The
Quality
Improvement
Model
Define
Process
Select
Measures
Collect &
Interpret
Data
Is Process Capable?
Purpose: Determine the adequacy
of the process with
respect to customer
/management needs.
Is
Process
Capable
?
Is
Process
Stable
?
No
Investigate &
Fix Special
Causes
Yes
Improve
Process
Capability
No
Is
Process
Capable
?
Yes
Use SPC to
Maintain
Current
Process
8-1
Is
Process
Capable
?
Capable Process
A stable process that meets customer requirements.
Histogram
Control Chart
UCL
CL
LCL
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
Run Order
Lower Spec
Target
Upper Spec
Capability assessments for unstable processes, may not be indicative of
how the process is actually performing.
8-2
Assessing Process Capability

Counting Measures



Is
Process
Capable
?
The average percent defectives.
The average number of defects.
Instrument Measures

Comparing both the center of the process and the process
variation
8-3
Capability Assessment for Counting Measures
“Order Entry Process”
Week # Errors
1
15
2
22
3
18
4
10
5
13
6
9
7
27
8
12
9
24
10
22
11
8
12
8
13
26
14
16
15
20
16
10
17
16
18
9
19
15
20
20
Total
320
Control Chart
35
30
Number
of Errors
Is
Process
Capable
?
UCL=28.0
25
20
Avg=16.0
15
10
5
0
LCL=4.0
5
10
15
20
Week
Is this process adequate as is?
Should it be improved?
8-4
Measures of Process Capability
USL - LSL
Cp = Specification Range =
6sc
True Process Range
Is
Process
Capable
?
Cp < 1.0  Process is not capable of meeting specs
Cp = 1.0  Process is marginally capable
Cp > 1.0  Process is capable of meeting specs
Problem: We are assuming the process has a target that is
in the center of the specification range, and that
the process is in fact centered on that target.
Distance from process average
specification limit = min (USL - x , x - LSL)
Cpk = to closest
1 True Process Range
3sc
2
Note: a negative result is possible if the process average is outside specifications
Cpk < 1.0  Process is not capable of meeting specs
Cpk = 1.0  Process is marginally capable
Cpk > 1.0  Process is capable of meeting specs
Benefits: • Optimal values are attained by running exactly
between specs.
• Can (must) be used for 1-sided specifications
Warning: Capability assessments for unstable processes, may not be
indicative of how the process is actually performing.
8-5
Is
Process
Capable
?
Process Capability
LSL
USL
How much material is out of spec?
 In the short term?

In the long term?
8-6
Is
Process
Capable
?
Process Capability Ratios
LSL
USL
Voice of The Process
Voice of The Customer
8-7
Is
Process
Capable
?
8-8
Process Capability - The Strategy
Is
Process
Capable
?
Centering –The Process Is On Target
Spread – Reduce The Variation
Defects
LSL
Defects
USL
8-9
Process Capability Ratios
Is
Process
Capable
?
2 Key Metrics for Measuring Capability
USL  LSL
Cp 
6sc
X- LSL USL- X
Cpk  Min(
,
)
3sc
3sc
8-10
Process Capability Ratios - Concept
Is
Process
Capable
?
USL  LSL
Cp 
6sc
Cp 
Total Tolerance
Process Spread
8-11
CP & CPK Measure Short-term
I Chart for C1
Capability 39
Is
Process
Capable
?
Is The Process
In Control ?
Is It Producing
Defects ?
Individual Value
3.0SL=37.36
34
X=30.60
29
24
-3.0SL=23.84
0
5
10
15
20
25
30
35
Observation Number
A Short-term Capability study covers a relatively
short period of time (days, weeks) generally
consisting of 30 to 50 data points. The actual
number depends on the subject under study.
8-12
Long Term Performance
I Chart for C3
Is
Process
Capable
?
50
Is The Process
In Control ?
Is It Producing
Defects ?
Individual Value
3.0SL=47.12
40
Short term
Capability
X=33.80
30
-3.0SL=20.49
20
0
50
100
Observation Number
A long-term capability study covers a relatively long
period of time (weeks, months) generally consisting of
100-200 data points. Again, the actual amount depends
on the subject under study.
8-13
A Further Look at Capability
Is
Process
Capable
?
Compare the estimates of the process deviations
from the short-term and long-term data
Descriptive Statistics
Variable
short term
long term
N
30
180
Mean
30.6
33.8
StdDev
2.23
4.44
What is the difference between the short-term and the
long-term data?
What implication does this have in doing capability
studies?
8-14
Measures of Process Performance
Pp =
Specification Range = USL - LSL
6ss
True Process Range
Is
Process
Capable
?
P p < 1.0  Process Performance is not meeting specs
P p = 1.0  Process Performance is marginally meeting specs
P p > 1.0  Process Performance is meeting specs
Problem: We are assuming the process has a target that is
in the center of the specification range, and that
the process is in fact centered on that target.
Distance from process average
to closest specification limit
min (USL - x , x - LSL)
P pk =
=
1
3ss
True Process Range
2
Note: a negative result is possible if the process average is outside specifications
Ppk < 1.0  Process Performance is not meeting specs
Ppk = 1.0  Process Performance is marginally meeting specs
Ppk > 1.0  Process Performance is meeting specs
Benefits: • Optimal values are attained by running exactly
between specs.
• Can (must) be used for 1-sided specifications
8-15
Performance vs. Capability
Is
Process
Capable
?
Days
Outstanding
55 Days
CO2Sales
Levels
for 55 Timefor
Points
14
DSO
CO2-Shrt
13
12
11
10
Index
10
20
30
40
50
These data show that the process, if well controlled can
perform much better than it currently is
8-16
Is
Process
Capable
?
Capability vs. Performance
Days
Outstanding
55 Days
CO2Sales
Levels
for 55 Timefor
Points
14
DSO
CO2-Shrt
13
12
11
10
Index
10
20
30
40
50
Capability: Only
random or short
term variability
Process Performance:
Total Variation including
shifts and drifts
(Cp & Cpk)
(Pp & Ppk)
8-17
Process Performance Ratios
P
p

Is
Process
Capable
?
USL  LSL
6ss
X- LSL USL- X
P pk  Min(
,
)
3ss
3ss
The P-family of indices are computationally the same as
the C-family of ‘capability’ indices, but use the observed
long-term standard deviation.
8-18
WARNING!!!
Is
Process
Capable
?
Statistical Assumptions Made In Capability Studies
1.
Data Comes From a Stable Process


If not, work towards getting the process in
control
Don’t despair, you can still make some
assumptions about your process in the mean
time
8-19