Machine/Process Capability Study

- A Five Stage Methodology For

Characterizing Processes -

Mario Perez-Wilson
President
Advanced Systems Consultants

v
 "Machine/Process Capability Study"
For books, software, public seminars,
in-house training seminars, and
consulting services

please contacts:

Advanced Systems Consultants

Post Office Box 5257
Scottsdale, Arizona 85261
U.S.A.

Phone: (480) 423-0081

www.mpcps.com

MACHINE/PROCESS CAPABILITY STUDY

First Published 1989

Second Edition 1994
Third Edition 1999
Fourth Edition 2004
Fifth Edition 2012
Sixth Edition 2014

Copyright © 1989-2014, by Mario Perez-Wilson.

All Rights Reserved.
No part of this publication may be reproduced or transmitted in any form or by any means,
electronic or mechanical, including photocopy, recording, or any information storage and
retrieval system, without permission in writing from Advanced Systems Consultants.

Current Printing (last digit)

20 19 18 17 16 15 14 13 12

PRINTED IN THE UNITED STATES OF AMERICA

ISBN 1-883237-10-6

vi
 M/PCpS™

Table of Contents

FOREWORD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

Section 1
Definition of a Process .................................1
Definition of Capability ................................1
Definition of Process Capability ..........................1
Definition of Machine/Process Capability Study ..............3
The Capability of the Parts Makes the Capability of the
Whole ...........................................6
Strategy for Implementing a Machine/Process Capability
Study Program .......................................7
Rank Order the Sub-processes and Machines . . . . . . . . . . . . . . . . . . . . 8
M/PCpS Teams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
M/PCpS Coordinator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Important Roles of Team Members . . . . . . . . . . . . . . . . . . . . . . . . 11
Pareto Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Stages of the Machine/Process Capability Study Methodology . . . . . 27

Section 2
1st Stage: Process Delineation - Machine Definition
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Types of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Scales of Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Cause and Effect Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Brainstorming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Four Steps for Machine Definition . . . . . . . . . . . . . . . . . . . . . . . . 39

Section 3
1st Stage: Process Delineation - Sub-Process Definition
Four Steps for Sub-Process Definition . . . . . . . . . . . . . . . . . . . . 51

Section 4
2nd Stage: Metrology Characterization - Measurement
Definition
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Four Steps for Measurement Definition . . . . . . . . . . . . . . . . . . . . 63

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson xi P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 M/PCpS™

Table of Contents continuation

Section 5
2nd Stage: Metrology Characterization - Gauge Capability
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Precision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Repeatability and Reproducibility . . . . . . . . . . . . . . . . . . . . . . . . . 80
Six Steps for Gauge Capability . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Section 6
3rd Stage: Capability Determination - Machine Definition
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Frequency Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Measures of Central Tendency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Measures of Spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Measures of Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Percentiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
The Ogive Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Standard Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Machine and Process Potential, Cp . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Machine and Process Capability, Cpk . . . . . . . . . . . . . . . . . . . . . . . 118
Short and Long Term Capability Studies . . . . . . . . . . . . . . . . . . . . . . 121
Ten Steps for Machine Capability . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

Section 7
4th Stage: Optimization - Reduction of Variability
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Experimentation - An iterative process . . . . . . . . . . . . . . . . . . . . . . . 183
Factorial Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
Experimental Design Funnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Multi-Vari Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
Ten Steps for Reduction of Variability . . . . . . . . . . . . . . . . . . . . . 191

Section 8
5th Stage: Control - Preventive Control
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Control Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
PosiTrol Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
Five Steps for Preventive Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson xii P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 M/PCpS™

Table of Contents continuation

Section 9
Standard Worksheets and Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

Section 10
Example
"Guggenheim" Wafer Back Sizing . . . . . . . . . . . . . . . . . . . . . . . . 272
Plasma Etch Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
Flowchart of the Machine/Process Capability Study
Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
Six Sigma or + Six Sigma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
Likert Scale for PWB Solder Deposition . . . . . . . . . . . . . . . . . . . . 316
Nonparametric Statistical Tests . . . . . . . . . . . . . . . . . . . . . . . . . . 317
Relationship Between the Range Average and Sigma . . . . . . . . . . . 318
Charting the Range against the UCL for the Range . . . . . . . . . . . . 321
Transforming from the Normal Distribution to a Standard
Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322
Fitting a Continuous Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
Possibilities of M/PCpS at the end of the Capability
Determination Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324
Objective of an M/PCpS Study . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
Cumulative Normal Distribution Table . . . . . . . . . . . . . . . . . . . . . . 326
Unilateral Normal Distribution Table . . . . . . . . . . . . . . . . . . . . . . . . 327
Minitab Instructions for the Capability Determination Stage . . . . . 329
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
About the Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
Comments from Our Customers . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
Letters: Motorola - Six Sigma . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354
Order Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson xiii P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 M/PCpS™

Foreword

In recent years, American industry has made some progress in product design through
techniques such as the design of experiments. Products have been made more
"robust" against "noise" and environmental factors through parameter design and
tolerance design. Yet, the process that produces the product is often treated as a
stepchild. Development engineers do not feel responsible for the process. They
relegate that to the process engineer, who, in turn, is heavily dependent on the supplier
of the equipment used in the process. And all of them use arbitrary process
specifications, antiquated procedures and hit-and-miss experiences in determining
process parameters. The result is confusion, finger-pointing, low yields and the high
cost of poor quality.

A cooking analogy can be used to describe the chaos in production processes. The
task is to bake a cake. But imagine the quality of the cake if the cook had no recipe,
no knowledge of the ingredients or their respective quantities! Yet industry moves
along blithely with little knowledge of which are the important process variables that
must be tighly controlled and which are the unimportant variables where costs can be
substantially reduced. In short, poor process characterization and optimization are of
epidemic proportions in industry.

To this pall of darkness, Mario Perez-Wilson, with his book on "Machine/Process

Capability Study," brings a beacon of light. He carefully orchestrates a step-by-step
methodology--process delineation; metrology characterization; process capability
determination; optimization; and control. It is a landmark book that fills a gaping void
in manufacturing. He utilizes a series of powerful problem-solving tools, spanning
different approaches to the design of experiments. He captures the techniques of
repeatability and reproducibility in order to assure the accuracy and capability of
instrumentation. He marshals the disciplines of statistical experimentation and
evolutionary optimization. And he is able to weave these separate and independent
strands into a robust cloth that can be used by the novice and the veteran, by the line
worker and the professional, by individual contributors and managers.

American industry will do well to pay particular heed to Mario Perez-Wilson's

"recipe" in its quest to restore its manufacturing leadership in the world.

Keki R. Bhote
Senior Corporate Consultant
Quality and Productivity Improvement
Motorola Inc.

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson xv P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 M/PCpS™

Preface

The purpose of this book is to serve as a single source of reference to those

individuals who are involved in the implementation of statistical methods
(Statistical Process Control, and Design of Experiments) in manufacturing. It
presents a standard methodology for conducting machine and process capability
studies. The methodology has been designed to prove industry with a standard
approach for studying processes, and enable them to produce within
specifications.

