inspection-paradox · shipping · also Length-biased inspection

Inspection paradox

The inspection paradox is the length bias by which sampling a time point overrepresents long intervals compared with sampling intervals equally.

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. [1]

Applied 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. [2]

Relations

related

mean-time-to-detection, data-scrubbing, interval-censoring, adaptive-scrubbing

Citations

1. Gallager: Discrete Stochastic Processes, ch. 4, Example 4.4.1 and Eq. 4.15, pp. 167-169 (MIT 6.262, 2011). (accessed 2026-10-17)
2. Hesela: exact inspection-interval worksheet and storage assumptions. (accessed 2026-10-17)

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