033_Process Capability

Why Do We Need Process Capability?
REJECTREJECT ACCEPT
Voice of Process
Voice of Customer
Upper
Spec
Limit
Lower
Spec
Limit
REJECTREJECT ACCEPT
Voice of Process
Voice of Customer
Upper
Spec
Limit
Lower
Spec
Limit
Upper
Spec
Limit
Lower
Spec
Limit
REJECTREJECT ACCEPT
Voice of Process
Voice of Customer
Is the Process Capable of
meeting customer expectations?
Test by comparing Voice of
Process to Voice of Customer
Why Process Capability?
4
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7
Step 1: Select the process KPOV or Big “Y”.
Step 2: Validate the specification limits.
Step 3: Collect data and calculate the capability.
Step 4: Assess the process stability.
Step 5: Assess the data “Normality”.
Step 6: Calculate basic statistics (Xbar and σ).
Step 7: Calculate the Z scores and defect rates.
Step 8: Calculate Z bench.
Step 9: Shift data to account for short or long term.
Step 10: Draw conclusions. Is capability acceptable?
Step 11: Calculate capability indices (Cp, Cpk, Pp, Ppk).
Perform A Capability Analysis
- Variable Data -

10
Step 3: Collect data and calculate the capability
Knowing how many data points to collect is covered in more depth
in a later module. As a rule of thumb, collect 30 data points. As
this is only a guide, more data is better. Determine if the collected
data is short term or long term.
• Short term data is:
Free of assignable causes
Collected across a narrow inference space e.g. one shift, one
machine, one operator, etc.
• Long term data is
Subjected to the effects of both random and assignable cause
variation
Collected across a broad inference space i.e. multiple shifts,
machines, operators, etc..
Capability Analysis – Collect Data

13
Capability Analysis – Process Stability
Step 4: Assess the Process Stability
What you hope to see
What you don’t hope to see
All points are inside
the red lines
(Control Limits) –
the process is in
control, capability
estimates will be
valid

16
Capability Analysis – Basic Statistics
Step 6: Calculate basic statistics
Normally distributed data can be completely described by the
mean (µ) and standard deviation (σ )
Since we are interested in a portion of the area under the curve
we must have a way to find this area
22
2/)(
2
1
)( σµ
σπ
−−
= x
exf
x
Where:
e = 2.71828
π= 3.14159
X = point of interest
Available options:
Planimeter – high cost and low accuracy
Calculus – “impossible” math
Tables – impractical – need many, one for
each µ and σ combination

19
Suppose that after several months of collecting the delivery
service time to your customers, the sample resulted in a mean
Xbar = 25.188 minutes and a standard deviation S = .265
minutes. You would like to know the probability that your
delivery service time will be greater than 25.5 minutes.
First calculate Z = 25.5 - 25.188 = 1.1774
.265 .265
Using a cumulative Standard Normal Distribution table,
with Z = 1.1774, the table value yields 0.11952, which
means there is a 11.95% chance that your delivery service
time will exceed 25.5 minutes.
= 0.312
Z Transformation - Example
What is the probability that the delivery service time will
be less than 24.5? Treat 25.5 & 24.5 as spec limits

22
Standard Normal Table
Step 7 (Cont.): Calculate the Z scores and defect rates
• Find the defect rate in the table
using the Z Score = 1.177 ≈ 1.18:
The first two digits of the Z
Score are found on the left hand
side of the table (i.e. 1.18)
The last digit is found on the top
of the table (i.e.1.18)
• Defect rate = 0.1190 or 11.90%

Step 9: Shift data to account for short or long term
• If your data is long term (LT), short term can be
estimated as shown:
ZST = ZLT + 1.5
ZST = 1.155 + 1.5
ZST = 2.655
Capability Analysis - Example
No Action
No Action- 1.5
+ 1.5
Conversion of Z’s
From
To
Short-Term Long-Term
Long-Term
Short-Term
25

Capability Analysis – The Final Product
13.512.010.59.07.56.04.5
LSL USL
LSL 3.3
Target *
USL 13.1
Sample Mean 9.9184
Sample N 100
StDev (Within) 1.48912
StDev (O v erall) 1.53672
Process Data
Z.Bench 2.14
Z.LSL 4.44
Z.USL 2.14
C pk 0.71
Z.Bench 2.07
Z.LSL 4.31
Z.USL 2.07
Ppk 0.69
C pm *
O v erall C apability
Potential (Within) C apability
PPM < LSL 0.00
PPM > USL 0.00
PPM Total 0.00
O bserv ed Performance
PPM < LSL 4.40
PPM > USL 16316.92
PPM Total 16321.32
Exp. Within Performance
PPM < LSL 8.28
PPM > USL 19208.40
PPM Total 19216.68
Exp. O v erall Performance
Within
Overall
Process Capability of Size
191715131197531
12
11
10
9
8
Sample
SampleMean
__
X=9.918
UC L=12.020
LC L=7.817
191715131197531
8
6
4
2
0
Sample
SampleRange
_
R=3.643
UC L=7.703
LC L=0
Xbar-R Chart of Size
• Projects, such as those
with an objective to
reduce the number of
defects can be illustrated
using the traditional
capability analysis at the
left
• Projects focused on lead
time or cycle time
reduction might be better
illustrated using an SPC
chart at the right.
28

31
Capability Analysis – Collect Samples
Step 1: Collect samples.
• The purpose of the data collection is to review the number
of defects present within a group of expected acceptable
units.
• When dealing with attribute data, considerably more
samples are required than with variable data. Expect to
collect several hundred samples – and probably more.

34
Capability Analysis – Count the Defects
Step 4: Calculate the defect rate:
Proportion defective for Binomial data
Defects per Unit (DPU) for Poisson data
• Binomial data (e.g. Yes/No, Pass/Fail, On/Off):
187 failures / 3,000 samples = .0623
• Poisson data (e.g. Number of uncompleted calls in a call center
in 1 day)
DPU = 14 uncompleted calls out of 388 = 14/388 = .0361

Exercise
Step 1 Print the Helicopter Template and construct helicopter
Step 2 Drop the helicopter 25 times from a height of about 5 feet and record
the drop time
Step 3 Record the results in "ControlChart.xls" on the "IMR" tab
Step 4 Determine if the process is in control
Step 5 Check Data normality using 'Anderson Darling.xls'
Step 6 Record the results in "Process Capability.xlsx".
Step 7 Enter Upper Spec Limit (USL) = 1.5
Step 8 Enter Lower Spec Limit (USL) = 0.5
Step 9 Sub Group size = 1
Step 10 Determine Z, PPM & Cp
37

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033_Process Capability