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Managing and ImprovingQuality
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Managing and ImprovingQuality
Integrating Quality, StatisticalMethods and Process Control
Amar Sahay
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Managing and Improving Quality: Integrating Quality, Statistical Methods
and Process Control
Copyright Business Expert Press, LLC, 2016.
All rights reserved. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted in any form or by any
meanselectronic, mechanical, photocopy, recording, or any other
except for brief quotations, not to exceed 400 words, without the prior
permission of the publisher.
First published in 2016 by
Business Expert Press, LLC
222 East 46th Street, New York, NY 10017
www.businessexpertpress.com
ISBN-13: 978-1-63157-341-5 (paperback)
ISBN-13: 978-1-63157-342-2 (e-book)
Business Expert Press Supply and Operations Management Collection
Collection ISSN: 2156-8189 (print)
Collection ISSN: 2156-8200 (electronic)
Cover and interior design by Exeter Premedia Services Private Ltd.,
Chennai, India
First edition: 2016
10 9 8 7 6 5 4 3 2 1
Printed in the United States of America.
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Abstract
Quality is a discipline that focuses on product and service excellence.
Tis book is about improving the quality of products and services. Te
improved quality and reliability lead to higher perceived value and
increased market share for a company, thereby increasing revenue and
profitability.
Te book discusses the concepts and dimensions of quality, costs of
poor quality, the importance of quality in this highly competitive global
economy, and quality programsSix Sigma and Lean Six Sigma thatfocus on improving quality in industries. Te text integrates quality
concepts, statistical methods, and one of the major tools of quality
Statistical Process Control (SPC)a major part of Six Sigma control
phase. A significant part of the book is devoted to process control and
the tools of SPCcontrol chartsused for monitoring, controlling, and
improving the processes by identifying the causes of process variation.
Te fundamentals of control charts, along with SPC techniques for vari-ables and attributes, and process capability analysis and their computer
applications are discussed in detail.
Tis book fills a gap in this area by showing the readers comprehen-
sive and step-wise solutions to model and solve quality problems using
computers.
Keywords
capability analysis, common cause of variation, control charts, control
charts for attributes, control charts for variables, control limits, cost of
quality, lean six sigma, pattern analysis, p-chart, process spread, process
variation, rational subgroup, R-Chart, run charts, s-chart, Six Sigma,
special causes of variation, specification limits, statistical process control,
three-sigma limits, total quality management (QM),x chart
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ContentsPreface ..................................................................................................ix
Acknowledgments .................................................................................xiii
Chapter 1 Introduction to Quality ....................................................1
Chapter 2 Quality Programs in Use oday: Lean Six Sigma
and otal Quality Management ......................................15Chapter 3 Statistical Methods Used in Quality ................................39
Chapter 4 Making Inferences About Process Quality .......................95
Chapter 5 Process VariationHow It Affects Product Quality ......137
Chapter 6 Control Charts: Fundamentals and Concepts ...............155
Chapter 7 Control Charts for Variables .........................................167
Chapter 8 Control Charts for Attributes .......................................209
Chapter 9 Process Capability Analysis ...........................................237
Chapter 10 Summary, Applications, and Computer
Implementation ............................................................265
Appendix A Standard Normal Distribution Table...............................275
Appendix B Partial t-Distribution Table............................................277
Appendix C Table of Control Chart Constants....................................279
Bibliography .......................................................................................281
Index .................................................................................................283
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PrefaceTis book provides an overview of the field of quality, the importance of
quality in todays competitive global economy, and one of the major tools
used to manage and improve quality of products and servicesstatistical
process control (SPC). In this book, we explore quality programs used in
industry today with a focus on SPC. We discuss one of the major quality
and process improvement tools known as control charts. Computerizedapplication, and implementation of various control charts. is one of the
major focuses of this text. SPC is a part of overall quality programLean
Six Sigma.
Quality is a discipline that focuses on product and service excellence.
Both manufacturing and service companies have quality programs. Te
quality is closely related to the variation in both products and processes.
Variation is an inherent part of products and processes that createthese products and services. For example, no two parts produced by a
production process are the same, and no machine can dispense exactly
the same amount of beverage in two cans. Tis is because of the vari-
ation. You may recall that statistics is the tool that allows us to study
variation. Most of the quality programs are data driven and almost all
data show variation that can be studied using statistics. One of the major
objectives of the quality programs is to reduce the variation in productsand processes to the extent that the likelihood of producing a defect
is virtually nonexistent. Tis means improving quality and meeting or
exceeding customers expectations.
