Probability of kill
Encyclopedia
Computer games, simulation
s, models
, and operations research
programs often require a mechanism to determine statistically whether the engagement between a weapon and a target resulted in a kill, or the probability of kill. Statistical decisions are required when all of the variables that must be considered are not incorporated into the model, similar to the actuarial methods used by insurance companies to deal with large numbers of customers and huge numbers of variables. Likewise, military planners rely on such calculations to determine the amount of weapons necessary to destroy an enemy force.
The Probability of Kill (or Pk) is usually based on a uniform random number
generator. This algorithm creates a number between 0 and 1 that is approximately uniformly distributed in that space. If the Pk 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 "not 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. 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 “Phit” of 0.9. If the percentage of hits is nine out of ten, but the probability of a kill with a hit is .5, then the Pk becomes .45 or 45%. This reflects the fact that even modern warheads may not always destroy a target such as an aircraft, missile or main battle tank.
Additional factors include probability of detection (Pd), reliability of the targeting system (Rsys), and reliability of the weapon (Rw), to name a few. For example, if a missile operates properly 90% of the time (assuming a good shot), the targeting system operates properly 85% of the time, and enemy targets are detected at %50, we can increase the accuracy of our Pk estimation.
Pk = Phit * Pd * Rsys * Rw
Pk = 0.9 * 0.5 * 0.85 * 0.90 = 0.344
You can also specify a probability according to a class of targets, for example, it has been stated that the SA-10 surface-to-air missile
system has a Pk of 0.9 against highly maneuvering targets, whereas its Pk against non-maneuvering targets is much higher.
Simulation
Simulation is the imitation of some real thing available, state of affairs, or process. The act of simulating something generally entails representing certain key characteristics or behaviours of a selected physical or abstract system....
s, models
Mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...
, and operations research
Operations research
Operations research is an interdisciplinary mathematical science that focuses on the effective use of technology by organizations...
programs often require a mechanism to determine statistically whether the engagement between a weapon and a target resulted in a kill, or the probability of kill. Statistical decisions are required when all of the variables that must be considered are not incorporated into the model, similar to the actuarial methods used by insurance companies to deal with large numbers of customers and huge numbers of variables. Likewise, military planners rely on such calculations to determine the amount of weapons necessary to destroy an enemy force.
The Probability of Kill (or Pk) is usually based on a uniform random number
Random number
Random number may refer to:* A number generated for or part of a set exhibiting statistical randomness.* A random sequence obtained from a stochastic process.* An algorithmically random sequence in algorithmic information theory....
generator. This algorithm creates a number between 0 and 1 that is approximately uniformly distributed in that space. If the Pk 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 "not 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. 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 “Phit” of 0.9. If the percentage of hits is nine out of ten, but the probability of a kill with a hit is .5, then the Pk becomes .45 or 45%. This reflects the fact that even modern warheads may not always destroy a target such as an aircraft, missile or main battle tank.
Additional factors include probability of detection (Pd), reliability of the targeting system (Rsys), and reliability of the weapon (Rw), to name a few. For example, if a missile operates properly 90% of the time (assuming a good shot), the targeting system operates properly 85% of the time, and enemy targets are detected at %50, we can increase the accuracy of our Pk estimation.
Pk = Phit * Pd * Rsys * Rw
Pk = 0.9 * 0.5 * 0.85 * 0.90 = 0.344
You can also specify a probability according to a class of targets, for example, it has been stated that the SA-10 surface-to-air missile
Surface-to-air missile
A surface-to-air missile or ground-to-air missile is a missile designed to be launched from the ground to destroy aircraft or other missiles...
system has a Pk of 0.9 against highly maneuvering targets, whereas its Pk against non-maneuvering targets is much higher.