The Machine/Process Capability Study methodology, M/PCpS, presents the

steps necessary to achieve process capability in sequential order. It is divided
into five progressive stages: 1) Process Delineation, 2) Metrology
Characterization, 3) Capability Determination, 4) Optimization, and 5) Control.
Prior to introducing each stage, necessary background information is presented.
This information usually consists of problem solving tools and/or statistical
techniques. Each stage is then thoroughly explained and broken down into
further steps. Each step is then defined and described in detail using a "real
world" manufacturing process example.

An attempt was made to illustrate the complete methodology using the same
manufacturing process example. However, to simplify the explanation of
certain steps a different manufacturing process was utilized. The
manufacturing process operation selected to demonstrate the methodology is
the Wafer Sizing operation done on silicon wafers in the semiconductor
industry. Other areas of the methodology have been demonstrated using a
Printed Wiring Board (PWB) wave soldering system, a fuze assembly
operation, and an electronic component manufacturing process.

The methodology utilizes many techniques and problem solving tools that are
usually covered independently. In the methodology, these tools and techniques
have been incorporated in sequential order of execution, and integrated into one
logical approach for optimizing manufacturing processes and machines. Some
of the techniques are: Design of Experiments (Full Factorial Design and
Fractional Factorial Designs), Analysis of Variance, Yates Algorithm, Pareto
Diagrams, Concentration Diagrams, Ishikawa Diagrams, Control Chart,
PosiTrol Plans, Pre-control, etc.

The book is divided into ten sections. The first section describes the author's
derivation of the Machine/Process Capability Study methodology. It also
suggests how the methodology should be implemented in a manufacturing
environment. Sections two through eight present the five stages of the M/PCpS

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson xvii P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 M/PCpS™

methodology in order of execution. The basic format is an introduction and a

description of the tools and techniques necessary to understand the section,
followed by a step by step description of the M/PCpS stage, each with an
example. Within each section, the pages describing the tools and techniques are
characterized by an icon [ ] at the top right-hand corner of the page. The
Pareto

pages describing the methodology have "M/PCpS" in its place. Section nine
presents all the standard worksheets (forms) used for guiding the user through
the methodology and for complete documentation of the study. Finally, section
ten contains a complete example of a M/PCpS study.

To the academic reviewers of this book, I must confess that this book is not for
you, but rather for the individuals (engineers, managers and practitioners) in the
manufacturing world struggling to find a method for reducing variation in their
processes.

It has been my intention to provide a standard methodology that industry could

adopt as an operating procedure for studying and optimizing manufacturing
processes. It is my personal belief (as my years of experience in applying this
methodology have proven to me) that this methodology, if followed thoroughly,
will inevitably reduce the major sources of processes variation, increase the
quality of your products, and speed up the successful optimization of your
manufacturing processes. The United States' competitive edge in manufacturing
is currently at a disadvantage against our Asian competitors. We are in an
economic war, and it is time to "buckle up", apply first gear, conduct smart
statistical experimentation and optimization, and win this economic war.

Mario Perez-Wilson
Kowloon, Hong Kong , December 10, 1988

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson xviii P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 D ata & S tatistics

Standard Normal Distribution

The cumulative normal distribution table gives the area under the curve from
minus infinity to the z-score or z value chosen.

µ Z Value +

Percent of product that falls below the Percent of product that falls ouside the
USL = 45 comes from the Table: USL = 45 is equal to:

0.83147 1 - 0.83147 = 0.16853

100 x 0.83147 = 83.147 % 100 x 0.16853 = 16.853 %

LSL USL LSL USL

T T

AA A
Percent of product
outside specification

15 30 37.5
X 45 15 30 37.5
X 45
A
Cumulative Normal Distribution
Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 Z
0.0 0.500 00 0.503 99 0.507 98 0.511 97 0.515 95 0.519 94 0.523 92 0.527 90 0.531 88 0.535 86 0.0
0.1 0.539 83 0.543 79 0.547 76 0.551 72 0.555 67 0.559 62 0.563 56 0.567 49 0.571 42 0.575 34 0.1
0.2 0.579 26 0.583 17 0.587 06 0.590 95 0.594 83 0.598 71 0.602 57 0.606 42 0.610 26 0.614 09 0.2
0.3 0.617 91 0.621 72 0.625 51 0.629 30 0.633 07 0.636 83 0.640 58 0.644 31 0.648 03 0.651 73 0.3
0.4 0.655 42 0.659 10 0.662 76 0.666 40 0.670 03 0.673 64 0.677 24 0.680 82 0.684 38 0.687 93 0.4

0.5 0.691 46 0.694 97 0.698 47 0.701 94 0.705 40 0.708 84 0.712 26 0.715 66 0.719 04 0.722 40 0.5
0.6 0.725 75 0.729 07 0.732 37 0.735 65 0.738 91 0.742 15 0.745 37 0.748 57 0.751 75 0.754 90 0.6
0.7 0.758 03 0.761 15 0.764 24 0.767 30 0.770 35 0.773 37 0.776 37 0.779 35 0.782 30 0.785 23 0.7
0.8 0.788 14 0.791 03 0.793 89 0.796 73 0.799 54 0.802 34 0.805 10 0.807 85 0.810 57 0.813 27 0.8
0.9 0.815 94 0.818 59 0.821 21 0.823 81 0.826 39 0.828 94 0.831 47 0.833 97 0.836 46 0.838 91 0.9

1.0 0.841 34 0.843 75 0.846 13 0.848 49 0.850 83 0.853 14 0.855 43 0.857 69 0.859 93 0.862 14 1.0
1.1 0.864 33 0.866 50 0.868 64 0.870 76 0.872 85 0.874 93 0.876 97 0.879 00 0.881 00 0.882 97 1.1
1.2 0.884 93 0.886 86 0.888 77 0.890 65 0.892 51 0.894 35 0.896 16 0.897 96 0.899 73 0.901 47 1.2
1.3 0.903 20 0.904 90 0.906 58 0.908 24 0.909 88 0.911 49 0.913 08 0.914 65 0.916 21 0.917 73 1.3

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 114 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 A
Machine or Process Potential
A
P rocess C apability

Machine/Process Potential, (Cp)

The Cp is a process potential index that measures the potential of capability of

a machine or process. The Cp is the ratio of the allowable spread over the
actual spread. The allowable spread is the range or tolerance of the
specification, and is calculated by subtracting the lower specification limit
from the upper specification limit. The actual spread is the spread from data
collected from the machine or process and is calculated by multiplying 6 times
the standard deviation, S, of the data.

A high value of Cp does not guarantee that the process is capable of producing
product within specification. Furthermore, the whole distribution of the
process, might not overlap with the specification range. The process potential
does not measure the location of the average of the actual spread with respect
to the center (target) of the allowable spread, it only compares their widths.
The capability index, Cpk, measures the degree of centering of the actual
process spread with respect to the allowable spread.

