When setting up a burner its important to set a burner up properly and to measure all inflows, capture all the "Products Of Combustion" and analyse everything in a very controlled manner.
Adjustments & changes then can be reliably measured and honed to a "situation perfect" state of tune.
With a sealed unit (like the internal combustion engine), this is extremely easy. All the fuel and air is extremely tightly controlled, and all the POC's are conveniently routed out of a small round tube that you can capture in its entirety. The computer then checks the exhaust and adjusts ignition timing and injector timings every couple of milliseconds to meet all situations.
Industrial Combustion is infinitely more complex. "Tramp Air", excess air, process air, air for other combustion processes that share the chamber, old instrumentation & control systems, worn tips, corroded registers, worn or damaged FD & ID fans, dampers, etc. are all issues that are encountered often around burners.
Stack analysis basically tells you what is going into the environment without being able to tell you directly everything that is occurring in the combustion zone. It can give you clues, however about what has occurred upstream. eg: High NOx may indicate that temperatures are too high in the burn zone. High CO may well be the result of an incorrect air rate, flame impingement and chilling, or poor mixing. High flue gas temp could indicate that the heat transfer to the load is less than designed. (Design problems eg. firewall height, buildup in or on boiler tubes) or it could be insufficient primary air.
It follows that one must be capable of processing the few "raw" figures available, developing a theory about the situation, then using, installing, or developing, measurement methods to condense all the data and prove or disprove the theory in a safe manner. The flue gas can look good, even though there are many issues happening further upstream due to things like excess air. Thinking "outside the box" is essential to produce good outcomes, & my greatest satisfaction is solving a problem that initially "just doesn't make sense".