hesela.devPoisson rate model
A Poisson rate model represents an event count over a specified exposure by a Poisson distribution with mean equal to the event rate multiplied by that exposure.
For fixed exposure E, the model is X ~ Poisson(lambda E), with lambda measured in events per unit exposure. At zero observed events, P(X = 0) = exp(-lambda E), giving the exact one-sided upper bound lambda_U = -ln(alpha)/E under this count model. At 95% confidence alpha = 0.05. Exposure in drive-years gives a bound in events per drive-year, not a failure probability. [1] [2]
A homogeneous Poisson process has independent exponential gaps and constant event intensity. An arbitrary fleet failure count is not automatically Poisson because its drive-days are known: dependence, a changing risk set, selective withdrawal and varying hazards require analysis of the observation design. Under common exponential survival, p(t) = 1 - exp(-lambda t); equal follow-up alone does not justify that conversion. [1] [3] [4]
Relations
- related
- confidence-interval, binomial-proportion, afr, drive-day, hazard-rate, interarrival-time, rate-of-occurrence-of-failures, right-censoring