What is a problem and how can we define it?

Can we really define a problem as shown below?

Desired condition – Actual condition = Problem (original equation)

I think the equation is wrong logically, because the desired condition, the actual condition and the problem are not defined accurately.
I´ll try to shift the current equation and see what happen. You will get the following:

Desired condition = Problem + Actual condition (Shifted)

Analysis
Why the equation is wrong logically? Well, because it’s a false statement. Why the statement is false? Well, we will know that by asking these questions. Is it reasonable that the “desired condition” equal to what we have plus problem? Shall we add problems to the “Actual condition” in order to achieve the desired condition?

I think in order to understand the theme, the terms such as Actual condition and Problem should be defined properly, because when mentioning “Actual condition” does not mean that the current system contains problems. How?
Well, the word “Actual” means the current or what we have right now, but not necessarily it contains problems. For example, when a new project starts, normally everything is new(or in good condition)  such as machines, equipment, assets etc and we also assume that the current condition is good, because the assets are new or in good condition. Additionally, that leads logically to an expected/desired outcome, which means, it could be ”Actual condition” = “Desired condition”.
What I want to say is the actual condition could be the desired condition according to the example above if it does not contain any problem and gives the expected outcome. That means we cannot generalize “Actual condition” as a system which contains problem.
I think it could be better and more reasonable if we replace ”Problem” with “Requirement” as you can see below:

Desired condition – Actual condition = Requirement (Suggested equation)

We will get a reasonable result even when we move one of the terms to the right or to the left. See the equation below:
An assumption (In this case we assume that the actual condition contains problems).

Desired condition = Requirement + Actual condition


Here can you see the difference between the original and the new equations. It’s acceptable and reasonable when I add “Requirement” to the “Current condition” I will achieve the “Desired condition”, in case the “Current condition” suffering of some problems, but I think it’s unacceptable and unreasonable when adding “Problem” to the “Actual condition” in order to achieve the “Desired condition”.
Or
Actual condition = Desired condition – Requirement
It’s understandable that the “Desired condition” is missing such “Requirement” and so cannot be achieved.



Conclusion

I think the usage of “Requirement” is more reasonable in this case, because it’s broader and includes everything thing in which can impact company´s profitability and competitiveness. Furthermore by using “Problem” it seems you mean something specific, however the problems are varied for instance it could be technical, organizational, managerial, or human factors. Moreover, “Requirement” could include all of these areas.


This is the website if you want to check the original article/video.
http://www.reliableplant.com/Article.aspx?articleid=21550

Best regards
Hamid Al-najjar