The Cp may only be calculated when two sided specifications are available.
Numerical properties such as addition and averages, cannot be applied to the
Cp because it is a unitless index and would not yield meaningful information.

Engineering Specification or
what engineer judgment What the
establishes as allowable customer
Allowable Spread for that machine or process.
Cp = WANTS.
Actual Spread The spread from the data What the
collected from the machine or customer
process. GETS.

AA
LSL ALLOW ABLE
USL
SPREAD [ USL LSL ]

AA
ACTUAL
SPREAD

X
6 x S where S is based on a large
sample size (Long term study)

15 30 45

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 116 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 A
Machine or Process Potential
A
P rocess C apability

Formula:
USL LSL (Short Term Study)
Cp =
8 x S

Cp = USL LSL (Long Term Study)

6 x S
where,
S = standard deviation of the actual process
LSL = lower specification limit
USL = upper specification limit.

A
LSL ALLOWABLE USL
SPREAD
Actual Process Data:
T

A
Mean, X : 34

A
Standard Deviation, S: 3.75

A
45 - 15 30
Cp = = = 1.33

A
6 x 3.75 22.5

15 30 X 45
ACTUAL
SPREAD 6xS
Actual Process Data:

Mean, X : 60 45 - 15 30
Cp = = = 1.33
Standard Deviation, S: 3.75 6 x 3.75 22.5

A
LSL ALLOWABLE USL
SPREAD

A
Defective units: 100%
T

A
A
ACTUAL
SPREAD 6xS

A
15 30 45
AX

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 117 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 A
A
Machine or Process Capability P rocess C apability

Machine or Process Capability, (Cpk)

The Cpk is a machine or process capability index that measures the ability
of a machine or process to produce product within specification. The Cpk is
the ratio of the distance between the actual process average and the closest
specification limit over three times the standard deviation of the actual
process. The capability index measures the degree of centering of the actual
process spread with respect to the allowable spread. When the actual
process average is outside the specification limits, then the Cpk defaults to
zero.

X LSL ; USL X }
Cpk = {Smallest of: 3xS 3xS

AA A
LSL T USL LSL T USL

AA A
A
15 X 45
Distribution Mean is centered
to the Target of the Specification
15
A X 45
Distribution Mean is NOT centered
to the Target of the Specification

A machine or process is referred to as being capable when its Cpk has a

minimum value of one, and process stability has been proven. A Cpk equal
to one implies that at least 99.73% of the product is within specifications
limits, provided that the process is stable. Stability of the process can be
proven through the use of a control chart. Once the process data is plotted on
a control chart, the process can be regarded as being stable only if it exhibits
statistical control. Statistical control is exhibited when the points plotted do
not extend beyond the upper and lower control limits, and also by the
absence of non-random patterns or trends within the control limits.

The Cpk can be calculated for both single-sided or double-sided

specifications. Numerical properties such as addition and averages cannot be
applied to the Cpk because it is a unitless index and would not yield
meaningful information.

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 118 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 A
A
Machine or Process Capability P rocess C apability

Let's assume that a product characteristic has a specification of 30 + 15. The

target of the specification becomes 30 and the tolerance is equal to two times 15
or 30. Let's calculate Cpk for different distribution means and standard

A
deviations. Specification: 30 + 15

{
AA
LSL USL
Target
Target
Tolerance
USL X (One Half)
Actual Process Data:
Allowable

AA
Spread X = 30
S = 3.75
(One Half) 45 - 30 15
Cpk = = = 1.33
3xS Actual
3 x 3.75 11.25
Spread

30 Defective units : 64 Parts per million

15 45
X
In the example below, the sampling distribution is not centered with the target (T)
of the specification. The standard deviation is small enough that if the
distribution was centered, the process capability, Cpk, would be equal to the

AA
process potential, Cp.
LSL USL
T (One Half)
Allowable Actual Process Data:
Spread
X = 34

AA
USL X
S = 3.75
45 - 34 11
Cpk = = = 0.98
(One Half) 3 x 3.75 11.25
3xS Actual
Spread 45 - 15 30
Cp = = = 1.33
34 6 x 3.75 22.5
15 45
X
In the next example, the sampling distribution is not centered with the target, T,
of the specification. The standard deviation is very large and even if the
distribution were centered, the process would still not be capable. The process
potential is less than 1.0, which indicates that centering the distribution would not
make the process capable. To make this process capable, the standard deviation
has to be reduced.

AA
LSL T USL
Actual Process Data:
USL X
X = 37.5

AA
S = 7.82
45 - 37.5 = 7.5 = 0.32
Cpk =
3 x 7.82 23.46
3xS
Cp = 45 - 15 30
= = 0.639
37.5 6 x 7.82 46.92
15 45
X

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 119 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 M/PCpS™
Stage 3: Capability Determination

Machine Capability
Interpretations of the Normal Probability Paper plots.

Capable Machine/Process Normal Distributed

LSL USL
+4σ
(Symmetrical)

A
+3σ

A
A
µ

−3σ
−4σ
A
Negatively Skewed
LSL USL Negatively Skewed

A
+4σ
+3σ

A
µ
A
A
−3σ
−4σ
A
Positively Skewed Positively Skewed
LSL USL
+4σ

A
+3σ

A
A
µ

−3σ
−4σ
A
Machine/Process Capability Study Advanced Systems Consultants
© 1989-2014, Mario Perez-Wilson 152 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 M/PCpS™
Stage 3: Capability Determination

Platykurtic Flat Distribution

(Kurtosis << 3.0)
LSL USL
+4σ
+3σ

µ
A
A
−3σ
−4σ
A
Leptokurtic
(Kurtosis >> 3.0)
Peaked Distribution

A
LSL USL
+4σ

A
+3σ

µ
A
A
−3σ
−4σ
A
Non-Capable Machine/Process
Bimodal Bimodal Distribution
LSL USL
+4σ
+3σ

−3σ
−4σ

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 153 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 M/PCpS™
Stage 4: Optimization

The Taguchi Orthogonal Array L27 (313-11) design.

