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Born in 1900, Mr. Deming was a statistics professor in 1950 when he was invited to Japan to run seminars for business leaders, according to a 1999 profile in the Los Angeles Times, which listed him among the top 50 most influential business leaders of the 20th century.

“Essentially, his idea was to record the number of product defects, analyze why they happened, institute changes, then record how much quality improved, and to keep refining the process until it is done right.”

In his last book, “The New Economics,” Mr. Deming wrote that the prevailing style of management required transformation.

“A manager of people needs to understand that all people are different,” he wrote. “This is not by ranking people. He needs to understand that the performance of anyone is governed largely by the system he works in, the responsibility of management.”

Mr. Deming’s relationship with Mr. Gingrich grew more personal over time. Mr. Gingrich invited Mr. Deming to be his guest for the State of the Union address, an invitation that Mr. Deming politely declined, citing travel.

“Give me a chance next year,” he told the lawmaker.

In February 1992, Mr. Deming wrote to Mr. Gingrich about planned lessons for an upcoming meeting, including the “futility of pay for performance,” the “destruction of people from the merit system” and “the evils of ranking divisions and plants.”

Mr. Deming drew comparisons between the situation in the U.S. and his experiences nearly a half-century earlier in Japan.

“Our country is in a crisis, an invisible crisis,” Mr. Deming told Mr. Gingrich. “Japan was in a crisis. The crisis was obvious, the country blown to bits, destroyed by fire.

“Japanese management asked me in 1950 to come to help. Japan soon became an economic power. The secret: management of a system, cooperation between components, not competition. Management of people.”

“Newt,” he added later in the letter, “transformation is required: not mere change. Transformation requires Profound Knowledge.

“It is only through you that the required transformation may reach the ears of our President and others in authority that can act. There is no time to lose.”

In September 1992, Mr. Gingrich and wife Marianne sent Mr. Deming a birthday note.

Signing the letter as “your students and friends,” the couple referred to Mr. Deming as “the man who created an understanding of profound knowledge as a system for all people.”