Tere is a close relationship between quality, profitability, and market
share. Quality is achieved through customers perception; therefore,
organizations must understand customer needs and expectations in
order to meet and exceed them. Customer needs and expectations can
be achieved through quality improvement. Quality is important to the
consumers. In todays highly competitive and global economy, a company
cannot survive and stay in business unless they are able to provide high
quality products and services. Improving quality can help organizations
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x PREFACE
increase their market share and profitability. Te improved quality and
reliability in products and services lead to higher perceived value and
increased market share for a company. Tis leads to increased revenue
and profitability.
Tis book provides a comprehensive coverage of quality. We first
explore what is quality before discussing various statistical tools and
methods that are used to monitor and improve the quality of products
and services. We explain the term quality from the perspective of a
manufacturer, a design engineer, a service provider, and the end user of a
product or servicethe customer.
Quality has been defined from several perspectives. For example,
quality may have a different meaning to the engineer who designs the
product, or to the manufacturer involved in the production of a product.
Although we define quality from many different perspectives, the final
judge of the product or service quality is the customer, and therefore,
quality is the customers perception of the degree to which the product or
service meets his or her expectations.
Te book begins with an introductory chapter where we explain
quality, dimensions of quality, and its importance in this highly
competitive global economy. Tis chapter also discusses the quality costs
and costs of poor quality. Quality is important, because qualityboth
good and badcosts money. Tere is a cost involved with improving
the quality of products and services; because, poor quality can signifi-
cantly affect an organizations competitiveness and market share. In his
book Quality is Free, Phillip Crosby has described quality costs or thecosts of quality as having two components: (1) costs of good quality
(or the cost of conformance), and (2) costs of poor quality (or the cost
of nonconformance). We will explore the costs of poor quality and its
impact on the organizations in the first chapter.
o improve quality, it is important to have an understanding of
systems and processes. A system converts inputs into useful products
or services through a conversion process. Te products or services arethe output of the system. Quality is concerned with the variation in the
output of a system or the products and the processes of the system. Te
quality of the products and services are improved by reducing the defects
and variation. Quality is inversely proportional to the variation in the
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PREFACE xi
products and processes. Tis means that as the variation is reduced and
controlled, significant improvement in quality can be achieved. Te
quality programs including otal Quality Management (QM), Six
Sigma, and Lean Six Sigma all focus on quality improvement by reducing
variation and removing waste from the system. Almost all types of orga-
nizations and systems have two things in common: waste and variation.
Te quality programs focus on removing the waste and reducing variation
and defects to improve quality.
While a complete coverage of the quality programs is beyond the
scope of this book, we devote a chapter describing these programs. We
also provide sufficient statistical background for the reader to understand
the principles of quality in a separate chapter.
In the remaining chapters of the book, we turn our attention to SPC
and control charts. Tese are graphical tools for monitoring the process,
identifying the causes of process variation, and taking necessary actions to
control and improve the process. Before going into the details of control
charts and their applications, we explain the run chart, a tool used to
describe the variation of the process output in the form of a time series
plot. Te run charts are an excellent way of understanding the variation
and pattern of variation in the process.
Te chapters on the run chart is followed by chapters on fundamentals
of control charts, why and how control charts work, control charts
for variables, computerized applications of control charts, additional
SPC techniques for variables, control charts for attributes, and process
capability analysis.
Who Can Benefit from This Book?
SPC is an integral part of quality improvement program in industries.
Tis book provides an overview of one of the major tools used to manage
and improve quality of products and services. Te topics are dealt with
in a concise and simple to understand format. Troughout the book,we emphasize the computer applications and implementation of quality
programs in the real world. Te book is unique in the sense that it shows
the importance of SPC, and its place, in overall quality improvement pro-
grams. Te reader is also provided with necessary statistical background
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xii PREFACE
to understand the subject matter and is introduced to quality programs
used in industry today. Computerized application and implementation of
various SPC tools is one of the major focuses of this text.
Tis book fills a gap in this area by showing the readers comprehensive
and step-wise solutions to model process quality and solve quality prob-
lems. Where applicable, we provide data files, computer instructions,
computer output, and interpretation of results.
Tis book is written with a wide audience in mind both managers and
future professionals. Also, undergraduate and graduate data analysis and
statistics students and MBAs, as well as audience in engineering taking a
course in quality and process control will find the book to be useful.
Six Sigma professionals and those implementing Six Sigma in their
companies will find the book to be very useful. Te quality professionals
and particularly those implementing Six Sigma quality in their companies
will find the book to be a valuable resource.
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AcknowledgmentsI would like to thank the reviewers who took the time to provide excellent
insights which helped shape this book.
I would especially like to thank Mr. Karun Mehta, a friend and
engineer. His expertise and tireless efforts in helping to prepare this text
is greatly appreciated.
I would like to thank Dr. Roger Lee, a senior professor and colleaguefor administering invaluable advice and suggestions.
Tanks to all of my students for their input in making this book
possible. Tey have helped me pursue a dream filled with lifelong learning.
