Reliability engineering is an engineering field, that deals with the study of reliability: the ability of a system or component to perform its required functions under stated conditions for a specified period of time (Wikipedia).
Ps = R = e^(-t/MTBF) Where,Ps = R = probability of failure free operation for a time period equal to or greater than t
e = 2.718
t = specified period of failure free operation
MTBF = mean time between failures (the mean TBF distribution)
The probability that failure will occur before time t = (1 - Ps)
An increase in MTBF does not result in a proportional incresase in reliability (the probability of survival).
Px = P1 * P2 * … * Pn, where Pn is the probability of each part's functioning when activated
The formula assumes that (1) the failure of any part causes failure of the system and (2) the reliabilities of the parts are independent of one another. This formula shows the effect of increased complexity of equipment on overall reliability. As the number of parts in a system increases, the system reliability decreases dramatically.
Px = P1 + (1 - P1) * P2, where Pn is the probability of each part's functioning when activated
Px = 1 - [(1 - P1) * (1 - P2) * ... * (1 - Pn)], where Pn is the probability of each part's functioning when activated
Availability has been defined as the probability that a product, when used under given conditions, will perform satisfactorily when called upon. Availability considers the operating time of the product and the time required for repairs. Idle time, during which the product is not needed, is excluded. Availability is calculated as the ratio of operating time to operating time plus downtime.
Total downtime – this period includes active repair (diagnosis and repair time), preventive maintenance time, and logistics time (time spent waiting for personnel, spare parts, etc). When total downtime is used, the resulting ratio is called operational availability (Ao).
Ao = MTBF / (MTBF + MDT)
Active repair time – the resulting ratio is called intrinsic availability (Ai).
Ai = MTBF / (MTBF + MTTR)
MTBF = mean time between failures
MDT = mean downtime
MTTR = mean time to repair