)
) a tic
e ar dr
in ua
(L (Q
er B B e n
Treatment
H o ld A
&
A
&
e d im e T im Co
d e e
Combination of ee ee
n en S p h T lis h e iv
e d n S p e tw t w e p in l i s o at
e
R at c e r as b ras
e e P R r b
Sp pi b b S Po r z z o A A
or
n a l e r S tio n t i o n tte r tte r u tte t t er t te r in g F tte r t t e r te r
t
tt c c u u u
t
io
a t C u te r a e ra d C t C u nd C t C u d C r in d t Cu d C t Cu
t 2n 1s 2 s 2n s 2n s
Run R o 1 st In In 1 G 1 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 1 1 1 1 1 1 1 1 1
3 0 0 0 0 2 2 2 2 2 2 2 2 2

4 0 1 1 1 0 0 0 1 1 1 2 2 2
5 0 1 1 1 1 1 1 2 2 2 0 0 0
6 0 1 1 1 2 2 2 0 0 0 1 1 1

7 0 2 2 2 0 0 0 2 2 2 1 1 1
8 0 2 2 2 1 1 1 0 0 0 2 2 2
9 0 2 2 2 2 2 2 1 1 1 0 0 0

10 1 0 1 2 0 1 2 0 1 2 0 1 2
11 1 0 1 2 1 2 0 1 2 0 1 2 0
12 1 0 1 2 2 0 1 2 0 1 2 0 1

13 1 1 2 0 0 1 2 1 2 0 2 0 1
14 1 1 2 0 1 2 0 2 0 1 0 1 2
15 1 1 2 0 2 0 1 0 1 2 1 2 0

16 1 2 0 1 0 1 2 2 0 1 1 2 0
17 1 2 0 1 1 2 0 0 1 2 2 0 1
18 1 2 0 1 2 0 1 1 2 0 0 1 2

19 2 0 2 1 0 2 1 0 2 1 0 2 1
20 2 0 2 1 1 0 2 1 0 2 1 0 2
21 2 0 2 1 2 1 0 2 1 0 2 1 0

22 2 1 0 2 0 2 1 1 0 2 2 1 0
23 2 1 0 2 1 0 2 2 1 0 0 2 1
24 2 1 0 2 2 1 0 0 2 1 1 0 2

25 2 2 1 0 0 2 1 2 1 0 1 0 2
26 2 2 1 0 1 0 2 0 2 1 2 1 0
27 2 2 1 0 2 1 0 1 0 2 0 2 1
450 4 210 4 0 s e 5 µm 1 µm 2 5 0 3 2 0 6 /9 10
rpm000 rp 0 rp sec c /s e c /s e c 0 p s i µm
/s e
m m
Level for each experimental factor in run # 27.

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 204 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 M/PCpS™
Stage 5: Control

Example 3.- "Guggenheim" Wafer Sizing

At the culmination of the stage of Control, the wafer thickness process

capability index was Cpk=1.89 and its process potential index was Cp=1.99.

Wafer Thickness
LSL USL

X: 253.38
S: 2.18
Cpk: 1.89
Cp: 1.99

241 246 253 260 267

For wafer strength, the process potential index was further improved by
experimenting with cutter grit sizes and water flow rates during grinding. The final
experimental results lowered the number of cracks/wafer to an average of 0.769 and
a standard deviation of 1.107; thus making the wafer very strong.
80

70

60

50

40

30

20

10

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 250 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 M/PCpS™
Stage 5: Control

The specification limits were changed from 30 + 15 cracks/wafer, to a lower

specification limit of 0, and an upper specification limit of 10 cracks/wafer.
The standard deviation was reduced from 8.42 to 1.107, far exceeding the
+ Six Sigma goal performance capability. The "Guggenheim" wafer grinder
achieved best-in-class status, and the wafer breakage yields were improved
from 80.8% to 92.7%. An overall savings of $714,000 a year.

Wafer Strength Pre and Post Improvements

Final Results After

New Spec Limits Experimentation
(Distribution #3) (Distribution #2)
New LSL USL

AA A
LSL USL
X: 0.769
Before
S: 1.10 Experimentation

A
Cp: 1.51 (Distribution #1)

AA A
A
A 0 10 15
A
30 31.25 45 47.86

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 251 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 M/PCpS™

Bond Pad Corrosion MACHINE/PROCESS CAPABILITY Study # 012503

STUDY Date 5-20-94
Program
Operation Etching
Plasma Etch M/PCpS Team C&E CROSS-REFERENCE
TABLE Equip # T-903
Responsible Person
Page 3 of 26
MACHINE/PROCESS RANK-ORDER: Yes No
DEPENDENT

Consistency
Uniformity
T

End Point
Selectivity
Etch Rate
LEVEL OF
O
INDEPENDENT
T
A
INDEPENDENT L
Pressure 24 22 15 20 81
N2 24 20 12 10 66
SF 6 22 22 4 10 58
CHF 3 20 18 9 8 54
T.S. Upper Electrode 7 5 7 19
T.S. Bottom Electrode 9 8 13 9 36
T.S. Chamber 12 8 4 12 36
P.S. Throttle Valve 19 13 3 19 54
P.S. Pump System 19 13 3 19 54
P.S. Transducer Accuracy 19 12 3 19 53
P.S. Chamber Vacuum Integ. 18 13 3 19 53
E.S. Detector 18 18
E.S. High Voltage 18 18
E.S. Wave Length 18 18
E.S. Gain 18 18
E.S. Window 10 10
E.S. Cleanliness 10 10
B.C.S. Clamping Spring 11 15 5 11 42
B.C.S. He Flow Pressure 9 12 4 9 34
B.C.S. Wafer Placement 2 10 1 2 15
B.C.S. Wafer Flatness 2 10 1 2 15
P.S. Matching Efficiency 21 10 12 21 64
P.S. Phase Splitter 20 10 12 21 63
P.S. RF Power 22 10 13 22 67
Gas Flow Consistency 20 14 15 20 69
Gap Parallelism 16 20 3 16 54
Gap Spacing Accuracy 16 20 4 10 50
Shower Head 13 18 3 8 42
Environment
Manpower 17 4 2 1 24
Wafer Thickness 18 8 13 3 42

© 1994, Advanced Systems Consultants

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 285 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 M/PCpS™

Bond Pad Corrosion Study # 012503

MACHINE/PROCESS CAPABILITY STUDY Date 5-20-95
Program
Operation Etching
Plasma Etch M/PCpS Team DRAWING Equip # T-903
Responsible Person Page 10 of 26
DRAWING Within Wafer Thickness Uniformity
(Edge to Center Thickness of Silicone Nitride from Metalization - from 30 Wafers'
Average)

10000
9900
9800
9700
9600 Wafer's Center
9500
9400 Slope = 462 Å
9300
9200
9100 Wafer's Edge
9000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Silicone Nitride

Substrate

Within Wafer Thickness Uniformity

(Edge to Center Thickness after Plasma Etching - From 30 Wafers'
Average)

7400
7200
7000
6800
Wafer's Center
6600
6400
6200 Slope = 1,278Å
6000
5800 Wafer's Edge
5600
5400
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

AAAAAAAAAAAAA Silicone Nitride

AAAAAAAAAAAAA
© 1994, Advanced Systems Consultants
Substrate

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 291 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 M/PCpS™

Bond Pad Corrosion Study # 012503

MACHINE/PROCESS CAPABILITY STUDY Date 5-20-95
Program
Operation Etching
Plasma Etch M/PCpS Team DRAWING Equip # T-903
Responsible Person Page 25 of 26
DRAWING