I am indebted to senior acquisitions editor, Scott Isenberg; director of
production, Sheri Dean; marketing manager, Charlene Kronstedt; and all
the reviewers and collection editors for their counsel and support during
the preparation of this book. I acknowledge the help and support ofExeter Premedia ServicesChennai, Indiateam for reviewing and editing
the manuscript.
I would like to thank my parents who always emphasized the
importance of what education brings to the world. Lastly, I would like to
express a special appreciation to my wife Nilima, to my daughter Neha
and her husband David, my daughter Smita, and my son Rajeev for their
love and support.
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CHAPTER 1
Introduction to Quality
Quality as a Field
Tis chapter provides an overview of the field of quality, the importance
of quality in todays competitive global economy, and statistical processcontrol. Te chapter explores these topics and shows how various statistical
tools can be used in improving the quality of the products and services.
Quality is a discipline that focuses on product and service excellence.
Both manufacturing and service companies have quality programs.
Quality is closely related to the variation in both products and processes,
and statistics is the tool that allows us to study variation. Most of the
quality programs are data driven and almost all data show variation
that can be studied using statistics. One of the major objectives of the
quality programs is to reduce the variation in the product and process
to the extent that the likelihood of producing a defect is virtually
nonexistent. Tis means improving quality and meeting or exceeding
customers expectations. Te improved quality and reliability in products
and services lead to higher perceived value and increased market share,
thereby, increasing revenue and profitability.
Before discussing various statistical tools and methods that are used to
monitor and improve the quality of products and services, we explain the
term qualityand outline many different ways quality has been defined.
Some of the definitions of quality are presented here.
Quality Defined
Quality means different things to different people. Terefore, quality canbe defined from several different perspectives. From the perspective of
the customer or the end user of the product or service, the quality of a
product or service is the customers perception of the degree to which
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2 MANAGING AND IMPROVING QUALITY
the product or service meets his or her expectations. Tis also means that
the quality of a product or service can be determined by the extent to
which the product or service satisfies the needs and requirements of the
customers. Tis definition is a customer-driven quality approach that
aims at meeting or exceeding customer expectations.
Quality has also been defined from several other perspectives. For
example, quality may have a different meaning to the engineer who
designs the product, or to the manufacturer involved in the production
of a product. Tus quality can be defined from the perspective of the
manufacturer or the designer. Quality has a transcendental definition and
can also be product based, user based, manufacturing based, and value
based (Garvin). Following are some of the other ways quality has been
defined:
Transcendent: Quality is something that is intuitively
understood but nearly impossible to communicate, such as
beauty or love.
Product-based: Quality is found in the components andattributes of a product.
User-based: If the product or service meets or exceeds
customers expectations, it has good quality.
Manufacturing-based: If the product conforms to design
specifications, it has good quality.
Value-based: If the product is perceived as providing good
value for the price, it has good quality.
Quality has also been defined as:
Meeting or exceeding customer expectation
Fitness for intended use
Conformance to specifications
Inversely proportional to variation otal customer service and satisfaction
Te degree or standard of excellence of something
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INTRODUCTION TO QUALITY 3
Tese definitions of quality show that although we can define quality
from many different perspectives, the final judge of the product or service
quality is the customer, and therefore, quality is the customers perception
of the degree to which the product or service meets his or her expectations.
Dimensions of Quality
Te dimensions of quality specify the characteristics the product or
service should possess in order to be high quality. Garvin has identified
eight dimensions of quality described here. Tese dimensions describe
the product quality that is critical to developing high quality products
or services. Te recognition of these dimensions by the management and
the selection of these dimensions along which the business will compete
is critical to business success.
1. Performance: Will the product do the job?
2. Features or added features: Does it have features beyond the basic per-
formance characteristics?3. Reliability: Is it reliable? Will it last a long time?
4. Conformance: Does the product conform to the specifications? Is the
product made exactly as the design specified?
5. Serviceability: Can it be fixed easily and cost effectively?
6. Durability: Can the product tolerate stress without failure?
7.Aesthetics: Does it have sensory characteristics such as taste, feel,
sound, look, and smell?8. Perceived quality: What is the customers opinion about the product
or service? How customers perceive the quality of the product or
service?
Importance of Quality
Tere is a close relationship between quality, profitability, and marketshare. Quality is achieved through customers perception, therefore,
organizations must understand customer needs and expectations to meet
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4 MANAGING AND IMPROVING QUALITY
and exceed them. Customer needs and expectations can be achieved
through quality improvement. Quality is important to the consumers.
In todays highly competitive and global economy, a company cannot
survive and stay in business unless they are able to provide high quality
products and services. Figure 1.1 shows how improving quality can help
organizations increase their market share and increase profitability.
