Transcript Ch_9_s01_605

Process Capability
• Process capability
– For Variables
• The 6 versus specification limits
– For attributes
• Pareto chart
• Cause and effect diagram
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Process Capability
• There is a difference between a process conforming
to the specifications and a process performing within
statistical limits
• A process in statistical control will not necessarily
meet specifications as established by the customer
• The control limits on the charts represent what the
process is capable of producing
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Process Capability
• Specifications are set by the customer. These are the
“wishes.”
• Control limits are obtained by applying statistical
rules on the data generated by the process. These
are the “reality.”
• Process capability refers to the ability of a process to
meet the specifications set by the customer or
designer
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The 6 Versus Specification Limits
• It is important to compare the natural tolerances, 6,
with the specification range (USL-LSL).
• Recall that  may be estimated as follows:
R
 
d2
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The 6 Versus Specification Limits
• Suppose that process mean = (USL+LSL)/2
• Case I: 6 < USL - LSL
– The specifications will be met even after a slight
shift in process mean
• Case II: 6 = USL - LSL
– As long as the process remains in control with no
change in process variation, the specification will
be met
• Case III: 6 > USL - LSL
– Although the process may be in statistical control,
it is incapable of meeting specifications
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The 6 Versus Specification Limits
USL  LSL
• Capability potential C p 
6
• The relationship between process mean,  and its
target value, X 0 is obtained from an index
k
X0 
min( X 0  LSL,USL  X 0 )
• Exercise: If the target mean value = (USL+LSL)/2, is
the process capable if C p  1.33 and k  0.4 ? if k  0.2 ?
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Process Capability
• Some indices:
  LSL
USL  
C pL 
, C pU 
3
3
C pk  min( C pL , C pU )
• If the above indices are more than 1, the 3-sigma
control limits are within the specification limits, and
the process is capable - all but at most 0.27% items
meet the specification
• If CpL < 1, too many items are outside LSL
• If CpU < 1, too many items are outside USL
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The 6 Versus Specification Limits
• Sometimes, only one of CpL and CpU may be relevant
e.g., testing for steel hardness
• If the process is not capable, actions may be taken to
adjust the
– process mean
– variation
– specifications
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Problem 9.6: A certain manufacturing process has been
operating in control at a mean  of 65.00 mm with
upper and lower control limits on the X chart of 65.225
and 64.775 respectively. The process standard
deviation is known to be 0.15 mm, and specifications
on the dimensions are 65.00±0.50 mm.
(a) What is the probability of not detecting a shift in the
mean to 64.75 mm on the first subgroup sampled after
the shift occurs. The subgroup size is four.
(b) What proportion of nonconforming product results
from the shift described in part (a)? Assume a normal
distribution of this dimension.
(c) Calculate the process capability indices Cp and Cpk for
this process, and comment on their meaning relative to
parts (a) and (b).
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Number of defects
50
100
40
80
30
60
20
40
10
20
0
0
Cumulative percentage
Pareto Chart
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Pareto Chart
40
100
80
C
30
60
20
40
10
20
D
A
0
Cumulative percentage
Number of defects
50
B
0
Defect type
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Pareto Chart
40
100
80
C
30
60
20
40
10
20
D
A
0
Cumulative percentage
Number of defects
50
B
0
Defect type
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Cause and Effect Diagram
Measurement
Faulty testing equipment
Incorrect specifications
Improper methods
Inaccurate
temperature
control
Dust and Dirt
Environment
Men/Women
Machines
Out of adjustment
Poor supervision
Lack of concentration
Tooling problems
Inadequate training
Old / worn
Quality
Problem
Defective from vendor
Not to specifications
Materialhandling problems
Materials
Poor process design
Ineffective quality
management
Deficiencies
in product design
Methods
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Cause and Effect Diagram
• Common categories of problems in manufacturing
– 5 M’s and an E
• Machines, methods, materials, men/women,
measurement and environment
• Common categories of problems in service
– 3 P’s and an E
• Procedures, policies, people and equipment
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Reading and Exercises
• Chapter 9:
– pp. 324-330 (Section 9.2)
– 9.1, 9.5
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