Final Results after Characterization

After Characterization and Before Characterization and

Optimization Optimization

LSL USL
LSL USL

5715 5955 6268.2 6539 6882.73 7227

X 6582 X

X = 6268.2 X = 6882.73
R = 230 R = 1209
S = 50.24 S = 389.32
Cp = 1.56 Cp = 0.22
Cpk = 1.56 Cpk = 0.22

Silicone Nitride

Substrate
© 1994, Advanced Systems Consultants

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 305 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 Appendix

Appendix A
+ Six Sigma

Appendix B
Likert Scale for PWB Solder Deposition

Appendix C
Nonparametric Statistical Tests

Appendix D
Relationship Between Average and Sigma

Appendix E
Charting the Range in a GR&R Study

Appendix F
Transforming a Normal Distribution to a Standard Normal Distribution

Appendix G
Fitting a Continuous Curve

Appendix H
Possibilities of M/PCpS After the Capability Determination Stage
Objective of M/PCpS Studies

Appendix I
Cumulative Normal Distribution Table
Unilateral Normal Distribution Table

Appendix J
Minitab Instructions for the Capability Determination Stage

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 313 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 Appendix A

Six Sigma or + Six Sigma

Six Sigma is an optimized level of performance approaching zero-defects in a

process producing a product, service or transaction. It indicates achievement and
maintenance of world-class performance.

Motorola, on Thursday, January 15, 1987, defined Six Sigma as having plus or minus
six sigmas (±6s) or standard deviations within specification limits. In other words,
given a particular product characteristic, which has a design specification, that design
specification has an upper specification limit, USL, and a lower specification limit,
LSL, these two limits demarcated a design tolerance. Motorola held the design
tolerance to be such, that it should allow to fit twelve (±6) sigmas or twice the
process variation.

Theoretically, under the above stated condition, a process would have Cp=2, Cpk=2,
in-process yield around 99.9999998%, and a defective rate below 0.002 parts-per-
million (PPM). For all practical purposes, + Six Sigma implies zero-defects.

What is the objective of + Six Sigma? To reduce the process variation, such that
twelve standard deviations will fit within specification limits, and to center the mean
in the middle of the specification limits.

Six Sigma => 0.002 ppm

LSL USL
Design Specification

.001 ppm Process Width .001 ppm

-6σ -3σ µ +3σ +6σ

6σ 6σ

Six Sigma or plus or minus six sigma within specification limits.

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 314 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 Appendix A

Areas under Normal Curve

99.73%
95.45%
68.26%

-6σ -5σ -4σ -3σ -2σ -1σ µ +1σ +2σ +3σ +4σ +5σ +6σ
99.994%

99.999939%
99.9999998%

Sigma Level
(± xσ) Cp Cpk PPM

[+ 1σ] ~ One Sigma 0.33 0.33 317,320

[+ 2σ] ~ Two Sigma 0.67 0.67 45,500
[+ 3σ] ~ Three Sigma 1.0 1.0 2,700
[+ 4σ] ~ Four Sigma 1.33 1.33 63.5
[+ 4.5σ] ~ Four and a half Sigma 1.50 1.50 6.9
[+ 5σ] ~ Five Sigma 1.67 1.67 0.6
[+ 6σ] ~ Six Sigma 2.0 2.0 0.002

[Assumptions: Normality, Stability and Distribution centered.]

Yields, sigmas, Cp, Cpk and PPM levels when + sigmas coincide with specification limits.

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 315 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 M/PCpS™

References

American National Standards Institute, (1985), Guide for Quality Control Charts,
ANSI Z1.1-1985 (ASQC B1-1985)

American National Standards Institute, (1985), Control Chart Method of

Analyzing Data, ANSI Z1.2-1985 (ASQC B2-1985)

American National Standards Institute, (1985), Control Chart Method of

Controlling Quality During Production, ANSI Z1.3-1985 (ASQC B3-1985)

Barker, T.B. (1985), Quality by Experimental Design, New York: Marcel

Dekker, Inc.

Box, G.E.P, Hunter, W.G., and Hunter, J.S. (1978), Statistics for Experimenters,
New York: John Wiley & Sons, Inc.

Charbonneau, H.C., and Webster, G.L. (1978), Industrial Quality Control, New
Jersey: Prentice-Hall, Inc.

Downie, N.M., and Starry, A.R. (1977), Descriptive and Inferential Statistics,
New York: Harper & Row, Publishers, Inc.

Duncan, A.J. (1974), Quality Control and Industrial Statistics, Illinois: Richard
D. Irwin, Inc.

Ford Motor Company, Inc., (1983), Continuing Process Control and Process
Capability Improvement, Statistical Methods Office, Operations Support Staffs,
Ford Motor Company.

Ford Motor Company, Inc., (1980), Machine Capability Studies, Ford Motor
Company.

General Motors, (1984), Statistical Process Control Manual, General Motors

Corporation, SPEAR Administrative Staff, G.M. Technical Center, Warren,
Michigan.

Hald, A. (1955), Statistical Theory with Engineering Applications, New York:

John Wiley & Sons, Inc.

Hicks, C.R. (1982), Fundamental Concepts in the Design of Experiments, New

York: Holt, Rinehart and Winston.

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 339 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 M/PCpS™

Hines, W.W., and Montgomery, D.C. (1972), Probability and Statistics In

Engineering and Management Science, New York: The Ronald Press
Company.

Ishikawa, K. (1982), Guide to Quality Control, Tokyo: Asian Productivity

Organization.

Juran, J.M., Gryna, F.M. and Bingham, R.S. (1974), Quality Control Handbook,
New York: McGraw-Hill Book Co.

Juran, J.M., and Gryna, F.M. (1970), Quality Planning and Analysis, New
York: McGraw-Hill Book Co.

Kane, V.E. (1986), "Process Capability Indices", Journal of Quality

Technology, January 1986, Vol 18, No.1, pp. 41-52.

Keeney, K.A. (1987), "What is Process Capability", Machine and Tool BLUE
BOOK, September 1987, pp. 65-67.

Koosis, D. (1985), Statistics, New York: John Wiley & Sons, Inc.

Love, S.F. (1983), Planning and Creating Successful Engineering Designs, Los
Angeles: Advanced Professional Development, Inc.

Ott, L. (1984), An Introduction to Statistical Methods and Data Analysis,

Massachusetts: PWS Publishers.

Perez-Wilson, M. (2003), Gauge R&R Studies - For Destructive and Non-

Destructive Testing, Arizona: Advanced Systems Consultants.

Perez-Wilson, M. (1992), Multi-Vari Chart & Analysis - A Pre-experimentation

Technique, Arizona: Advanced Systems Consultants.

Perez-Wilson, M. (1993), Positrol Plans and Logs, Arizona: Advanced Systems

Consultants.

Perez-Wilson, M. (1994), The M/PCpS Methodology, Arizona: Advanced

Systems Consultants.

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 340 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 M/PCpS™

Perez-Wilson, M. (1993), The Total Control Methodology, Arizona: Advanced

Systems Consultants.