Costs of Quality and Costs of Poor Quality
Quality is also important because the qualityboth good and badcosts
money. Tere is a cost involved with improving the quality of products
and services, because poor quality can significantly affect an organizations
competitiveness and market share. In his book Quality is Free, Phillip
Crosby has described quality costs or the costs of quality (COQ) as having
two components: (1) costs of good quality (or the cost of conformance)and (2) costs of poor quality (or the cost of nonconformance). Tese are
shown in Figure 1.2.
Te focus of many quality programs is to reduce the cost of poor
quality. Since the cost of poor quality is significant, reducing this cost will
lead to increased revenue and improved productivity. A quality program
should be focused on preventing poor quality. A prevention system is
focused on preventing the poor quality and is far superior to a detectionsystemthat detects the defects and nonconformities in the products after
they are produced.
Figure 1.1 Quality, profitability, and market share
Improvement in
products/service
quality
Higher perceivedvalue by customers
Increased market
share
Claim higher prices
Increase revenue
Increase profitsMeet and exceed
customer
expectations
Lower overall costs,
improve productivity
Reduce cost of
poor quality
Reduced defects,
minimize waste,
improve cycle time
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INTRODUCTION TO QUALITY 5
Figure 1.2 Costs of quality
Costs of quality
Appraisal costs
Costs of poor
qualityExternal failure
costs
External failurecosts
Internal failure
costs
Costs of good
quality
Te major components of costs of good qualityprevention costs
and appraisal costs, and the costs of poor qualityinternal failure and
external failure costs, are explained in able 1.1.
Detection Versus Prevention Quality Systems
Figure 1.3 shows the quality costs under detection and prevention systems
(Griffith 2000). Te costs under the detection system are similar to the
costs that are measured for the first time in a company that has no formal
quality prevention system in place. In the detection system, the costs of
internal failure (e.g., scrap, rework, repair, and retest) are almost equal to
the appraisal costs (e.g., inspection, testing, and auditing). Te internal
failure and appraisal costs tend to increase simultaneously. Since no or
little prevention efforts are in place, more inspection is performed thatfinds more defects. On the other hand, as more defects are produced,
more inspection is required. In a detection system, the external failure
costs are small because of high inspection. Te prevention costs are also
small in a detection system.
A prevention quality system focuses on preventing failures and
defects. Several companies have reported significant reduction in cost of
poor quality through Six Sigma quality, which is a prevention qualityprogram.
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6 MANAGING AND IMPROVING QUALITY
Prevention cost
Attempts to prevent poor quality from
being produced. These costs include:
Quality planning and engineering
Product and process design
Process control
New product review
Manufacturing engineering tasks
Quality Training
Vendor relations
Variability analyses
Design reviews and manufacturing
planning
Designing equipment and processes to
measure and control quality
Appraisal costs
Related to functions that appraise or
evaluate. These are the cost of:
Inspection and testing of incoming
material
Inspection and testing of products
Staffing inspectors and supervisors
Maintaining the accuracy of test
equipment
Maintaining test or inspection records
Performing audits and field tests
Internal failure cost
Related to failure or nonconformance that
occurs in-house. These costs include the
cost of:
Scrap Repairs
Rework Failure analysis
Retest Downtime Loss in profit due
to substandard
product
External failure cost
Related to failures or nonconformance
in the customers facility. These costs
include:
Returned products or material that
must be inspected, reworked, or
scrapped Customer complains
Cost of testing, legal services,
settlements
Other costs related to product liability
Customer dissatisfaction (not directly
measurable)
Table 1.1 Quality costs
Systems and Processes
Te quality methods and tools are applied to the systems and the processes
that make the systems. Te system and the processes within the system are
Figure 1.3 Quality costs: Detection system versus prevention system
(a) Quality costs in a detection system, (b) Quality costs in a
prevention system
Internal failure
Appraisal
(a) (b)
PreventionExternal failure
Quality costs under detection system
(costs measured the first time)
PreventionAppraisal
Internal failureExternal failure
Quality costs under prevention system
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INTRODUCTION TO QUALITY 7
responsible for creating the products or services. Terefore, it is important
to understand the systems and the processes.
Systems
A system usually consists of a group of interacting, interrelated, or
interdependent processes forming a complex whole. Tus a system is
a collection of processes with a specific mission or purpose. Figure 1.4
shows the model of a basic system. A process can be viewed as a part of
a system.
Some examples of systems are electronic manufacturing or food
processing companies which produce electronic or food products. Such
systems are usually a collection of interacting or interrelated processes;
for example, both the electronic manufacturing and food processing
plants may consist of a number of departments including manufactur-
ing engineering, marketing, design engineering, sales, transportation,
warehousing, finance and accounting, and distribution systems.
