I am sorry, I do not understand question properly. An algorithm is always goal oriented that is it provides correct solution for the problem it is designed for. However, there are cases when it fails. During testing phase, one has to find conditions when it will fail or will not work. It is nothing like sometime it is successful and sometime it is failure.From black and white box testing one has to find conditions when it will fail.
Not sure I understand the context of the question. But assuming I have any idea, I suppose the success rate would be measured by varying all of the inputs, throughout the range of values that each input can achieve, and then determining whether the algorithm's output is valid or not, for each change in input variables.
Ideally, an algorithm would never break. However there might be problems if some of the input signals can roll over. Take, for example, a sensor that transmits an 8-bit integer, let's say a value meant to indicate -128 to +127, where negative is expressed as a two's complement. An algorithm which uses such a sensor might break badly, if the sensor is not correctly calibrated. A value which should read -128 might be transmitted (and then interpreted) as +127. Something like that.
Not always easy to defend against this, although it's usually possible to reduce the vulnerability, by creating some invalid input settings in the values around binary 10000000.
Mathematically, some problems is considered as non-deterministic polynomial hard (NP-hard). By means, the algorithms that you designed is not easily transformed to solve other problems. By purpose, it is good if we have a very general algorithm that can solve many type of problems. But this is very difficult to achieve. An algorithm is usually fit to solve a limited problem instances. It depends on what kind of problem that you are dealing with. If you prefer to have a faster solution time, then classical heuristics is the best way. If you prefer to have the best solution (optimum) but with longer searching time, then you can choose metaheuristics such like GA, TS or SA.
You can simply measure the success rate of your algorithm by calculating how close (or how far) is your optimum point with the best optimum. The more closer your point to the best known optimum is the better. Good luck.