probethrough

Probethrough is a concept in probability theory and decision science that describes the probability that a chosen proposition, signal, or item remains valid as it passes through a sequence of probabilistic transformations or filters. In its simplest form, each stage i of a process has a pass probability p_i, possibly conditioned on the item having passed all previous stages. The overall probability that the item passes through every stage, or the probability that the proposition remains true after the entire sequence, is PT = p_1 × p_2 × ... × p_n. When conditional dependence is explicit, p_i denotes P(pass_i | passed_1,...,passed_{i-1}).

The term is used in reliability engineering, screening, and sequential testing to quantify compounded likelihoods. It is analogous to throughput in manufacturing, but applied to probabilities. The term can be extended to continuous or stochastic horizons, and to logarithmic form where log PT is the sum of the log p_i (logprobethrough).

Example: a three-stage quality control line with pass probabilities 0.95, 0.98, and 0.97 yields probethrough 0.95 × 0.98 × 0.97 ≈ 0.904. In information filtering, a message might survive a spam filter, a malware scan, and a classification step; the probethrough is the chance it reaches final evaluation.

Limitations include sensitivity to dependencies, misestimation of stage probabilities, and non-static conditions. Critics note that real systems exhibit path dependence and feedback, which complicates a simple product model. Proponents view probethrough as a compact summary of sequential reliability or screening performance.

Related concepts include conditional probability, sequential testing, and reliability engineering. The term is used in theoretical discussions and applied contexts to compare designs and quantify risk across multi-stage processes.