All these departments can be viewed as processes. In manufacturingor food processing companies, the raw materials are converted into useful
products, which are outputs. Such systems as shown in Figure 1.4 have a
feedback through which the companies receive information about their
products from the customers and market. Tis information is helpful in
changing or modifying their processes and products to adapt to the needs
and requirements of their customers.
Te other types of systems are the service systems. Tese systems existto provide various types of services to their customers. Examples of such
systems are education institutions, government organizations, technical
call centers, health care organizations, hospitals, and insurance companies.
Tese systems also consist of a number of processes and provide services
Figure 1.4 A basic system
System
InputSupplier
Feedback
Output Customer
Process 1
Process 4
Process 2 Process 3
Process k
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8 MANAGING AND IMPROVING QUALITY
through the collection of processes. Te outputs of the service systems are
usually intangible.
Processes
In many cases, the focus of statistical analysis has been to draw conclusions
or make decisions about the population using the sample data. Te
other aspect of statistical analysis is to study and reduce the variation
in the products or processes studied using data. Statistics and statistical
methods enable us to study variation in the processes. Almost all data
show variation and controlling or minimizing variation in products and
processes lead to improved product quality. Te variance in a process
is an important measure of the quality of the products and processes.
A large variation in any product, process, or both is not desirable and is
an indication that the process be improved by finding ways to reduce the
process variance. As variation in the products and processes is reduced,
the product or the process becomes more consistent. Terefore, one of the
major objectives of quality programs like Six Sigma is to reduce variationin product, process, or service.
In this text, we will study how the variations in the processes affect the
product quality. o study this, we will explore the relationship between
the variation and product quality, and the statistical tools that are used to
study, monitor, and control the variation. Tis area comes under statisti-
cal process control.
Since the quality of products and services is related to the variationin products and the processes that create the products, we will first
define and study the processes. A process can be a chemical process, or
a manufacturing process. Te processes in general use the inputs that go
through a transformation to produce outputs or useful products.
Any organization, or any of its parts, can be viewed as a process.
A process is a transformation of inputs into outputs. Some examples of
processes include electronic and appliance manufacturing processes,computer and car assembly lines, and chemical processing plants.
A process in its simplest form is shown in Figure 1.5.
A process usually consists of a sequence or network of activities that
depicts the flow of the complete procedure required to transform the
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INTRODUCTION TO QUALITY 9
inputs into outputs (useful product or service). Te transformation is
achieved by flows through network of activities that are performed by
various resources. Figure 1.6 shows an input output process.
Outputs of Processes and Variation
Te processes, as discussed earlier, take inputs and convert them into
outputs using some type of transformation process. Systems, on the other
hand, may consist of a number of processes. It is important to note the
following characteristics of the system outputs and the outputs producedby the processes of the system:
1. Te outputs of the process always vary.
2. Te products produced by the same processes are different. Tis
means that no two products are identical and the measured quality
characteristic of products vary. For example, the volumes of two
beverage cans labeled 16 oz. are not exactly the same; the two tiresthat are 13.0 inches in radius are not both exactly the same radius.
Figure 1.7 shows the measurements of the diameters of a 13.0-inch
radius tires that are manufactured by the same process. Te radius
in this case is a critical quality characteristic of the product or the
Figure 1.5 A process in its simplest form
InputsProcess
Outputs
Figure 1.6 An input-output process
Inputs
Machine
material
people
energy
informationmethods
Process
Sequence of activities/operations
A B
E
C
D F
IG H
Outputs
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10 MANAGING AND IMPROVING QUALITY
output. Notice how the measured radius varies from product to
product (the last block in Figure 1.7 that shows the measured values
of several products). Similarly, the computers and calculators made
by the same processes are not exactly the same. Although the products
look alike, they always vary in critical quality characteristics. Te
variation in many cases is not noticeable. Te variations in product
characteristic do not affect the functionality as long as the variation
is within a certain limit.
3. Variation is an inherent characteristic in products and processes.
As long as the variation in products and processes that produce
these products is within certain limit, the product is acceptable. Whenthe variation increases beyond the desired or set limits, the product
quality, functionality, and reliability are affected. Tis is the reason why
the variation in the products and processes must be monitored and
controlled. Te variation in the products and processes can be studied
using statistical tools.
Sources of Variation in Products and Processes
Te major sources of variation in the products and processes are attributed
to the following factors:
1. Materials
2. Men (Operator)
3. Machines
4. Methods
5. Measurement
6. Environment
Tese sources of variation are shown in Figure 1.8(a) and (b) where
(a) shows the general categories that are common sources of variation
Figure 1.7 Variation in quality characteristic (diameters of tires)
Input Output D
iameter
Variation in quality
characteristic
Measure several
diameters (quality
characteristic) andplot
Transformation
process
Plot of diameter
1 5
6
7
8
9
10
51510 20 25 30 35 40
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INTRODUCTION TO QUALITY 11
and (b) shows the details. Note that all categories may not apply to allproducts or services.
