PDSA

No, not a typo. There is definitely an "S" in PDSA rather than a "C". Most likely the "C"-version is best known because of the same behavior Deming tried to correct on so many occasions.

The well-known PDCA and SPC were invented by Walter A. Shewart   The impression he made on W. Edwards Deming was such, that Deming became a great advocate of Shewart's methods. It lay out the foundation of how Demming helped Japan after being defeated in WOII to become one of the biggest industrial players in the world.

"I called it Japan in 1950 and onward the Shewhart cycle. It went into immediate use in Japan under the name of the Deming cycle, and so it has been called there ever since" Out of the Crisis by W. Edwards Deming

Still, some of the credits have to go to Deming as well. In the words of Deming "Shewhart has the uncanny ability to make things difficult". So Deming spent a great deal on figuring out Shewhart's ideas, and devise ways to present them with his own twist. In this way the simple concept of PDCA came into existence.

The idea of PDCA was to act as a guide for all projects, not just quality projects.

PLAN	Objective Questions and predictions Plan to anwer the questions(who, what, where, when)
DO	Carry out the plan Collect the data Begin analysis of the data
STUDY	Complete the analysis of the data Compare data to predictions Summarize what was learned
ACT	What changes are to be made? Next cycle

When looking at the last bullet under Study, summarize what was learned, it is not hard to imagine why Deming changed the "C" into an "S". A check will only look whether something did or didn't meet the expectations. A study will look as well into why the deviations occured; both in a positive and negative sense.

In orde to do the Study correctly, the Plan must minimally contain the predictions (second bullet under Plan). And, ideally the Plan should contain the fundamental assumptions on which the predictions are based.

If you want to read a bit more about the background, there is a nice paper called Evolution of the PDSA Cycle.. It step-by-step shows how Shewhart's original ideas evolved into what we now know as PDSA.