Phillips, D.T. (1972), Applied Goodness of Fit Testing, Georgia: American

Institute of Industrial Engineers, Inc.

Singh, J. (1972), Great Ideas of Operations Research, New York: Dover

Publications, Inc.

Sullivan, L.P. (1986), "Japanese Quality Thinking at Ford", Quality, April 1986,
pp. 32-34.

Taguchi, G. (1987), Introduction to Quality Engineering, Tokyo: Asian

Productivity Organization.

Walpole, R.E., and Myers, R.H. (1972), Probability and Statistics for Engineers
and Scientists, New York: The Macmillan Company.

Western Electric Company, Inc., (1956), Statistical Quality Control Handbook,

North Carolina: Delmar Printing Company.

Woodlsey, R.E.D., and Swanson, H.S. (1975), Operations Research for

Immediate Application A Quick & Dirty Manual, New York: Harper & Row,
Publishers.

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 341 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 M/PCpS™

Index

A Centiles, 107
A2 Factor, 165 Charts:
Accuracy, 67 Average, 168
Actual Spread, 116 c, 219, 233
Allowable Spread, 116 Control, 167, 218
Attribute Data, 30 Individuals, 220-233
Attributes Measurement, 219 MR, 220-233
Average, 101 Multi-vari, 188
Average: np, 219, 233
Chart, 168 p, 219, 233
Range, 90 Pareto, 17
Shewhart, 217
B u, 219, 233
Best Fit Line, 149 X & R, 161, 218, 233
Between-Piece Variation, 189 Concentration Diagrams, 194
Between-Operator Variation, 78 Continuous Data, 30
Bimodal Distribution, 153 Control Chart, 167, 218
Blank Forms and Worksheets, 253 Control Chart Flowchart, 233
Brainstorming, 37 Control Limits, 161
Corrective Action Logs, 217
C Cp, 99, 116, 126, 171, 325
c Charts, 219 Cpk, 99, 116, 126, 171, 325
C&E, 29 Cumulative Frequency, 107-9, 145
C&E Cross-Reference Cumulative Frequency
Table, 45-49, 58-9, 134-5, Distribution, 109
195-6, 198, 273-4, 285, 296 Cumulative Normal
CAL, 217 Distribution, 113, 326
Capability, 1 Customer-Supplier Variation, 79
Capability: Cyclical Variation, 188, 189
Determination, 99
Index, 99, 171 D
Cause and Effect (C&E), 29 D3 Factor, 165
Cause and Effect Diagram, 34-6 D4 Factor, 165
Cell Width, 100 Data:
Center Line (CL), 168 Attribute, 30
Coded, 140

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 343 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 M/PCpS™

Index Continued

Continuous, 30 DOE, 181

Discrete, 30
Interval, 33 E
Measurement, 30 Edge Force Variable Pressure
Nominal, 31 Test, 66
Ordinal, 32 Experimental Design Funnel, 187
Qualitative, 30 Experimental Factors, 203
Quantitative, 30 Experimentation, 183
Ratio, 33
Variable, 30 F
Delineation, Process, 29 Factorial Designs, 186
DeMoivre, Abraham, 110 Factors, 165, 184
Dependent Variables, 42 Factors:
Descriptive Statistics, 99, 127, 155, A2, 165
158 D3, 165
Design Matrix, 184-5 D4, 165
Design of Experiments, 181 Experimental, 203
Diagrams: Family of Variation, 188
C&E, 34 Fishbone Diagram, 34
Concentration, 194 Flat Distribution, 153
Fishbone, 34 Flowcharts:
Pareto, 3-8, 17-26 Control Charts, 233
Discrete Data, 30 M/PCpS, 307-11
Dissectible Characteristics, 53-4 Forms:
Distributions: Blank, 253
Bimodal, 153 Gauge Short Method Study, 93,
Cumulative Frequency, 109 257
Cumulative Normal, 113 GR&R Data Collection
Flat, 153 Sheet, 94, 98, 258
Frequency, 100 Pareto Diagram, 25, 265
Gaussian, 110 Standard, 253
Normal, 110 Frequency Distribution, 100
Peaked, 153 Frequency Histogram, 100
Standard Normal, 112 Frequency, Cumulative, 145
u, 112 Full-Factorial Designs, 186, 201

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 344 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 M/PCpS™

Index Continued

Functional Characteristics, 29, 39-41, Ishikawa, Kauro, 34

44 Iterative Process, 183
Fuze Example, 196-7, 200-1, 205-6,
208, 210-1, 213-4 K
Kurtosis, 106, 157
G
Gauge: L
Accuracy, 67 Laplace, Pierre Simon, 110
Capability, 67, 81 LCL, 165
Error (GRR), 91-2 Leptokurtic, 106, 153
Precision, 67 Levels, 184
Variability, 97 Likert Scales, 61, 316
Gauss, Karl, 110 Limits, Control, 161
Gaussian Distribution, 110 Logs:
Goodness of Fit, 142 Corrective Action (CAL), 217
GR&R, 67 PosiTrol, 217, 235, 238, 242-3
Grinding Component System, 38-9, Long Method Study, 82, 84, 86, 94
44 Long-Term Capability Study, 124
GRR, 91 Lower Control Limit (LCL), 165
Guggenheim Wafer Sizing Lower Specification Limit, 116
Machine, 40, 199, 203-4, 207,
209, 210, 212-3, 215 M
M/PCpS, 3
H M/PCpS:
Hypothesis, 183, 196 Coordinator, 10
Data Collection Sheet, 138
I Flowchart, 307-11
Inaccuracy, 70 Stages, 27
Independent Variables, 5, 39, 42-50, Teams, 10
184 Machine Capability, 99
Index: Machine Definition, 39, 40, 50
Capability, 99, 171 Machine/Process:
Process Potential, 116, 173 Capability, 118
Interval Data, 33 Capability Study (M/PCpS), 3
Ishikawa Diagram, 34 Potential, 116

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 345 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 M/PCpS™

Index Continued

Material Variation, 79 Operator Variability, 97

Mean, 156, 159 Optimization, 181, 191
Mean Rank Plot Points, 147 Order of Production, 140
Measurement: Ordinal Data, 32
Attributes, 219 Out-of-Control Action Plans, 217
Data, 30 Out-of-Control Condition, 168
Definition, 61
Scale, 33 P
Measures: p Charts, 219
of Central Tendency, 156 Parameter Standard Deviation, 125
of Shape, 156 Pareto:
of Variability, 156 Chart, 17
Median, 101 Diagram, 3-8, 17-26
Mesokurtic, 106 Principle, 17
Metrology Characterization, 61 Pareto, Vilfredo, 17
Minitab, 329-38 Peaked Distribution, 153
Mode, 101 Percent-Out-of-Specification, 178
Moment About the Mean, 156-7 Platykurtic, 106, 153
Multi-vari Chart, 188 Point of Interest, 112
Positional Variation, 188
N Positive Control, 235
Nominal Data, 31 PosiTrol, 235
Nondissectible Characteristics, 53-4 PosiTrol:
Normal Distribution, 110 Logs, 217, 235, 238, 243
Normal Probability: Plans, 217, 235-6, 281, 306, 325
Paper, 142 Precision, 67, 72, 318
Paper, Interpretations, 152 Preventive Control, 217, 239, 248
Table, 177 Process:
Normality Determination, 142 Capability, 1, 118
np Charts, 219 Delineation, 29
Potential Index (Cp), 116, 173
O
OCAP, 217 Q
Ogive Curve, 109 Qualitative Data, 30

