{
  "slug": "inspection-paradox",
  "term": "Inspection paradox",
  "aliases": [
    "Length-biased inspection"
  ],
  "definition": "The inspection paradox is the length bias by which sampling a time point overrepresents long intervals compared with sampling intervals equally.",
  "note": "For a renewal process with positive independent identically distributed gaps D and finite second moment, the long-run time-average residual wait is E[D^2] / (2 E[D]), not generally E[D] / 2. [renewal]\n\nApplied to storage checks, the observation unit must be a particular block and a specified detection property. The finite-window worksheet assumes uniform fault onset and complete intervals between detecting checks; it is not measured failure latency or a durability guarantee. A mean scrub-job frequency alone does not establish those assumptions. [hesela-intervals]",
  "related": [
    "mean-time-to-detection",
    "data-scrubbing",
    "interval-censoring",
    "adaptive-scrubbing"
  ],
  "citations": [
    {
      "id": "renewal",
      "title": "Gallager: Discrete Stochastic Processes, ch. 4, Example 4.4.1 and Eq. 4.15, pp. 167-169 (MIT 6.262, 2011).",
      "url": "https://ocw.mit.edu/courses/6-262-discrete-stochastic-processes-spring-2011/931ffa0940899c27f34b71ad64fd2bb0_MIT6_262S11_chap04.pdf",
      "accessed": "2026-10-17"
    },
    {
      "id": "hesela-intervals",
      "title": "Hesela: exact inspection-interval worksheet and storage assumptions.",
      "url": "https://hesela.com/analyses/scrubbing-detection-not-durability/#interval-variability",
      "accessed": "2026-10-17"
    }
  ],
  "updated": "2026-10-17",
  "status": "shipping",
  "advantages": [],
  "limitations": [],
  "supersedes": [],
  "supersededBy": [],
  "firstSeen": null,
  "lastSeen": null
}