Transcript No Slide Title

Agenda

Review homework
•


Problems: Chapter 5 2, 8, 18, 19
Process capability
Other variable control
charts
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Week 10
Week 11 Assignment
•
•
Read Chapter 8
“Probability”
Homework
• Chapter 6: 1, 2, 3, 4, 13
• Chapter 7: 2, 5, 11
Process Capability
Chapter Six
Process Capability
Defining process capability
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Process capability refers to the ability of
the process to meet the specifications set
by the customer or designer.
Process Capability
Process capability analysis
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Objective is to determine how well the
output from a process meets
specification limits
Compare total process variation and
tolerance.
LSL
USL
-3
Target
Process Capability
+3
Individual values compared
with averages

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When distributions of averages are
compared to distributions of individual
values, the averages are grouped closer
to the center value than are the individual
values, as described by the central limit
theorem.
What does this imply for averages in
control limits versus individual values in
specification limits?
Process Capability
Estimation of population
sigma from sample data
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The relationship between the standard
deviation for individual values and the
standard deviation for their averages is
given by the formula:

x 
n
Where n = subgroup sample size
Process Capability
To simplify calculation
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If the process can be assumed to be
normal, the population standard deviation
can be estimated from either the
standard deviation associated with the
sample standard deviation or the range:


R
d

or

S
c
4
2
Process Capability
Control limits and
specification limits
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Xbar charts do not reflect how widely the
individual values composing the plotting
averages spread.
The spread can only be seen by
observing what is happening on the s or r
chart.
Process Capability
The Six sigma spread
versus specification limits
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Case I: 6 < USL - LSL
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Case II: 6 = USL - LSL
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Most desirable; individual values fall
within specification limits
Okay, as long as the process remains
in control
Case III: 6 > USL - LSL
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Undesirable; process incapable of
meeting specifications
Process Capability
Calculating process
capability indices
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Process capability indices: ratios that
quantify the ability of a process to
produce within specifications
See examples - pages 318 - 320
Process Capability