The document discusses process capability metrics, particularly focusing on six sigma quality control, the importance of measurement systems, and gage capability studies. It highlights the significance of measuring variations in manufacturing processes and utilizing statistical studies to assess and improve process capability. Additionally, it outlines specific metrics for evaluating process performance including potential process capability (Cp), process capability index (Cpk), and instability index (St).

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Table of Content
1. Introduction
2. Process Control flow chart
3. Measurement System Capability
4. Process Performance Metrics
5. Product/Process Improvement flow chart

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Nature of the Manufacturing Process
* Due to uncontrollable variations, the units produced are
different from the design target and from each other.
* The unit-to-unit variations usually follow a normal distribution
(Figure 1).
The standard deviation of the distribution, Sigma ( ), is a
measure of the amount of the variation.
Figure 1
Normal distribution of process variation is represented by a bell-shaped curve.
σ

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Traditional Process Capability
* Traditionally, a process was judged to be satisfactory with a 3 sigma
capability with centreline at target.
* For a 3 sigma process, 99.73 % units produced conform to
specification, 0.27% (2,700 ppm) out of specification (Figure 2).
* With 1.5 Process shift from target, only 93.32 % conform to spec
whereas 6.68% (66,800 ppm) out of specification (Figure 3).
Traditional 3 Sigma capability Three sigma capability process with a typical shift
Figure 2 Figure 3

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Six Sigma Capability
* With a six sigma process capability with centre at target, only 0.002
ppm defective units produced (Figure 4).
* In reality, very few processes are perfectly centered. Process shift of
# 1.5 sigma is typical. With six sigma process capability and 1.5
process shift, only 3.4 ppm defective units produced (figure 5).
# Refer to Benda. (1975) !tatistical Tolerancing as it Relate Quality Control and the Designer?Automotive Division Newsletter
Evans, David H. (1975) !tatistical tolerancing : The State of the Art, Part II : Methods for Estimating Moment
A centered 6 sigma process. A 6 sigma process with typical 1.5 sigma shift
Figure 4 Figure 5

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Six Sigma & Beyond ....
* When six sigma goal is reached, room for improvement still remains
for achievement of Total Customer Satisfaction.
* Motorola continues striving for 10-fold reduction in defects every two
years with quality goal set beyond the six sigma.
* The unit for quality measurement is defined at kppb level.
* To archive this level of performance, we have to strive for a centered
process and minimise process variation. With a centered & six sigma
process, only 2 ppb defects appear.

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JAD000502
Summary of Process Control Chart
Evaluate
Metrology
MSA
OK?
Test process
stability
Process
Stable?
Collect
Enough data
Normal
Distribution?
Calculate Cp/Cpk
Cp/Cpk
OK?
Review
Control Limits
Continuous
Improvement
Reduce
Variation
Stabilize
process
Transform
data
Optimize
Process
Y
N
YN
N
Y
Y
N
N

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Measurement System Capability
* The capability of the measurement system must be ensured
before the system is used for process control or process
capability study.
* A measurement system consists of a gage, the people who use
it, the techniques, procedures, etc..
* A measuring system must be assessed using appropriate
statistical studies for Accuracy, Stability, Linearity,
Repeatability & Reproducibility. The studies should be
repeated periodically. Local organizations should
establish time guidelines for repeating these studies.

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Why Gage Capability is important
* The Process Variation, SigmaTotal,
actually combined of two components : the process variation itself
and the gage variation :
* Suppose we have a centered process (Cp = Cpk) which has an
allowable tolerance of +/- 10. The gage variation is 2.5.
Suppose the Process Variation is zero (an impossibility).
For this process, Cpk will never exceed 1.33 because of gage variation.
222
GageprocessTotal SigmaSigmaSigma +=
22
0 GageTotal SigmaSigma +=
33.1
5.26
20
6 2
=
×
=
×
==
Total
ppk
Sigma
Spec
CC

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Gage Repeatability & Reproducibility (R&R) Studies
* A typical gage R&R study is done using three different operators
measuring the same set of 10 parts.
* The study will result in two components : variation due to
instrument (repeatability) and variation due to the operators
(reproducibility).
* The two components are combined into one single R&R number.
* The R&R number then is compared with either the process
variation (5.15 Sigma) or allowable tolerance. The results is a
gage R&R Percentage (%R&R).

