This calculator estimates the probability of at least one failure occurring within a given time frame, based on the mean time between failures (MTBF) of the system and the time frame in question.
It uses the Weibull distribution (with a k factor of 1, equivalent to an exponential distribution) to model the failure behavior over time.
The MTBF value (in years) is converted to hours by multiplying by 365 and 24, while the failure time is provided in days (also converted to hours).
For a single unit, the survival probability is calculated as:

S(t) = exp(-t / (MTBF × 365 × 24))

and the failure probability is:

1 – S(t).

When considering N multiple independent units, the overall probability that at least one unit fails becomes:

1 – [S(t*N)].

This approach is widely used in reliability engineering to assess risk, plan maintenance schedules, and design systems with redundancy.