In the rest of the chapter, we will see how the variation in the products
and processes are studied, measured, and controlled.
Measuring Variation
Te variation in the data is measured using the variance and standard
deviation. Te Greek letter 2 (read as sigma-squared) represents the
variance of a population data and represents the standard deviation.
Te corresponding symbols for the variance and standard deviation of a
sample data are s2and s. Te standard deviation is a measure of spread
or deviation around the mean as shown in Figure 1.8(c). We may have
two or more sets of data all having the same average, but their spread
or variability may be different. Tis is shown in Figure 1.8(d). It can be
seen from this figure that the data sets A and B have the same mean but
different variationscurve B has less spread or variability than curve A.
Te more variation the data has, the more spread out the curve will be.
We may also have a case where two sets of data have the same variation
but different mean.
Figure 1.8(a) Sources of variation in products and processes
Machine Materials
PeopleMeasurement Environment
Methods
Measured qualitycharacteristic (output)
Figure 1.8(b) Sources of variation in products and processes
Machines
Suppliers
Sources of variation in a process
Material quality
Operators Methods
Critical quality
characteristics
Inspectors and
inspection methods
Measurement
systems
Inspection methods
Environment
OUTPUTSPROCESSINPUTS
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12 MANAGING AND IMPROVING QUALITY
Te variation in the data can also be plotted using a graph. Suppose
that the average time to assemble a product is 4.0 minutes. Te average
assembly time for all the products is not going to be exactly 4.0 minutes.
Tis means that the assembly time will vary from product to product.
Figure 1.8(c) The measure of variationstandard deviation
Mean ()
Figure 1.8(d) Data sets A and B with same mean but different
variation
A
B
Figure 1.8(e) Plot showing the variation in assembly time
2
Observation
Time
Variation in assembly time (minutes)
3.0
3.5
4.0
4.5
5.0
4 6 8 10 12 1 4 16 1 8 20 22 24 26 28 30
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INTRODUCTION TO QUALITY 13
Te variation in the assembly time can be studied using a graph that is
shown in Figure 1.8(e). Tis graph shows the assembly time of a sample
of 30 products. Note how the assembly time varies around the average of
4.0 minutes.
Summary
Tis chapter provided an overview of the field of quality, various ways
quality has been defined, and the importance of quality in todays
competitive global economy. Quality is a discipline that focuses on productand service excellence. Both manufacturing and service companies have
quality programs. Quality is closely related to the variation in both
products and processes, and statistics is the tool that allows us to study
variation. Most of the quality programs are data driven and almost all
data show variation. One of the major objectives of the quality programs
is to reduce the variation in the product and process to the extent that
the likelihood of producing a defect is virtually nonexistent. Tis means
improving quality and meeting or exceeding customers expectations.
Te chapter described the dimensions of product quality. Tese are the
characteristics that the product and service should possess in order to be
of high quality. Te COQ were also discussed. Cost of poor quality is a
significant percent of the sales dollars in companies. Reducing these costs
leads to improved quality, higher perceived value by the customer, and
increased market share. Te chapter emphasized on the importance of
prevention quality programs like Six Sigma and Lean Six Sigma quality
programs. Tese programs have been applied with tremendous success
in a large number of companies. Te tools of quality are applied to sys-
tems and processes within the systems. Tese systems and processes are
responsible for creating goods and services. Te chapter provided an
overview of the systems and processes. Finally, the sources of variation
in products and processes were discussed and it was shown that there is
always a variation when we measure the critical quality dimensions. Notwo products are exactly the same. Tere is always some degree of varia-
tion in them. Quality is all about studying, reducing, and controlling the
variations to improve product or service quality.