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* Traditionally, the gage error was compared with the part tolerance
to estimate the %R&R resulting in P/T ratio. This practice is no
longer recommended as our interest is to find out a gage is
capable characteristic which has its own uniquely variability.
Precision-to-Tolerance Ratio (P/T Ratio)
* With Motorola Six Sigma program, an otherwise capable gage as
determined by a small P/T ratio may not be capable for a process
with small process variability.
* For the purpose of calculating the gage %R&R, the process
variability is defined as 5.15 sigmas. (Number chosen by #AIAG
while developing GR&R study. 5.15 sigma represents 99% area
under normal curve)
%R&R
R&R x 100
Process Variability
= =
R&R x 100
5.15 sigma
# : Automotive Industrial Action Group

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GAGE CAPABILITY & REPRODUCIBILITY STUDY
GAGE TYPE : IQ1500 TV USED : UCL represents the limit of
PART MEASURED : 17CSH00768A COMBINED R&R AND PV individual R's. Circle those
CHARACTERISTIC : DIMENSION (DOWNSET DEPTH) PROCESS 5.15 SIGMA ranges that are beyond this
SPEC : 0.16 - 0.26 UNIT : MM X PART'S TOLERANCE limit. Identify the cause and
1 2 3 4 5 6 7 8 9 10 AVG AVERAGE /R = (/RA+/RB+/RC) correct. Repeat those
1 0.183 0.190 0.188 0.202 0.195 0.194 0.201 0.194 0.201 0.184 0.193 /X(diff) = /X(max) no. of operators readings using the same
Operator 2 0.180 0.195 0.196 0.201 0.197 0.197 0.205 0.192 0.205 0.186 0.195 /XA = - /X(min) = 0.003 operator and units as originally
A 3 0.185 0.190 0.187 0.203 0.199 0.198 0.204 0.194 0.205 0.184 0.195 0.195 = 0.000 UCLR = /R * D4 used or discard those readings
R 0.005 0.005 0.009 0.002 0.004 0.004 0.004 0.002 0.004 0.002 /RA = 0.004 = 0.008 and reaverage and recompute
1 0.180 0.195 0.185 0.201 0.194 0.194 0.204 0.194 0.204 0.184 0.194 # TRIALS D4 K1 OPERATORS K2 ranges and UCL from the
Operator 2 0.185 0.193 0.185 0.204 0.196 0.196 0.206 0.196 0.206 0.186 0.195 /XB = 2 3.27 4.56 2 3.65 remaining readings.
B 3 0.185 0.195 0.184 0.205 0.195 0.194 0.204 0.195 0.205 0.185 0.195 0.195 3 2.56 3.05 3 2.7
R 0.005 0.002 0.001 0.004 0.002 0.002 0.002 0.002 0.002 0.002 /RB = 0.002 PARTS 2 3 4 5 6 7 8 9 10
1 0.183 0.195 0.187 0.210 0.196 0.195 0.201 0.192 0.205 0.185 0.195
Operator 2 0.180 0.190 0.185 0.205 0.192 0.198 0.204 0.193 0.204 0.185 0.194 /XC = K3 3.65 2.70 2.30 2.08 1.93 1.82 1.74 1.67 1.62
C 3 0.184 0.192 0.183 0.204 0.195 0.194 0.204 0.192 0.204 0.184 0.194 0.194
R 0.004 0.005 0.004 0.006 0.004 0.004 0.003 0.001 0.001 0.001 /RC = 0.003n = number of parts =10 r = number of trials = 3
tot. readngs 1.645 1.735 1.680 1.835 1.759 1.760 1.833 1.742 1.839 1.663 AV DEFAULTS TO ZERO IF A NEGATIVE IS no. of operators = 3
Avg /Xp 0.183 0.193 0.187 0.204 0.195 0.196 0.204 0.194 0.204 0.185 RangeRp = 0.022CALCULATED UNDER THE SQUARE ROOT SIGN
REPEATABILITY (EV) REPRODUCIBILITY (AV) COMBINED R & R PART VARIATION (PV) TOTAL VARIATION (TV)
ANALYSIS EV = /R * K1 AV = SQRT((X(diff)*K2)^2- R&R = SQRT(EV^2 PV = Rp * K3 TV = SQRT(R&R^2 + PV^2) =
(EV^2/(n*r))) +AV^2) OR
TV = 5.15 * PROCESS
EV = 0.010 AV = 0.000 R&R = 0.010 PV = 0.035 STD. DEVIATION =
OR
% PROCESS %EV = 100(EV /TV) %AV = 100(AV / TV) %R&R = 100(R&R/TV) %PV = 100*(PV/TV) TV = PART's TOLERANCE = 0.100
VARIATION
%EV = 9.963% %AV = 0.000% %R&R = 0.100 %PV = 34.92% TV = 0.100
P/T Ratio = 100%*(R&R)/Tolerance =N/A
Figure 6. Typical example of GR&R report

