First it's important to understand broadly what workforce productivity is, please see Wikipedia's page on Workforce productivity
The OECD defines it as "the ratio of a volume measure of output to a volume measure of input".1 Volume measures of output are normally gross domestic product (GDP) or gross value added (GVA), expressed at constant prices i.e. adjusted for inflation. The three most commonly used measures of input are:
hours worked;
workforce jobs; and
number of people in employment.
Commonly understood, it's very difficult to imagine that working fewer hours increases productivity. However, the education, health and satisfaction level of workers is also very important. Increases in those levels can make up for fewer hours worked to some degree. When a business would would like to implement these they offer more benefits, industry specific training programs and can make the management process more democratic in certain ways.
Also:
recent research has examined why U.S. labor productivity rose during the recent downturn of 2008–2009, when U.S. gross domestic product plummeted.
Lay-offs would be the obvious reasons, but there are other reasons for this and it will be discussed.
The changes to the 21st century work-force have made highly skilled "knowledge workers" more "productive" even while working longer hours than 40 hours per week. Factory workers are increasingly skilled workers now, too in Europe; but over-working factory workers may also cause industrial accidents, so it is not only a "productivity" issue, as you mention. Factory work is very monotonous, which makes it actually more mentally stressful, which is a major reason why their hours must be kept down to prevent bad quality work.
Worker productivity can be defined in a number of ways. Measurements try to approximate work quality and quantity. One issue that is consistently re-evaluated is whether sleep deprivation or working longer hours causes more medical mistakes (sort of like an industrial accident in principal).
"A review of studies concerning effects of sleep deprivation and fatigue on residents' performance." Samkoff JS1, Jacques CH.
The data presently available suggest that sleep-deprived or fatigued house officers can compensate for sleep loss in crises or other novel situations. However, sleep-deprived residents may be more prone to errors on routine, repetitive tasks and tasks that require sustained vigilance, which form a substantial portion of residents' workload. The authors concur with the recommendation of the Executive Council of the Association of American Medical Colleges that the total working hours for residents should not exceed 80 hours per week averaged over four weeks.
A "routine paperwork error" can occasionally be a very serious error as well that might also kill someone, but according these meta analysis is doesn't occur until over 80 hours/week. A mediocre and sleep deprived doctor is however much more productive than no doctor, but a bad doctor can be less productive than no doctor, as their job is to improve your health, not make you sick, in other words. This is a very extreme case, but in general, it shows the principal that as the knowledge level goes up, the more it makes sense to promote long work hours for the profession even if it causes a decline in work quality up to a certain point. I'm setting the point at increased accidents, although Ford in the quote in the question set his at unacceptable rates of unacceptable quality products and one or other would still be most appropriate to any modern factory.
In regards to other "knowledge workers" or office workers, their productivity is as human resources- seen in terms of the annual financial position of the company minus the cost of the workers salaries and benefits. The US department of Labor tracks employment data by full time and part-time workers and tries to keep track how many hours people are working. Since the Great Recession of 2008, there has been more part-time employment and a drop in hours worked hourly. But there is much evidence that many workers, especially the full-time, working greater than 40 hours/ week has been increasing.
This is a long-term trend that has helped companies to strengthen financial positions through this process, so their workforce is more "productive" for them, as defined.
Why High Earners Work Longer Hours (National Bureau of Economic Research, 2013)
During most of the 1900s, the hours of work declined for most American men. But around 1970, the share of employed men regularly working more than 50 hours per week began to increase. In fact, the share of employed, 25-to-64-year-old men who usually work 50 or more hours per week on their main job rose from 14.7 percent in 1980 to 18.5 percent in 2001.
The linked paper examines some of the reasons for this change and theorizes that much of it has occurred because high income workers make more money in benefits if they work more hours. As suggested before, benefits, training and democratic input are encouraged in companies to increased productivity BUT also usually these accompany more hours worked too. Many more hours in many cases.
So, the statement "increasing hours doesnt proportionally increase productivity" is true for some people and not for others and the law of diminishing returns always applies in all cases. At this time in the US, the number of people who are beneficial for a company working long hours is lower than those that can work roughly 40 hour/ week and be "productive"
