“You can expect what you inspect” has been credited by Wikipedia to the American statistician and author W. Edwards Deming (1900-1993), but there’s no evidence that he either coined or popularized the saying. Lawrence Appley (1904-1997), president of the American Management Association from 1948 to 1968, was credited with the saying in 1967.
 
“People do what you inspect not what you expect” has been cited in print since 1959 and “you get what you inspect, not what you expect” from 1962. The saying is sometimes said to have a military origin, but documented citations are lacking to support this.
 
“Don’t expect what you don’t inspect” was written by W. Clement Stone (1902-2002) in his book, The Success System That Never Fails (1962).
 
   
Wikipedia: W. Edwards Deming
William Edwards Deming (October 14, 1900 – December 20, 1993) was an American statistician, professor, author, lecturer and consultant. He is perhaps best known for his work in Japan. There, from 1950 onward, he taught top management how to improve design (and thus service), product quality, testing, and sales (the last through global markets) through various methods, including the application of statistical methods.

Deming made a significant contribution to Japan’s later reputation for innovative high-quality products and its economic power. He is regarded as having had more impact upon Japanese manufacturing and business than any other individual not of Japanese heritage. Despite being considered something of a hero in Japan, he was only just beginning to win widespread recognition in the U.S. at the time of his death. President Reagan awarded the National Medal of Technology to Deming in 1987. He received in 1988 the Distinguished Career in Science award from the National Academy of Sciences.
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Quotations and concepts
In his later years, Deming taught many concepts, which he emphasized by key sayings or quotations that he repeated. A number of these quotes have been recorded.
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. “You can expect what you inspect.” Deming emphasized the importance of measuring and testing to predict typical results. If a phase consists of inputs + process + outputs, all 3 are inspected to some extent. Problems with inputs are a major source of trouble, but the process using those inputs can also have problems. By inspecting the inputs and the process more, the outputs can be better predicted, and inspected less. Rather than use mass inspection of every output product, the output can be statistically sampled in a cause-effect relationship through the process.
 
New York (NY) Times
Lawrence Appley, 92, an Expert on Management
By EDWIN McDOWELL
Published: April 09, 1997
Lawrence A. Appley, a Methodist minister’s son who served on the boards of 35 corporations and for almost 45 years preached the gospel of quality management in corporate life and Government service, died on Friday at his home in Hamilton, N.Y. He was two weeks short of his 93d birthday.
 
Mr. Appley was most visible from 1948 to 1968, when he was president of the American Management Association, the world’s biggest and oldest management education organization. From 1968 until 1974 he was chairman of the association’s board.
 
Google Books
Creative Discussion
By Rupert L. Cortright and George Loran Hinds
New York, NY: Macmillan
1959
Pg. 200:
People do what you inspect not what you expect, and we meet today to devise a system of inspection.
     
Google Books
Supervisory Management
American Management Association
AMACOM
Volume 7
1962
Pg. 40:
“In delegation you get what you inspect rather than what you expect,” observed one supervisor.
 
Google Books
The Cornell Hotel and Restaurant Administration Quarterly
Cornell University. School of Hotel Administration
Volume 3
1962
Pg. 79:
As occurs in many cases, you get what you inspect, not what you expect.
 
Google Books
Journal of the New England Water Works Association
Volume 81
1967
Pg. 159:
The President of the American Management Association, Larry Appley, said it this way: “It is not what you expect that will produce results,— it is what you inspect.”
     
Google Books
Proceedings of the Annual Meeting
American Life Convention
Volume 65
1970
Pg. 78:
There is an ancient rule of management that I think we need to drag out, dust off and take a whole new look at: People do what you inspect, not what you expect.
 
12 January 1972, Gastonia (NC) Gazette, “Motivation is the idea,” pg. 2A, col. 2:
“If your plan is to become a reality, remember that people being human don’t necessarily do what you expect but what you inspect!” he said, using an old AMA motto.
 
17 September 1972, Big Spring (TX) Herald, “Star Light” edited by Wanda J. Campbell, The Texas Star, pg. 15, col. 4:
Senator Bentsen points out that in line with the business maxim, “you can expect what you inspect,” a periodic review of efficiency is conducted.
     
Google Books
State Government Administration
National Society of State Legislators
Volumes 8-9
1973
Pg. 31:
There’s an old saying which goes like this: People do what you inspect, not what you expect as long as you do it with respect.
   
Google Books
Learning Together
By Ronald G. Held
Springfield, MO: Gospel Pub. House
1976
Pg. 105:
As someone has said: “You get what you inspect, not what you expect.”
       
Google Books
The Successful Sunday School and Teachers Guidebook
By Elmer L. Towns
Carol Stream, IL: Creation House
1976
Pg. ?:
The Calvary Baptist Church in Ypsilanti, Mich., printed a motto over its visitation board, “People Expect What You Inspect.”
 
13 October 1976, Dallas (TX) Morning News, “Ford’s LBJ praise ‘amusing’” by Carolyn Barta, pg. 6A, col. 1:
“You can expect what you inspect,” he (Lloyd Bentsen, U.S. senator from Texas—ed.) said, claiming Ford is not “inspecting” the bureaucracy.
 
Google Books
The Key to Increase Productivity:
A manual for line executives together with a manual for corporate officers on increasing business credibility
By Fred Rudge
Washington, DC: Bureau of National Affairs, Inc.
1977
Pg. 31:
There’s a bit of folk wisdom, too, in the matter of getting results: You get what you inspect, not what you expect.
     
Google Books
Surface Warfare
United States. Office of the Chief of Naval Operations
Volume 7
1982
Pg. ?:
There is an old Navy adage that you can only “expect what you inspect.”
 
New York (NY) Times
THE VICE-PRESIDENTIAL DEBATE; Transcript of the Debate on TV Between Bentsen and Quayle
Published: October 06, 1988
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BENTSEN: And, one of the things I learned in business is that you can expect what you inspect.
 
Google Books
The Open Innovation Marketplace:
Creating Value in the Challenge Driven Enterprise
By Alpheus Bingham and Dwayne Spradlin
Upper Saddle River, NJ: FT Press
2011
Pg. 150:
W. Edwards Deming, famous for his approaches to quality and manufacturing, once said “You can expect what you inspect.”