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Under 10% Measuring system is acceptable
10% - 30 % May be acceptable based upon the important of the
applicable, cost of gage, cost of repair or other
consideration.
Over 30% Error is not acceptable; make every effort to identify
the measurement problem and get it impoved. In any
case, run another GR&R study after improving of the
problem to see if the %R&R will go down to the
acceptable level before releasing to use.
Gage R&R and P/T ratio Acceptance Guidelines

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Gage Calibration Interval Determination
* Gage calibration interval must be determined by appropriate technique.
* If arbitrarily chosen, the intervals might be too frequent (waste resources)
or too far apart (risk of using inaccurate gage).
* For these reasons, gage calibration intervals should be carefully
determined. Either an algorithmic method or a statistical method
should be employed to establish and adjust the gage calibration
intervals, to minimize the risk and optimize resources.

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PROCESS PERFORMANCE METRICS
There are three valuable metrics that must be used to measure the
performance of all significant processes :
(1) Potential Process Capability (Cp)
(2) Process Capability Index (Cpk)
(3) Instability Index (St)
(1) and (2) are used to assess process capability and (3) is used
to determine the stability of a process.

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Potential Process Capability Index (Cp)
Cp index is defined as the ratio of specification width over the process spread.
Sigma6
LSL-USL
SpreadProcess
WidthSpec.
×
==pC
Figure 13. Potential Capability Index Cp

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Process Capability Index (Cpk)
Cpk is the index to measure this real capability when the off-target penalty is
taken into consideration.
The penalty, or correction factor, k is defined as :
and the Process Capability index is defined as :
Cpk = Cp ( 1 - k )
When the process is perfectly on target :
k = 0 and Cpk = Cp
Figure 14. Capability Index Cpk
k = −−−−−−−−−−−−−−−−−−
Target - Process Mean
1/2 (Spec. Width)

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In the following cases :
--- When the target is not specified
--- When the target is in the middle of two specification limits
--- When there is a one-sided spec. limit.
Cpk may be more conveniently calculated as :
Cpk =
Mean - closer Spec. Limit
---------------------------------
3 sigma
Note : This formula cannot be used when the specified target is not in the
center of the two specification limits.

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Use of Cp and Cpk
Cp and Cpk are used to determine the capability of a process.
Cp, when shown together with Cpk, gives a quick estimate of how far
the actual process is from its target, thus how much work is needed to
bring the process to its potential.
Cpk and process stability :
Cpk is a meaningful measure of process capability only when a
process is in statistical control.
Cpk and normality of data :
Because of the definition of Cp and Cpk are for normal distribution,
the data to be used for Cp and Cpk calculation should be tested
for normality.
Cpk for a non-normal distribution :
Generally, there are three techniques which can be conveniently used
for non-normal distributions :
1) Transform the data into a normal distribution.
2) The non-normal data may be fitted using an empirical model.
3) Using the conventional method.

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Instability Index (St)
Instability index, or St, provides a means of estimating whether assignable
causes are present in the process.
The instability index St is calculated as :
St =
Number of out-of-control data points
Total number of data points
---------------------------------------------- x 100 %
If all data points are in control, St will be zero.
If all of the points are out of control, St will be 100 %
The instability index is correctly interpreted as the percent instability
present in the process.