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Index
assignable cause variations, 155157,238
assignable variation, 138139attribute charts, 267attribute control charts, 209
c-chart, 229234npchart, 226229
p-chart, 210226
background noise, 138bell-shaped distribution, 63box plot, 64
applications, 7071five-number summary, 6770of utility bill data, 69
business strategy, 21
capability indexesprocess capability using, 252257
capable process, 49categorical data, 41cause-and-effect diagram, 270, 271c-chart, 268. See alsonpchart;p-chart
construction and application,231234
development, 230
examples, 229Poisson distribution, 230steps for constructing, 230231
center line (CL), 158, 160central limit theorem, 96, 101103
in xchart, 169170chance causes of variation, 155class frequency, 44class intervals, 4445common cause variations, 238
confidence intervals, 103, 104estimation, 106interpretation, 106107for mean, 107110for population mean, 109for population proportion, 110
population standard deviation and,110
for population variances, 109for standard deviations, 109for variance, 107109
Constants for Control Chart,176178, 180, 184, 195
consumers risk, 120continuous data, 4142continuous probability distributions,
7677continuous random variable, 7376control charts. See alsoRchart; xchart
attribute, 163164attribute charts, 267for attributes, 209
cause-and-effect diagram, 270, 271c chart, 268centerline and control limits,
revising, 203208constructing and analyzing,
194199continued process monitoring,
199203cusum chart, 267definition, 157158
example, 158and hypothesis testing, 162163implementation, 273for individual measurements,
164166for individual values and moving
range, 266mean, 267median, 266for monitoring process mean,
167170moving average chart, 267npcharts, 267268out-of-control process, 188194Pareto chart, 270272pattern of variation, 188
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284 INDEX
process capability using, 248252process in control, 187188standard deviation, 267
statistical basis of, 159160three-sigma limits in, 160162types of, 163164uchart, 268variables, 163164, 266
control limits, 155, 237238costs of quality (COQ), 46critical quality characteristics (CQs),
20, 34, 36customer-focused approach, 21
cusum chart, 267
dataclassification of, 4142collection and presentation of, 42numerical measures to
summarizing, 5462organizing, 4248
data array, 44
defective products, 210Defect per Unit (DPU), 27defects per million opportunities
(DPMO), 26Define, Measure, Analyze, Design,
and Verify (DMADV)process, 3536
Define, Measure, Analyze, Improve,and Control (DMAIC)model, 29, 30
degrees of freedom, 110descriptive statistics, 3940of utility bill data, 68
Design for Six Sigma (DFSS), 1820,3437
in product life cycle, 3738detection quality systems, 46DFSS. SeeDesign for Six Sigmadiscrete data, 41discrete random variable, 7273
dispersionmeasures of, 5759
DMADV process. SeeDefine,Measure, Analyze, Design,and Verify process
DMAIC model. SeeDefine, Measure,Analyze, Improve, andControl model
DPMO. Seedefects per millionopportunitiesDPU. SeeDefect per Unit
empirical rule, 77equal width, 44estimation
confidence interval, 106110interval, 105106point, 105
review of, 103types of, 104
fencesinner, 70outer, 70
five measure summary, 64frequency distribution, 42, 4448
grouping, 42, 44
hingeslower, 69upper, 69
histogram, 47applications in quality, 4852detecting shift and the variation,
4849evaluating process capability using,
4952with fit and groups, 49, 52of lifetime data, 48process capability using, 246248
hypothesis testing, 103, 116117control chart and, 162163definition, 117for equality of two means, 128133formulating, 121123left-sided test, 122
for paired samples, 134135at 5 percent level of significance,
119120rejection and nonrejection areas,
120
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INDEX 285
right-sided test, 122123single population mean, 117125two-sided test, 123124
using the p-value approach,126128
Identify, Design, Optimize, andValidate (IDOV) process, 36
IDOV process. SeeIdentify, Design,Optimize, and Validateprocess
inferential statistics, 40tools of, 103104
instant-time method, 171interference problems, 40, 103interval estimate, 104106
just-in-time manufacturing, 31
lean manufacturing, 31Lean Sigma, 1820Lean Six Sigma, 3032
lean vs.Six Sigma, 3234lower class boundary, 44lower class limit, 44lower control limit (LCL), 157, 160
manufacturing-based quality, 2manufacturing process, 31margin of error, 104market share, 4matched sample test, 134
meancalculating, 5556confidence intervals for, 107110control chart, 267and standard deviation, 6364
measures of dispersion, 5759measures of position, 6465measures of variation, 5759median
calculating, 5657
control chart, 266methodology, 21MINIAB
attribute control charts in, 269pattern-analysis in control charts,
193
quality tools using, 270272special causes in control chart, 193variable control charts in, 269
moving average chart, 267
nondefective products, 210nonrandom variation, 156normal distribution, 63, 75, 7778,
161npchart, 226229. See alsoc-chart;
p-chartnp charts, 267268numerical methods, to summarizing
data, 5462
operating characteristic (OC) curve,163
ordered array, 42, 44out-of-control process, 188194
paired-test, 134parameters, 40
Pareto chart, 270272parts per million defective (PPM), 26p-chart, 209. See alsoc-chart; npchart
analyzing and interpreting,217218
center line, 211212chip manufacturing process, 221construction and application,
215222control limits, 211212
