Downloaded from https://www.everyspec.com ADS-79D-HDBK 3.2 Condition-based maintenance probability parameter definitions Complementary Probability : The probability of an event that can be expressed as a binomial probability if the event‘s outcomes can be broken down into two probabilities of events A and B . When A and B are complementary, the sum of their probabilities of occurrence is one (i.e. A + B = 1). + : CBM system provides an alarm indicating an unhealthy component and maintenance is required. - : CBM system does not provide an alarm, indicating a healthy component and no maintenance is required or is optional. F: Unhealthy component and maintenance is required. H:
Healthy component and maintenance is not required or is optional. PF: Proportion of population that are unhealthy components = 1-PH. PF is complementary to PH. Therefore, PF + PH = 1 and PF = 1-PH. P(F): Probability of an unhealthy component. P(+): Probability that a Health and Usage Monitoring System (HUMS) indicates an alarm = [P(+|F)*P(F)] + [P(+|H)*P(H)] = [(PF)(PODF)] + [(PH)(PFP)]. P(+) is complementary to P(-). Therefore, P(+) + P(-) = 1. P(-): Probability that a HUMS does not provide an alarm = [P(-|F)*P(F)] + [P(-|H)*P(H)] = [(PF)(PFN)] + [(PH)(PODH)]. P(+) is complementary to P(-). Therefore, P(+) + P(-) = 1. PFA or POFA:
Probability of a false alarm, also known as probability of false positive (PFP). PFN: Probability of a false negative. PFP: Probability of a false positive also known as probability of false alarm (PFA). PH: Proportion of population that are healthy components = 1-PF. PH is complementary to PF. Therefore, PH + PF = 1 and PH = 1-PF. P(H): Probability of a healthy component. POD: Probability of detection (also known as detection reliability of a CBM system). P(A|B): If A and B are events, then P(A|B) is the probability of event A occurring given that event B has occurred. P(F|+): Probability of having an unhealthy component given the system provides an alarm = P(F|-):
Probability of having an unhealthy component given the system does not provide an alarm = 13