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Cp = 2.0
Cp does not effect the process capability, need to
check the Cp and Cpk simultaneous!
Cpk = 1.0 Cpk = 2.0 Cpk = 1.0
LSL TARGET USL

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Cp = 1.5
Cp = 3.0
Cp = 2.0
Cp = 6.0
LSL USLTARGET
Cpk = 1.5
Cpk does not effect the process capability too, need to
Check the Cp and Cpk simultaneous!

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Cp
0.5
1.0
2.0
10
Process capability - Cp and Cpk
LSL=40 USL = 100Tbar = 70
ST = 20
ST = 10
ST = 5
ST = 1
Approx Fallout
1%
Approx Fallout
0.00000018%
Approx Fallout
13.4%
Approx Fallout
0.00000000%
Cpk
0.5
1.0
2.0
10

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1. Reason 3. Understand & confirm losses
4. Prioritize problems
6. Evaluation & Analysis
5. Implementation Plan
7. Corrective Actions 8. Confirm Effects
9.Institutionalization10. Future Plans
?
• Clearly explain the reason why
the team was formed
• State the critical business issue
confronting them and the
opportunities
Overall Loss
1st level
Losses Structure
3rd level
Pareto of loss
2nd level
Loss Trend A
Loss Trend B
A. Unit stuck at input track
B. Unit drop at sort shuttle
C. Contactor finger broken
No. Activities
1.
2.
3.
4.
AM1- Clean & restore
AM2- C/measures
AM3- Estb. Stds.
Problem analysis
Timeline
Why 1 Why 2
Phenomenon
Why 3
• Understand problem and have full grasp
of facts & phenomenon
• Always check for logical correctness of
each Why
• Continue Why until it leads to solution
• Verify all factors by thinking in reverse
Training Plans
Standard
Revision
One
Point
Lesson
PM
Chk.list
No. Action Items Resp. Date Status
1.
2.
3.
Action Item A
Action Item B
Action Item C
X
Y
Z
Action Followup
1/1
2/2
3/3
Time
L
o
s
s
e
s
Action Item A
Action Item B
Action Item C
Improve Machine # 1 and carryout
horizontal expansion to all machine
M/c # 1 ...................... ww10
M/c # 2 ...................... ww15
M/c # 3 ...................... ww18
M/c # 4....................... ww21
Done
Done
Troubleshooting
Guide
• Establish baseline and set
targets
BM
SMART
Goals
2. Target
Product/Process Improvement Flow Chart

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Project Selection1a
Step
Define clearly the Reason for this team to be formed.
State the critical business issue confronting the team and the
opportunities
Selection should be based on any of the following issues below:
1. Bottlenecks /Capacity 4. Delivery
2. Quality 5. Productivity
3. Yield Issues 6. Cost
Tools :
Pareto Analysis Benchmarking
Quality/RMA reportsYield reports
8-D report Failure Analysis reports

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REASON1b
Step
CAPACITY CONSTRAINT
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
July Aug Sept Oct Nov Dec
MONTH
TESTER
Capacity
Available
J971 TOP PRODUCT
360EM
43%
860ZP
26%
850ZT
10%
5244PV
9%
060RC
6%
823ZT/ZC
5%
5206FT
1%
DELINQUENCY IN DOLLAR
68360
27%
68302
24%
860/821
20%
EN302
11%
LC302
6%
850/801
5%
68606
3%
FDDI
2%
Limited
Capacity
UTS handler
Our
MainTarget
Top Product
Highest Delinquency
SAM
PLE

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REASON1b
Step
Limited Capacity
Top Product
Highest Delinquency
UTS handler was taken as our main
focus of attention due to :
SAM
PLE

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Name of Team : ...................................
Operation : ...................................
Equipment or : ................................…
Process
Team Leader : ...............................….
Secretary : ...................................
Members:………………………………..
........................................…..
..............................................
..............................................
.........................................….
..................................………. Meeting Schedule :
…………………. ............................…………... Meeting
Place: ...............................
.............................................. Meeting Time : ...............................
…...................................…… Duration : ...............................
………………………………...
Team Formation1c
Step

