But the confusion over what role signals play in the subway’s dismal performance underscores the ongoing debate — and news media scrutiny — over the data that the M.T.A. provides the public and how upfront it has been about identifying the causes of riders’ upended commutes.

“Being candid, we have archaic systems, multiple sources of the truth, databases galore, but it is very hard to pin down and get from multiple sources, true data,” said Andy Byford, the president of New York City Transit, which runs the subway and public buses. Mr. Byford has already expressed his belief that blaming delays on “overcrowding,” is woefully imprecise, and not in fact, a root cause of delays.

Mr. Byford said he had commissioned a review of the terminology the agency uses such as what constitutes a major delay or a power-related failure, and how it categorizes the various causes of delays.

“There is a huge amount of data to crunch and properly categorize,” Mr. Byford said. “But that doesn’t mean we are not fixing the right things. We must tackle equipment that we know is failing, but then also categorize these failures in an appropriate manner.”

For Mr. Lander’s report, the data was collected by a social media bot that scraped digital information from the subway’s Twitter feed and downloaded each mention of a signal failure into a spreadsheet. Anna Levers, the councilman’s policy director, then pored over the data to cull any duplicated tweets or tweets the bot may have pulled in error. She then cross-referenced each delay with the subway stop nearest to where it occurred. Next, based on M.T.A. data on hourly ridership numbers at subway stops across the city, Ms. Levers estimated how many riders were likely impacted by each delay. She posted her estimates periodically over the past few months on SignalFail.com.

For the three month period, using these methods, she estimated that 11.1 million riders were delayed by the signal failures the subway’s Twitter feed reported.

Of course, this analysis falls far short of any sort of reliability or scientific standard, Ms. Levers said, which was part of the point of the exercise.

“It’s best information we have to go on, and which is in part what we are objecting to,” Ms. Levers said. “It’s ridiculous that the way users are getting real time/real-time feedback in performance is by me scraping data from a Twitter feed.”