge and Measurement System
Capability Studies



Determining the capability of the measurement system
Variability are from (1) the items being measured, and (2) the
measurement system
We need to:
1.
Determine how much of the total observed variability is due to the
gauge or instrument
2.
Isolate the components of variability in the instrument system
3.
Assess whether the instrument of gauge is capable
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Dr. Karndee Prichanont
IES331 1/2005
Example 7-7
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Dr. Karndee Prichanont
IES331 1/2005
Setting Specification Limits on Discrete
Components



For components that interact with other
components to form the final product
To prevent tolerance stack-up where there are
many interacting dimensions and to ensure that
final product meets specifications
In many cases, the dimension of an item is a
linear combination of the dimensions of the
component parts
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Dr. Karndee Prichanont
IES331 1/2005
Exercise 7-30


Three parts are assembled in series so that their
critical dimensions x1, x2, and x3 add. The
dimensions of each part are normally distributed
with the following parameters:

µ1 = 100; std dev1 = 4

µ2 = 75; std dev2 = 4

µ3 = 75; std dev3 = 2
What is the probability that an assembly chosen
at random will have a combined dimension in
excess of 262
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