{
  "slug": "poisson-rate-model",
  "term": "Poisson rate model",
  "definition": "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.",
  "note": "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. [nist-hpp] [nist-zero-failures]\n\nA 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. [nist-hpp] [nist-exponential] [hesela-methods]",
  "related": [
    "confidence-interval",
    "binomial-proportion",
    "afr",
    "drive-day",
    "hazard-rate",
    "interarrival-time",
    "rate-of-occurrence-of-failures",
    "right-censoring"
  ],
  "citations": [
    {
      "id": "nist-hpp",
      "title": "NIST e-Handbook: Homogeneous Poisson Process",
      "url": "https://www.itl.nist.gov/div898/handbook/apr/section1/apr171.htm",
      "accessed": "2026-10-17"
    },
    {
      "id": "nist-zero-failures",
      "title": "NIST e-Handbook: Constant repair rate model and zero-failure confidence bounds",
      "url": "https://www.itl.nist.gov/div898/handbook/apr/section4/apr451.htm",
      "accessed": "2026-10-17"
    },
    {
      "id": "nist-exponential",
      "title": "NIST e-Handbook: Exponential lifetime distribution",
      "url": "https://www.itl.nist.gov/div898/handbook/apr/section1/apr161.htm",
      "accessed": "2026-10-17"
    },
    {
      "id": "hesela-methods",
      "title": "Hesela: AFR is a rate, not a one-year failure probability",
      "url": "https://hesela.com/analyses/afr-rate-not-probability/",
      "accessed": "2026-10-17"
    }
  ],
  "aliases": [],
  "status": "shipping",
  "advantages": [],
  "limitations": [],
  "supersedes": [],
  "supersededBy": [],
  "firstSeen": null,
  "lastSeen": null,
  "updated": "2026-10-17"
}