When is a quality assay worth its price? A value-of-information scheduler for latent-state process monitoring

This paper addresses the online scheduling of costly laboratory assays for quality characteristics that cannot be sensed in line. Rather than discretising the measurements into quality zones, we assign the Markov structure to a latent process condition and treat the continuous measurements as noisy emissions. A Bayesian filter propagates the posterior probability that the batch violates its specification, and sampling becomes an optimal stopping problem within a partially observable Markov decision process. We show that this construction is empty unless the assay informs an action: an affine cost of facing the future makes the belief martingale annihilate the value of every measurement. The batch disposition —release or downgrade—restores the curvature, and the value of information becomes a closed-form option value settling both when and which characteristic to measure. Applied to an industrial precipitated-calcium-carbonate process, the scheduler is the least-cost deployable policy, undercutting current practice while buying far fewer assays by substituting the cheap assay for the costly one through their correlation. The saving is modest—the window is quiet—and a specification-derived diagnostic bounds what is available in advance, before any assay is bought. • A latent-state HMM and Bayesian filter track a batch’s nonconformance risk. • When and which assay to buy is posed as a POMDP optimal stopping problem. • Information has value only once a release/downgrade disposition is restored. • On a PCC process it is the least-cost deployable policy using few assays. • A specification-derived test says in advance whether assaying can pay.