Process Capability Studies
Comparison of Process Output to
Product Requirements
Lynn Taylor – OISM 470W Section 002
Process Capability Studies
3 Steps
• Gauge Capability
• Process Characteristics
– Stability
– Normality
– Control
• Process Capability Analysis
– Comparison of process output(s) to
requirements.
Process Capability Studies
Definitions
• Process – Work performed on a set of inputs
to produce a result.
• Capability – The predictable result(s) of a
process allowed to operate without outside
interference.
• Process Capability Study – Comparison of
process output(s) to product requirements.
Process Capability Studies
Uses In Our Plant
•
•
•
•
Customer 1 < 407, Cpk > 1.25
Customer 1 > 407, Cpk > 1.50
Customer 2, Cpk > 1.33
With new clients, determine if tolerances
are reasonable, if our processes are capable
and robust, and if improvements are needed.
Process Capability Studies
Step 1 – Gauge Capability
Six Measures
• Gauge Accuracy
– Are the readings correct?
• Gauge Linearity
– Are the readings correct over the measurement
range of the instrument?
• Gauge Stability
– Does the gauge return similar values over time?
Process Capability Studies
Step 1 – Gauge Capability
Six Measures
• Gauge Repeatability
– Does one operator return a similar result time after
time (gauge variability)?
• Gauge Reproducibility
– Do different operators return similar results?
• Gauge Repeatability and Reproducibility
– Total variability of a test result (operator &
gauge).
Process Capability Studies
Step 2 – Process Characteristics
Analyze Process Data
• Normality – Evidenced by the descriptive
statistics skewness and kurtosis.
• Stability – The absence of shifts or trends
over time.
• Control – Control chart analysis passing
tests for special causes.
Process Capability Studies
Tests for Normality
Process Capability Studies
Tests for Stability and Control
Process Capability Studies
Comparing Distributions to Specifications
Process Capability Studies
Real World Example – Part 504
Process Capability Studies
Part 504 Continued
Process Capability Studies
Part 504 Continued
Process Capability Studies
Part 613 - An Exercise
0.1083
0.10819
0.10827
0.10817
0.10816
0.1081
0.10817
0.10801
0.10778
0.10784
0.10789
0.10835
0.10836
0.10809
0.10841
0.10807
0.10802
0.10794
0.10802
0.10843
0.10837
0.10846
0.10811
0.10834
0.1084
0.10838
0.10836
0.10835
0.10822
0.10827
0.10833
0.10799
0.1082
0.10817
0.10833
0.10824
0.10822
0.10812
0.10811
0.10813
0.10785
0.10809
0.10811
0.10822
0.10811
0.10828
0.10796
0.10832
0.10794
0.10838
0.10797
0.1078
0.10803
0.10819
0.10814
0.10794
0.10819
0.10808
0.10793
0.10819
0.10822
0.10824
0.10807
0.10811
0.10826
0.10803
0.10817
0.10794
0.10815
0.10805
0.10815
0.10794
0.10816
0.10802
0.10797
0.10833
0.10826
0.10844
0.10813
0.10828
0.10814
0.10816
0.10817
0.1081
0.1081
0.10837
0.10815
0.10839
0.10813
0.1082
0.10802
0.10849
0.10798
0.10833
0.10799
0.10818
0.10809
0.10856
0.10846
0.10804
Process Capability Studies
Part 613 – An Exercise
0.110 Diameter Part 613
35
Descriptive Statistics
30
Mean
0.1081636
Standard Error
1.64535E-05
Median
0.10816
Mode
0.10817
Standard Deviation 0.000164535
Sample Variance
2.70718E-08
Kurtosis
3.411886124
Skewness
0.017494357
Range
0.00078
Minimum
0.10778
Maximum
0.10856
Sum
10.81636
Count
100
Frequency
25
20
15
10
5
0
77 078 079 108 081 082 083 084 085 086 ore
0
1
1
1
M
0. 0.1 0.1 0.1 0.1 0.1 0.1
0.
0.
0.
dia - in.
Max Kurtosis
Max Skewness
4.49
0.745
Process Capability Studies
Part 613 – An Exercise
in.
Xbar Chart .110 dia Part 613- n=4
0.1085
0.1084
0.1083
0.1082
0.1081
0.108
0.1079
0.1078
0.1077
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
UCLXbar
Xbarbar
Observation #
Xbar
LCLXbar
R Chart .110 Dia Part 613
n=4
0.0008
0.0004
0.0002
R
LCLR
Observation #
25
23
21
19
17
15
13
11
9
7
5
0
3
UCLR
Rbar
1
in.
0.0006
Process Capability Studies
Part 613 – An Exercise
And the answer is:
Descriptive Statistics
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
0.1081636
1.64535E-05
0.10816
0.10817
0.000164535
2.70718E-08
3.411886124
0.017494357
0.00078
0.10778
0.10856
10.81636
100
LSL =
USL =
Cp =
CpL =
CpU =
Cpk =
0.105
0.115
10.1
6.4
13.8
6.4
Process Capability Studies
Summation
Three Steps:
• Gauge Capability
• Process Characteristics
• Process Capability Analysis
Process Capability Studies
Bibliography
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Introduction to Statistical Analysis – sixth ed – Dixon and Massey
Introductory Statistics – Weiss and Hassett, 1982
AT&T Statistical Quality Control Handbook – 11th Printing – 1985
Experimental Statistics – Mary G. Natrella – 1966 (NBS Handbook 91)
General Motors Statistical Quality Control Handbook – 1982
LTV Steel Integrated Process Control Handbook – Norman Bresky and
Joan Harley – 1986
• North American Refractories Co. SPC Handbook – 1988
• 1994 Annual ASTM Book of Standards- ASTM E 691 - 92