Analytical Solution to a Partially Observable Machine Maintenance Problem with Obvious Failures
Bibliographic record
Abstract
We study the maintenance of a machine that deteriorates according to a Markov process until it fails. When failure occurs (which is observable), corrective replacement is made. Otherwise, the machine can be in one of two unobservable working states, and the decision maker can choose production, inspection, or preventive replacement. The state is revealed upon inspection and is reset by corrective or preventive replacement. The objective is to minimize the expected total discounted cost over an infinite horizon. We derive an exact, analytical solution to this problem via a dual framework for partially observable Markov decision processes. The solution can be easily computed without value iteration. We identify six possible structures of the optimal solution, which are represented as graphs. Each graph contains an absorbing, cyclic subgraph that governs the steady-state behavior of the machine. The exact analytical solution facilitates comparative statics analysis, comprehensive numerical studies, and the generation of insights. This paper was accepted by Chung Piaw Teo, optimization. Funding: This work was supported by the Natural Sciences and Engineering Research Council of Canada [Grant RGPIN-2014-04979]. Supplemental Material: The online appendix and data are available at https://doi.org/10.1287/mnsc.2022.4547 .
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".