An Introduction to Acceptance Sampling and SPC with R

John Lawson

• Publisher: Chapman and Hall/CRC
• Year: 2021
• Print ISBN: 9780367569952
• eBook ISBN: 9781000336757
• Topic: Business
• Subtopic: Operations
• Index: Business

An Introduction to Acceptance Sampling and SPC with R is an introduction to statistical methods used in monitoring, controlling and improving quality. Topics covered include acceptance sampling; Shewhart control charts for Phase I studies; graphical and statistical tools for discovering and eliminating the cause of out-of-control-conditions; Cusum and EWMA control charts for Phase II process monitoring; and the design and analysis of experiments for process troubleshooting and discovering ways to improve process output. Origins of statistical quality control and the technical topics presented in the remainder of the book are those recommended in the ANSI/ASQ/ISO guidelines and standards for industry. The final chapter ties everything together by discussing modern management philosophies that encourage the use of the technical methods presented earlier.

In the modern world sampling plans and the statistical calculations used in statistical quality control are done with the help of computers. As an open source high-level programming language with flexible graphical output options, R runs on Windows, Mac and Linux operating systems, and has add-on packages that equal or exceed the capability of commercial software for statistical methods used in quality control. In this book, we will focus on several R packages. In addition to demonstrating how to use R for acceptance sampling and control charts, this book will concentrate on how the use of these specific tools can lead to quality improvements both within a company and within their supplier companies.

This would be a suitable book for a one-semester undergraduate course emphasizing statistical quality control for engineering majors (such as manufacturing engineering or industrial engineering), or a supplemental text for a graduate engineering course that included quality control topics.

1

Introduction and Historical Background

Statistical Quality Control includes both (1) the application of statistical sampling theory that deals with quality assurance and (2) the use of statistical techniques to monitor and control a process. The former includes acceptance-sampling procedures for inspecting incoming parts or raw materials, and the latter (often referred to as statistical process control or SPC) employs the use of control charts, continuous improvement tools, and the design of experiments for early detection and prevention of problems, rather than correction of problems that have already occurred.

1.1 Origins of Statistical Quality Control

Quality control is as old as industry itself, but the application of statistical theory to quality control is relatively recent. When AT&T was developing a nationwide telephone system at the beginning of the 20th century, sampling inspection was used in some form at the Western Electric Company (the AT&T equipment manufacturing arm). Also, according to an article in the General Electric Review in 1922, some formal attempts at scientific acceptance sampling techniques were being made at the G.E. Lamp Works.

At Western Electric, an Inspection Engineering Department was formed, which later became the Quality Assurance Department of the Bell Telephone Laboratories. In 1924, Walter Shewhart, a physicist and self-made statistician, was assigned to examine and interpret inspection data from the Western Electric Company Hawthorn Works. It was apparent to him that little useful inference to the future could be drawn from the records of past inspection data, but he realized that something serious should be done and he conceived the idea of statistical control. It was based on the premise that no action can be repeated exactly. Therefore, all manufactured product is subject to a certain amount of variation that can be attributed to a system of chance causes. Stable variation within this system is inevitable. However, the reasons for special cause variation outside this stable pattern can (and should) be recognized and eliminated.

The control chart he perceived was founded on sampling during production rather than waiting until the end of the production run. Action limits were calculated from the chance cause variation in the sample data, and the process could be immediately stopped and adjusted when additional samples fell outside the action limits. In that way, production output could be expected to stay within defined limits.

The early dissemination of these ideas was limited to the circulation of memos within the Bell Telephone System. However, the soundness of the proposed methods was thoroughly validated by staff at Western Electric and the Bell Telephone Laboratories. The methods worked effectively and were soon made part of the regular procedures of the production divisions. Shewhart’s ideas were eventually published in his 1931 book The Economic Control of Quality of Manufactured Product [86].

W. Edwards Deming from the U.S. Department of Agriculture and the Census Bureau, who developed the sampling techniques that were first used in the 1940 U.S. Census, was introduced to Shewhart in 1927. He found great inspiration in Shewhart’s theory of chance (that he renamed common) and special causes of variation. He realized these ideas could be applied not only to manufacturing processes but also to administrative processes by which enterprises are led and managed. However, many years later in a videotaped lecture Deming said that while Shewhart was brilliant, he made things appear much more difficult than necessary. He therefore spent a great deal of time copying Shewhart’s ideas and devising simpler and more easily understood ways of presenting them.

Although Shewhart’s control charts were effective in helping organizations control the quality of their own manufacturing processes, they were still dependent on the quality of raw materials, purchased parts and the prevailing quality control practices of their suppliers. For these reasons, sampling inspection of incoming parts remained an important part of statistical quality control.

