Volume 6 • Issue 2 • PP: 07 –11 • 2026
A Neutrosophic Control Chart for Monitoring Processes with Indeterminate Measurements: An Information-Fusion Approach to Statistical Quality Control
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© 2026 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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Classical Shewhart control charts assume each measurement is a single determinate number. In many real processes— automated gauges reporting tolerance bands, human inspectors giving ranges, or sensors whose readings are only trustworthy within an interval—each observation is better described by a lower and an upper value together with a degree of indeterminacy. We formulate process monitoring in the neutrosophic statistics framework, where a measurement is a neutrosophic number xN = xL+xUIN with indeterminacy interval IN ∈ [IL, IU], and we treat the reconciliation of the determinate and indeterminate parts as an information-fusion step. We derive neutrosophic control limits for the process mean, propose a three-state signalling rule (in-control / watch / out-of-control), and study the average run length (ARL) by simulation. The neutrosophic chart reduces to the Shewhart chart when indeterminacy vanishes, raises the in-control ARL modestly, and under moderate measurement indeterminacy detects a one-sigma mean shift with a smaller out-of-control ARL than a Shewhart chart applied to interval midpoints.
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References
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