I am very confused about the formula for availability because it is given by uptime/uptime+downtime.
Dear Parag Sen
Availability. Average probability that an item will perform its required function under given conditions at time.
Availability (A) = MTTF/(MTTF + MTTR) = MTTF/MTBF
Consult:
Page 9 of https://www.springer.com/gb/book/9783642395345
Equation 5 of https://doi.org/10.1016/j.aei.2004.07.002
Dear Parag,
The formula Availability=Uptime/(Uptime+Downtime) is the most general, and therfore will ALWAYS be correct.
The expression MTBF/(MTBF+MTTR) holds only if ALL MTBF & MTTR assumptions are in effect, and these assumptions are another, extensive discussion which is beyond our scope.
From the prctical point of view, Uptime is the interval during which a system is available WHEN WE NEED IT, and Downtime is the complementary period of time.
Downtime can result from faulty system, maintenance (both preventive and corrective), inspection/calibration, and sometimes also power-up and set-up etc.
A major contributor to Downtime is logistic times, during which a system is unavailable due to a missing part, an unavailable technician etc.
Best,
Alon Sneor
The formula for the availability you gave is true if and only if the failure probability density function as well as the repair / restoration pdf are exponential, and only for steady state (t goes to infinity). Like it or not, this is the mathematics behind it. Find a detailed explanation in Monte Carlo Applications in Systems Engineering, by A. Dubi to figure out more. The easiest way is to ignore it, but then any preventive maintenance consideration is a mathematical violation.
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