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 346 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 M/PCpS™

Index Continued

Quantitative Data, 30 Spread:

Quartiles, 107 Actual, 116
Allowable, 116
R Standard:
R-Bar, 164 Deviation, 102, 156, 180
Range, 102, 156, 321 Forms and Worksheets, 253
Range, Average, 90, 318 Normal Distribution, 112
Ratio Data, 33 Scores, 112
Recalibration, 70, 73 State of Statistical Control, 160
Reduction: Statistical Methods Engineer, 10, 13, 15,
of Variability, 181, 191 129
of Variance, 181 Statistically Designed Experiments
of Variation, 192 (DOE), 181
Repeatability, 67, 97 Study Number, 129
Replicated Measurements, 73 Sub-Grouping Size, 140
Reproducibility, 67, 97 Sub-Process, 7, 8
Response Variables, 42 Sub-Process:
Rinse and Drying System, 41, 44 Characteristics, 52
Definition, 29, 51
S
S-shaped Curve, 109 T
Sample Size, 100, 121, 125, 140 Tables:
Sample Standard Deviation, 125 C&E Cross-Reference, 45, 195
Sampling, 140 Cumulative Normal
Scale of Measurements, 31-3 Distribution, 178
Seder, Leonard, 188 Normal Probability, 177
Shewhart Control Charts, 217 Taguchi Orthogonal Array, 204
Shewhart, Walter, 218 TCM, 217
Short Method Study, 82-3, 90 Team:
Short-Term Capability Study, 121 Chairman, 11-2, 15
Six Sigma, 180, 249, 251, 272, 283, Champion, 11, 15
314-5 Coordinator, 10, 15
Skewness, 105, 152, 156 Facilitator, 13, 15
Sources of Variation, 75 Leader, 9, 12, 15
SME, 10, 13, 15,129 Member, 9, 10, 13-5
Specifications, 61, 63 Scribe, 12, 15

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 347 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 M/PCpS™

Index Continued

Temporal Variation, 188-9 Operator, 97

Test Equipment Variation, 88 Positional, 188
Test of Unnaturalness, 168 Reduction, 181, 191-2
Theories, 197 Sources, 75
Tolerances, 61, 65 Temporal, 188-9
Total Control Methodology Test Equipment, 78
(TCM), 217, 235 Total, 97
Total Variability, 97 Within-Operator, 75
Treatment Combination, 185 Within-Piece, 188
Trivial Many Variables, 5, 7, 17 Vital Few Variables, 5, 7, 17, 325

U W
u Charts, 219, 233 Wafer Gauging System, 41, 44
u Distribution, 112 Wafer Soldering System, 198
UCL, 165 Wafer Transportation System, 41, 44
Unilateral Normal Distribution Within-Piece Variation, 188
Table, 327-8 Within-Operator Variation, 75
Upper Control Limit (UCL), 165 Work Holding System, 41, 44
Upper Specification Limit, 116 Worksheets:
Blank, 253
V Standard, 253
Validation, 213
Variable Data, 30 X
Variables: X & R Chart, 161
Dependent, 42 X & R Chart Worksheet, 161
Independent, 5, 44-7, 184 X-Bar, 163
Response, 42 X-Double Bar, 164
Trivial Many, 5, 7, 17
Vital Few, 5, 7, 17 Z
Variation: Z Scores, 112, 174
Between-Piece, 189 Z Value, 113, 174
Between-Operator, 78
Cyclical, 188-9
Family of, 188
Material, 79

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 348 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 About the Author

Mario Perez-Wilson is the founder and CEO of Advanced Systems Consultants and
author of nine books: Machine/Process Capability Study - A Five Stage Methodology
for Characterizing Manufacturing Processes, Multi-Vari Chart and Analysis, Design
of Experiments, The Total Control Methodology - A Preventive Approach for Total
Control during Production, Six Sigma - Understanding the Concept, Implications and
Challenges, Positrol Plans and Logs, ANOVA - Analysis of Variance for Simple and
Complex Experiments, PCB Process Characterization - Applying M/PCpS to the PCB
Industry and Gauge R&R Studies - For Destructive and Non-destructive Testing.

Mr. Perez-Wilson has over 23 years of industrial experience in engineering, quality

and process improvement and has served at the executive level as Corporate Vice
President of Quality for Flextronics International. He holds a B.S. degree in
Industrial Engineering from the University of Arizona and Global Leadership from
the Thunderbird School of Global Management. He was awarded the "Da N To Tsu"
(Japanese for "Best of the Best") award from the Rochester Institute of Technology in
the QED 90 Symposium.

One of the original architects of Six Sigma, he served as a Division Statistical

Methods Engineering Manager at Motorola. During his tenure, he institutionalized
and standardized the application of statistical methods in Motorola's worldwide
manufacturing, production and engineering operations. His M/PCpS™ Methodology
for characterizing processes has received global recognition and has become the
standard in the achievement of Six Sigma.

Mr. Perez-Wilson has conducted seminars for over 18,000 individuals in Brazil,
Belgium, People’s Republic of China, Germany, Hong Kong, India, Japan, Korea,
Malaysia, Mexico, Philippines, Singapore, Sweden, Taiwan, and the United States,
and is currently listed in The International Who's Who in Quality.

Some of the companies that have implemented Mr. Perez-Wilson's methodologies

are: ADFlex Solutions, AMD, Alphatec U.S.A., Allied Signal Aerospace, Anadigics,
Arvin Industries, Arvin North America Automotive, Arvin Ride Controls, Astron,
Bausch & Lomb, Burr-Brown, Carsem, Chartered Semiconductor, Connector Service
Corp., Conexant, CRC Industries, Crystalline Materials, CTI Cryogenics, Duracell,
EG&G, Federal Reserve Bank of New York, Fiberite IBI, Flextronics, General
Electric, Guidant, Hewlett-Packard, Indy Electronics, Intel, Korea Electronic
Company, Legris, Los Alamos National Laboratory, LSI Logic, Lucas/Nova Sensors,
Maremont Exhaust Products, Martin Marietta Astronautics, Mitsubishi Silicon
America, Motorola Inc., Multek, Olin Interconnect Technologies, Pacesetter, Peavey
Electronics, Philips, Rodel, Ryobi, Sandia National Laboratories, Semi-Alloys,
Shimano, Sikorsky Aircraft, Vitelic (Hong Kong), Wavetek and Zimmer.