Harold F. Dodge joined Western Electric Corporation shortly after Shewhart did. He wondered, “how many samples were necessary when inspecting a lot of materials”, and began developing sampling inspection tables. When he was joined by Harry G. Romig, together they developed double sampling plans to reduce the average sample size required, and by 1927 they had developed tables for rectification inspection indexed by the lot tolerance and AOQL (average outgoing quality level). Rectification sampling required removal of defective items through 100% inspection of lots in which the number defective in the sample was too high. Dodge and Romig’s sampling tables were published in the Bell System Technical Journal in 1941 [22].

The work of Shewhart, Dodge and Romig at Bell Telephone constituted much of the statistical theory of quality control at that time. In the 1930s, the Bell System engineers who developed these methods sought to popularize them in cooperation with the American Society for Testing and Materials, the American Standards Association, and the American Society of Mechanical Engineers. Shewhart also traveled to London where he met with prominent British statisticians and engineers.

Despite attempts to publicize them, adoption of statistical quality control in the United States was slow. Most engineers felt their particular situation was different and there were few industrial statisticians who were adequately trained in the new methods. By 1937, only a dozen or more mass production industries had implemented the methods in normal operation. There was much more rapid progress in Britain, however. There, statistical quality control was being applied to products such as coal, coke, textiles, spectacle glass, lamps, building materials, and manufactured chemicals (see Freeman[28]).

1.2 Expansion and Development of Statistical Quality Control during WW II

The initial reluctance to adopt statistical quality control in the United States was quickly overcome at the beginning of World War II. Manufacturing firms switched from the production of consumer goods to defense equipment. With the buildup of military personnel and material, the armed services became large consumers of American goods, and they had a large influence on quality standards.

The military had impact on the adoption of statistical quality control methods by industry in two different ways. The first was the fact that the armed services themselves adopted statistically derived sampling and inspection methods in their procurement efforts. The second was the establishment of a widespread educational program for industrial personnel at the request of the War Department.

Sampling techniques were used at the Picatinney Arsenal as early as 1934 under direction of L. E. Simon. In 1936, the Bell Telephone Laboratories were invited to cooperate with the Army Ordnance Department and the American Standards Association Technical Committee in developing war standards for quality control. In 1942, Dodge and Romig completed the Army Ordnance Standard Sampling Inspection Tables, and the use of these tables was introduced to the armed services through a number of intensive training courses.

The Ordnance Sampling Inspection Tables employed a sampling scheme based on an acceptable quality level (AQL). The scheme assumed that there would be a continuing stream of lots submitted by a supplier. If the supplier’s quality level was worse than the AQL, the scheme would automatically switch to tightened inspection and the supplier would be forced to bear the cost of a high proportion of lots rejected and returned. This scheme encouraged suppliers to improve quality.

In 1940, the military established a widespread training program for industrial personnel, most notably suppliers of military equipment. At the request of the War Department, the American Standards Association developed American War Standards Z1.1-1941 and Guide for Quality Control Z.1-2-1941, Control Chart Method of Analyzing Data–1941, and the Control Chart Method of Controlling Quality during Production Z1.3-1942. These defined the American control chart practice and were used as the text material for subsequent training courses that were developed at Stanford by Holbrook Working, E. L. Grant, and W. Edwards Deming. In 1942 this intensive course on statistical quality control was given at Stanford University to representatives of the war industries and procurement agencies of the armed services.

The early educational program was a success. That success, along with the suggestion from Dr. Walter Shewhart that Federal assistance should be given to American war industries in developing applications of statistical quality control, led the Office of Production and Research and Development (OPRD) of the War Production Board to establish a nationwide program. The program combined assistance in developing intensive courses for high ranking executives from war industry suppliers and direct assistance to establishments on specific quality control problems. The specific needs to be addressed by this program for the war-time development of statistical quality control were:

1. Education of industrial executives regarding the basic concepts and benefits of statistical quality control.
2. Training of key quality control personnel in industry.
3. Advisory assistance on specific quality control problems.
4. Training of subordinate quality control personnel.
5. Training of instructors.
6. Publication of literature.

The training of instructors was regarded as an essential responsibility of the OPRD program. The instructors used were competent and experienced university teachers of statistics who only needed to (1) extend their knowledge in in the specific techniques and theory most relevant to statistical qu...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Contents
• Preface
• List of Figures
• List of Tables
• 1 Introduction and Historical Background
• 2 Attribute Sampling Plans
• 3 Variables Sampling Plans
• 4 Shewhart Control Charts in Phase I
• 5 DoE for Troubleshooting and Improvement
• 6 Time Weighted Control Charts in Phase II
• 7 Multivariate Control Charts
• 8 Quality Management Systems
• Bibliography
• Index