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Members Name
Workweek
10
20
30
40
50
60
70
80
90
100
PERCENTAGE
WORKWEEK
5 10 15 20 25 30
Team Name:
Dept :
Legend : P (Present) X (Absent) A (Annual Leave) MC (Medical leave) T (Training) H (Holiday)
Team Attendance Chart1d
Step

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Target2a
Step
S pecific : ........................
M easurable : ........................
A chievable : ........................
R ewarding : ........................
T imebased : ........................
Select Model Machine and start data collection to
identify the 8 Major Losses.
Review data collection over two weeks period.
Establish Baseline of selected equipment
Set S.M.A.R.T. goal

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2b
Step
Target
To Improve the Utilization of the ADV
Tester System (T33xx) for the
AZ/AB series product family
from 52% to 60 % by Sep’99
&
from 60% to 65% by Dec’99
SAM
PLE

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3a
Step
Understand and Confirm Losses
Overall Loss
(1st level )
Losses Structure
(3rd level)
Pareto of loss
(2nd level)
Loss Trend A
Loss Trend B
Team identify the overall loss structure and pareto the loss to determine the top
2 or 3 issues that need to be worked on.

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Breakdown ofV/M Yield loss
0
10
20
30
40
50
60
70
80
90
100
C
oplanarity
M
eas
E
rror
B
entLead
B
ow
M
ark
P
itch
Yield(%)
COPLANARITY SHIFT ANALYSIS ON BINNER
0
0.05
0.1
0.15
0.2
0.25
From
binner
to metal
rail
From
binner
to
plastic
From
Flipper
to
Binner
COPLASHIFT(mils)
COPLANARITY SHIFT ANALYSIS ON S400-13
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
BINNER LOADER STORAGE TEST TRACK
COPLASHIFT(mils)
Coplanarity Mapping
(% of leads with copla >3.0 mils)
10
61
60
9
44
43 27
26
5%5%
30%
15%
5%5%
15%
20%
1
side 2
side 3
side 4
3a
Step
Understand and Confirm Losses
SAM
PLE

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4a
Step
Prioritize Problems
Input Track jam
Core pickup
Setup Time
1
2
3
SAM
PLE

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5a
Step
Implementation Plan
Setup a milestone chart to determine the period required to do Autonomous Maintenance
Step 1 to 3 followed by the problem analysis as described in the prioritized list in step 4
Timeline
Activities 20 21 22 23 24 25 26 27 28 29 30
AM Step 1 - Clean, Tag & Restore
AM Step 2 - Countermeasures
AM Step 3 - AM Standards
Problem Analysis
Input Track
Core Pickup
Setup Time Reduction
Plan
Actual
SAM
PLE

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Analysis Tools
Why-Why P-M Fault Tree
Evaluation And
Analysis
6a
Step
Understand problem and have full grasp of facts & phenomenon
Apply any of the following techniques such as Fault Tree, Why-
Why, P-M, FMEA...
Always check for logical correctness of each Why
Continue Why until it leads to solution
Verify all factors by checking the “why” in reverse
IMPORTANT IS
Genba & Genbutsu

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Pusher cylinder limit
sensor not set properly
Pusher cylinder
jammed
Pusher did not push
at right position
Clamp motor jammed
Clamp bearing jammed
Bent frame
Magazine to track
out of alignment
Pusher bent
Pusher thickness
not appropriate
Magazine not sitting
properly on elevator
Elevator not moving
smoothly
T/F operator handling
From previous processes
Straighten pusher
Modify pusher
plate to 5mm thick
Perform strip check
thoroughly
Why-Why Analysis
Infeed Error
( Leadframe did
not reach S13 )
Infeed Pusher Leadframe
Pusher not hitting at
the right position
Pusher bent and not
at right angle <90‘
Pusher modified thicker
with concave tip. Misfeed solved
Phenomenon Countermeasure
NG
NG
NG
NG
OK
OK
OK
OK
OK
OK
OK
NG
Why 1 Why2
SAM
PLEEvaluation And
Analysis
6
Step