defective chips, 220defective microchips, 218defective motors, 215development, 210211general structure of, 212implementation, 226modification, 222rationale behind, 210sample proportion nonconforming,
211
sample size for, 212213special causes in, 218steps for constructing, 213214tests for special causes, 221for variable subgroup size, 222226
percentiles, calculating, 6567
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286 INDEX
percent nonconforming, noncenteredprocess, 2728
period-of-time method, 172
point estimate, 104, 105population mean, 40, 55confidence intervals for, 109
population parameters, 40, 9596,116
population proportion, 40confidence interval for, 110
population standard deviation, 40and confidence intervals, 110
population variances, 40
confidence intervals for, 109PPM. Seeparts per million defectiveprevention quality systems, 46probability density function, 7476probability distributions, 144
defining, 71and random variable, 7276
process, 89in-control, 218out-of-control, 217
outputs, 910sources of variation in, 1011
process capabilityapplications, 239assessing, 240245graphically assessing, 241245measurement and analysis, 239numerical measure, 246Six Sigma spread as, 240station, 239240using capability indexes, 252257using control charts, 248252using histogram, 246248using statistical package, 258262
process variationchance and assignable causes of,
155157change in process, 146, 151measuring, 138144
output variable, 144146producers risk, 120product-based quality, 2products, sources of variation in,
1011
profitability, 4project based approach, 21
qualitative data, 41qualitycosts of, 46definitions, 13detection vs.prevention systems, 5dimensions, 3as field, 1history of, 15, 16importance, 34and percent nonconforming, 2728
poor quality costs, 46processes, 89systems, 78tools, 270
Quality is Free(Crosby), 45quantitative data, 41, 64quartiles
calculating, 6567lower, 69middle, 69
upper, 69
random variableprobability distributions and,
7276random variation, 138, 156rational subgroups, 171raw data, 43Rchart. See alsocontrol charts; xchart
centerline for, 174177, 179181,185187, 195199
constructing and analyzing,182187
control limits for, 174177,179181, 185187, 195199
data collection, 173174general from of, 180monitoring variation, 178187out-of-control points, 205
quality characteristic for, 170171sample size for, 171173shaft diameter, 197, 198subgroups for, 171173summary of steps, 181182
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INDEX 287
summary of steps for, 177178for variable, 170178
run chart, 137144
output variable characteristics,144146patterns, 146152
sample mean, 40, 55, 100101mean and standard deviation of, 99sampling distribution of, 97100
sample median, 40sample proportion
sampling distribution of, 97
sample size determination, 111116sample size requirement, 104sample standard deviation, 40
calculating, 62sample statistics, 40, 95, 103, 104sample variance, 40, 5960
calculating, 6061sampling distribution, 96100
process of, 97of the sample mean, 97100
of sample proportion, 97sigma, 18single population mean
testing, 117125Six Sigma, 1820
business success of, 2223current trends, 23DMAIC model, 29, 30lean vs.,3234methodology, 29metrics and measurements in, 26objective of, 2022phases of, 30in product life cycle, 3738Quality Digestsurvey, 22service successes of, 28spread as process capability, 240statistical basis of, 2425three-sigma process vs.,22
and QM, 17specification limits, 238239standard deviation, 18, 61, 100101
mean and, 6364standard deviation control chart, 267standard deviations
confidence intervals for, 109standard error, 100101, 104standard normal distribution, 7881
statistical inference, 96, 104statistical methodscategories, 3940data
classification of, 4142collection and presentation of,
42numerical methods to
summarizing, 5462organizing, 4248
histogram, 47applications in quality, 4852detecting shift and the variation,
4849evaluating process capability
using, 4952with fit and groups, 49, 52of lifetime data, 48
numerical methods of describingdata, 5462
stem-and-leaf plots, 5254statistical package, process capability
using, 258262statistical process control, 152, 265
computer applications, 268269stem-and-leaf plots, 5254symmetrical distribution, 63systems, 78
three sigma control limits, 237
three-sigma limits, in control charts,160162
three-sigma process, 24time series plot, 137tolerance limits, 238total quality management (QM)
approach, 1517transcendent quality, 2two population means
hypothesis testing for, 128133
uchart, 268uncontrolled variation, 156ungrouped data, 4344upper class boundary, 44
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288 INDEX
upper class limit, 44upper control limit (UCL), 157, 160user-based quality, 2
value-based quality, 2variables, 43
control chart, 266xand Rchart for, 170178
variance, confidence intervals for,107109
variation, 137assignable cause of, 155assignable/special causes, 138139
calculating, 6162chance/random causes of, 155detecting in processes (Seeprocess
variation)measures of, 5759measuring, 1113outputs, 910in products and processes, 1011
voice of customer (VOC), 20, 34, 36
whiskers, 70
xchart. See alsocontrol charts; R chart
centerline for, 174177, 184185,195Central Limit Teorem in,
169170constructing and analyzing,
182187control limits for, 174177,
184185, 195data collection, 173174out-of-control points, 205
process mean monitoring, 167170quality characteristic for, 170171sample size for, 171173shaft diameter, 198, 199shaft manufacturing process, 197structure, 168169subgroups for, 171173summary of steps for, 177178for variable, 170178