Editing Probability of kill (section)

{{No footnotes|date=July 2024}}
[[Computer game]]s, [[simulation]]s, [[mathematical model|models]], and [[operations research]] programs often require a mechanism to determine [[statistic]]ally how likely the engagement between a weapon and a target will result in a satisfactory outcome (i.e. "kill"), known as the '''probability of kill'''. [[Performance audit]]ing and statistical decisions are required when all of the variables that must be considered are not incorporated into the current model, similar to the actuarial methods used by [[insurance companies]] to deal with large numbers of customers and huge numbers of variables.  Likewise, [[military planning|military planners]] rely on such calculations to determine the quantity of weapons necessary to destroy an enemy force.

The probability of kill, or "P<sub>k</sub>", is usually based on a uniform [[random number generation|random number]] generator. This algorithm creates a number between 0 and 1 that is approximately uniformly distributed in that space. If the P<sub>k</sub> of a weapon/target engagement is 30% (or 0.30), then every random number generated that is less than 0.3 is considered a "kill"; every number greater than 0.3 is considered a "no kill". When used many times in a simulation, the average result will be that 30% of the weapon/target engagements will be a kill and 70% will not be a kill.

This measure may also be used to express the [[accuracy]] of a [[weapon system]], known as the '''probability of hit''' or "P<sub>hit</sub>". For example, if a weapon is expected to hit a target nine times out of ten with a representative set of ten engagements, one could say that this weapon has a P<sub>hit</sub> of 0.9. If the chance of hits is nine out of ten, but the probability of a kill with a hit is 0.5, then the P<sub>k</sub> becomes 0.45 or 45%. This reflects the fact that even modern guided warheads may not always destroy a hit target such as an [[aircraft]], [[missile]] or [[main battle tank]].

Additional factors include the probability of detection (P<sub>d</sub>), reliability of the targeting system (R<sub>sys</sub>), and reliability of the weapon (R<sub>w</sub>), to name a few.  For example, if a missile operates properly ''e.g.'' 90% of the time (assuming a good shot), the targeting system operates properly 85% of the time, and enemy targets are detected at 50%, accuracy of the P<sub>k</sub> estimation can be increased:

P<sub>k</sub> = P<sub>hit</sub> * P<sub>d</sub> * R<sub>sys</sub> * R<sub>w</sub>

For example:

P<sub>k</sub> = 0.9 * 0.5 * 0.85 * 0.90 = 0.344

Users can also specify a probability according to a class of targets, for example, it has been stated that the [[SA-10 Grumble|SA-10]] [[surface-to-air missile]] system has a P<sub>k</sub> of 0.9 against highly maneuvering targets, whereas its P<sub>k</sub> against non-maneuvering targets is much higher.