how has the rate of designing complex machines changed since the industrial revolution?

The question of 'how long' is difficult to answer in this case, because the design of a machine for industrial purposes consumes a lot of time for logistical, and 'bureacratic' reasons. A steam locomotive would typically take a year or two from when the design was commissioned to the first prototype, and then possibly another year or more for further testing (this is basing on articles detailing the history of various locomotive classes, which I encourage you look up - a lot, in proportion to other machinery from the era, was written on this topic thanks to railway buffs). However, this varies from machine to machine, from designer to designer, from company to company and so on. There is nothing to say it could not be done in a shorter time. As steam engines, both stationary, industrial and locomotives are my 'area', I can tell you how it worked here. Engines were designed mostly using empirical data. When you look on the progress of the steam engine, you can see a very gradual evolution. This is both for technological (manufacturing), and design reasons - successful experiments would be repeated later by other designers. Most calculations for designing a steam engine were simplified to empirical equations, solvable on paper. Those were estimated in practice from other similar engines. Couple that with the fact that most of the thermodynamic and material strength calculations can be also simplified to using table values and simple equations. When such empirical simplifications could not be used, but the problem was common enough, graphical methods of estimation were often employed. For example, when designing steam engine valve gears, which are in theory kinematically complex mechanisms, methods such as the Zeuner diagram were often employed (and are to this day). Noting this, it is not an impossibility to design a fairly conventional steam engine (stationary. without a boiler) withing a day.

Lets say, I need to design a small low pressure engine for a sawmill. The data I have is the working pressure - 8 atm, the rotational speed - 120 rpm, and the necessary power of 10 PS (for example). What would I do as an engineer, in lets say 1910? First, select the cut-off point for the steam admission, arbitrarily at 35%. Not optimization - simply, that is the sort of value usually applied in similar engines. Then, draw the Zeuner diagram, to see how the valve events work out. This would possibly force me to change the cutoff in the range of 10 percentage points. Then, I decide to go with piston valves (because I am forward thinking like that). I draw an ideal expansion indicator diagram, use this to estimate cylinder diameter and stroke. I select the piston valve diameter from a textbook table. So I do with the piston rings. I calculate how thick the base needs to be using the maximum forces with a substantial safety coefficient. I design the cranks using the given stroke, and from similar equations for the tension. I select the bearings from a table. Calculating the valve gear is straightforward as I have done my Zeuner diagram. I get a governor from a catalogue. I may have missed a few magnitudes you need to estimate or arbitrarily select. Many of those would by coincidence be things that a period engineer would draw in the plans based on his feel alone (what looked right). Such a design could be done in a day by an experienced professional.

Then on the other hand, you have experimental designs. When Thomas Newcomen was developing his first atmospheric engines (the very first practical steam engine in the world) in the 17-hundreds, the first prototype took over a dozen years of experimentation (according to LTC Rolt, "Prehistory of the steam engine").

Steam engines are also an example of another problem in the history of engineering. That is the separation of science and technology. Steam engines were not developed by thermodynamicists, they were the work of artisans. Engines based on actual scientific principle, thoughtfully calculated, came far too late (1920's - 60's); Skinner, Lenz, Stumpf etc. This is one of the reasons why the steam engine was phased out of course. They are not flawed or inefficient per-se, but the most innovative manufacturers came to late and went out of business as a result. This is however another topic entirely.

/r/AskHistorians Thread