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Step 0: Select Improvement Topic
P-M Analysis Flow
Achieving Zero Defect by Eliminating Chronic Losses using P-M Analysis
Chronic loss1 %
A B C D
0
20
40
60
80
100
A B C D
A B C D
0
40
80
A B C D
P-M
Analysis
Item “B”
Improvement
Reduced to
ZERO
Prioritize problems
by defect type.
Item “A” Improvement
P-M Analysis
Chronic loss1 %
“A” Improvement
“B” Improvement
“C”
Improvement
Evaluation And
Analysis
6
Step

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Step 4: Plan Improvement
CUSTOMER: OPERATION: KLM ATTENDEES:
SUBJ: DATE:
ACTION RESPONSIBLE DATE STATUS
ACTION COORDINATOR:
INFO COPY:
STATUS UPDATE BY: FOLLOW-UP MEETING:
ACTION FOLLOW -UP
Corrective Actions7
Step

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Step 5: Implement ImprovementConfirm Effects8
Step
Verify that the actions taken as a result of the countermeasures from the analysis
corresponds to the improvement made as shown in the graph.
Input Quad Head Motor Jam Statistic
-15
-10
-5
0
5
10
15
20
25
30
35
40
45
50
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
01'99
02'99
03'99
04'99
05'99
06'99
07'99
08'99
09'99
10'99
11'99
12'99
13'99
14'99
15'99
16'99
17'99
18'99
WorkWeek
Jams
ReDesign
Input nest
Reduced Input ATU
Elevator speed Redesign Input
Elevator Catch
with additional 1mm
* Performed Full X-Y alignment
* Applied Screw Loctite on X-Y
Tensioning screw
* Lowering Z-pick up head
123 Goal = '0' jam
One major loss
eliminated !
SAM
PLE

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Institutionalization9
Step
One
Point
Lessons
Trouble-
shooting
guide
No. Activities
1.
2.
3.
4.
Timeline
Training plans
PM Checklist
PM Checklist
Use OPL’s to train and educate all
personnel
Modification or Changes in
design should be incorporated
into the Preventive Maintenance
checklist
Create step by step trouble- shooting
guide for tech’s and operators to
reduce MTTR(mean time to repair)
Provide training to all to
enhance knowledge and
skills

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Future Plans10
Step
Improve Machine # 1 and carryout horizontal expansion to all machine
Fan out item Completion date Machine No.
UTS1 UTS2 UTS3 UTS4 UTS5 UTS6 UTS7 UTS8 UTS9 UTS10UTS11
1. N2 Purge ring WW 10
2. LN2 cover WW21
3. Gauge Indicator WW18
4. Temper proof sticker WW18
5. Tray hole cover WW20
6. Greasing on Pusher Assy. WW26
7. Screw loctite for critical alignment WW27
8. Magnetic clip on core cover WW27
9. Handle for Input cover WW27
10. Input elevator catch WW12
11. Scrap container WW14
12. Ventilation fan ribbon WW16
SAM
PLE

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TPM Manager Model - Fan out
Activities Date Ase#15Ase#7 Ase#13Ase#4 Ase#8 Ase#17Ase#9 Ase#3 Ase#14Ase#6
1Venturi Vacuum System WW34
2Repainting of machine coversWW30
3Magnetic latch on all covers WW30
4Add filter under card cage WW15
5Frost free LN2 piping WW35
6Complete rewiring of machine wiring WW28
7Floor hole cover WW30
8Tube height guide scale coverWW25
9Binner station hole cover WW25
# Andon light wiring rewiring WW18
# Arrow marks on gauges and flow meters WW24
# Fan status indicator ( Ribbon )WW24
# Spring washer on chamber trackWW24
# Input entrance track cover WW30
# Rubber mat on manipulator WW26
# Fixing fuguai's WW30
Future Plans10
Step SAM
PLE

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Your team has breakthrough and achieved your improvement topic.
Celebrate your team success.
Congratulations !
Select Next
Improvement
Review latest losses structure.
Select next improvement topic.
Repeat improvement cycle.

44. www.smthelp.com
Welcome inquiry
1,Please visit : www.smthelp.com
2, Find us more: https://www.facebook.com/autoinsertion
3, Know more our team: https://cn.linkedin.com/in/smtsupplier
4, Welcome to our factory in Shenzhen China
5, Look at machine running video: https://www.youtube.com/jasonwuSMT
6, See more in Google: Auto+Insertion