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 351 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 Comments From Our Customers

"Good, practical approach to tackling difficult "The most comprehensive methodology I have seen
manufacturing problems. Good class notes, and to date for people who are serious about improving
straightforward, concise approach." machine/process capabilities and who are willing to
work at it without looking for the proverbial short
Stephen V. Crowder term windfall."
Senior Member Technical Staff
Sandia National Labs John Toto
Director, Quality Assurance
"The industry would do very well if people and Semi-Alloys
companies would make a deep commitment to the
M/PCpS methodology" "Excellent material and presentation on
Machine/Process Capability. Instructor has excellent
Pat Friend working knowledge of material"
Sales Engineer
Panasonic Factory Automation Merv Dunn
Vice President Total Quality
"Great format. Simplistic approach from start to Arvin Industries
finish of a complex problem -Machine/Process
Capability. Good explanation of not only how but "Your book is one of the easiest and useful ones I
with capability studies done in real life. Both have ever seen. With your presentations and book
theoretical and practical approaches in one. A class people are gaining the knowledge to do things right
that all production, engineering and managers should from the very beginning (knowledge so much needed
take." in the American Companies)."

John Reitter Ana Ley

Thin Films Engineering Supervisor Etch Engineer
LSI Logic Corporation LSI Logic Corporation

"The real genius of the Machine/Process Capability "I have taken classes with Deming and Montgomery
Study course is that it ties together and organizes all but this class was by far the best. Mario's approach is
the tools for process improvement. I've taken many very simple and practical. I look forward to taking
courses on S.P.C. and process improvement that have further classes with him."
presented one piece of the puzzle, but none of the
courses have put it all together as well as what Mario David Butler
does in the Machine/Process Capability course. This Director of Package Operations
is by far the best training course I have taken." Olin Interconnect

Brian Decker "An extremely structured and step-by-step

Senior Quality Engineer methodology -very clear and simplified. A superb
Martin Marietta book to have for application as well as reference. I
strongly recommend all personnel involved in
production or manufacturing at all levels to attend
"M/PCpS provided an outstanding and integrated this seminar if they are really serious about improving
overview of practical statistical methods and a clear their product quality."
direction for applying the methodologies to foster a
'take control' approach in manufacturing. Education Norman Sim Boon Heng
in their methods and actual application of them is SPC Analyst
now critical for American companies to 'close the Sundstrand Pacific (Atg) P.L.
gap'."

Scott P. Gucciardi
QA Engineer
Welch Allyn Corp.

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 352 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
"M/PCpS methodology is an extremely well planned, "M/PCpS, ... methodology is vital for U.S. to regain
step by step course on 'how to' design, plan and status and market share in world economy. This,
complete Machine/Process Capability Studies. Most together with concurrent engineering has potential of
seminars that I have attended are predominately reducing many problems of national scope."
theory with very little applications. The instructor's
experience and knowledge was excellent and made R.J. Tockey
the seminar extremely enjoyable. Probably the BEST MTS Division Supervisor
seminar I have ever attended - approximately ten in Sandia National Labs
the last three years."
"Mario Perez-Wilson brings complex manufacturing
Jim Angel techniques and tools and outlines a simple
Director Manufacturing Quality methodology that engineers can use in their day to
Arvin NAA day activities to characterize, improve and control
both simple and complex manufacturing steps. This
"Your methodology is concise and complete. You've methodology can help in the path of continuous
made a challenging subject very easy. There are no quality improvement and in becoming a 'total quality'
more excuses!" organization."

Don Wright Divyesh Shah

Statistical Methods Engineer Process & Product Engineering Manager
Motorola, Inc. Lucas Nova Sensor

"A concise and lively presentation of a set of "Step by step book clearly moves you through the
fundamental tools and a simple application of their capability study process. Format is well documented
use to control processes.." throughout the book."

T.A. Wiley Scott Schiefer

Quality Engineering Manager Supplier Engineer
Allied Signal Inc. Aerospace Western Digital

"Mario takes a no-nonsense approach to provide "The course goes to the heart of process
designers and manufacturers with what they need to improvement. This methodology is as complete as I
know and use M/PCpS." have seen."

W. David Williams James A. Schue

Quality Assurance Engineering Manager Senior SPC Specialist
Sandia National Labs Zimmer, Inc

"This is a very good course toward 6 Sigma quality. "The Methodology is very well structured and
It is a "life statistics", I encourage all manufacturing planned. The tools I learned are very powerful!"
engineers to attend this class."
Carlos A. Pinheiro
Tony C. R. Tsai Site Coordinator (Brazil)
R & QA Manager Multek/Flextronics
Motorola Electronics , Taiwan
"... Mario Perez-Wilson has significantly added value
"A very systematic step-by-step approach to by organizing these techniques into a workable
understand the behavior of a manufacturing process. methodology and demonstration how it can be
This methodology should be made known to all applied to produce the desired results."
manufacturing operations."
George Melchiorsen
Nakkina VRK Quality Engineer
Process/ IE Task Leader Hewlett Packard
Motorola (P) Ltd.

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 353 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
Machine/Process Capability Study Advanced Systems Consultants
© 1989-2014, Mario Perez-Wilson 354 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
Machine/Process Capability Study Advanced Systems Consultants
© 1989-2014, Mario Perez-Wilson 355 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
Machine/Process Capability Study Advanced Systems Consultants
© 1989-2014, Mario Perez-Wilson 356 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081
 Advanced Systems Consultants
P.O. Box 5257 • Scottsdale, AZ 85261
Tel: (480) 423-0081 • Fax: (480) 368-0614 • Email: consulting@mpcps.com
Order Form
Machine/Process Capability Study - A Five-Stage Methodology for
Characterizing Process
List Price: US$75 plus $10 S&H, add $3 for each additional book.
Gauge R&R Studies - For Destructive and Non-destructive Testing
List Price: US$69 plus $10 S&H, add $3 for each additional book.
Multi-Vari Chart and Analysis - A Pre-Experimentation Technique
List Price: US$35 plus $7 S&H, add $3 for each additional book.
Positrol Plans and Logs
List Price: US$45 plus $7 S&H, add $3 for each additional book.
Six Sigma - Understanding the Concept, Implications and Challenges
List
Quantity Price: US$88
Discount: plus $10 S&H, add $5 for each additional book.
Call 480-423-0081.
To order online visit website: www.mpcps.com
Book: Quantity:

Total Amount is US$:

Customer Information
Name:

Title:

Company:

Address:

City: State: Zip:

Phone: Fax:

Email:

Payment Method
Check Enclosed VISA MasterCard AMEX
Credit Card#: Exp. Date:

Machine/Process Capability Study Advanced Systems Consultants

© 1989-2014, Mario Perez-Wilson 357 P.O. Box 5257, Scottsdale, AZ 85261, Tel: (480) 423-0081