Exact decimal interval arithmetic · one-dimensional linear model
Controlled 1D Linear Interval Stack
Propagate documented lower and upper deviations through a scalar closure equation with coefficients +1 or −1. The result is a deterministic interval enclosure, not an RSS probability, confidence level, fit decision or ISO conformity verdict.
Documented scalar closure equation
Each active row represents one physical length term. Enter signed lower and upper deviations relative to its nominal value.
Exact interval model
xi ∈ [Ni + dLi, Ni + dUi]
For si = +1: yLi = Ni + dLi, yUi = Ni + dUi
For si = −1: yLi = −(Ni + dUi), yUi = −(Ni + dLi)
Ymin = ΣyLi, Ymax = ΣyUi
This is general interval arithmetic, not an ISO-prescribed formula. For the entered linear model it encloses every combination of independent term values inside their declared intervals. Coefficients other than ±1, nonlinear geometry and dependent/correlated term constraints are outside scope.
Why the former RSS result was removed
NIST TN 1297 describes RSS as a method for combining components estimated as standard deviations or standard uncertainties, with covariances as appropriate. A drawing tolerance half-width is not automatically a standard deviation. Consequently, √Σt² cannot be labelled “3σ”, “99.73% confidence” or expected production yield unless a validated statistical model supplies the distributions, centering, dependence/covariance and coverage interpretation.
- No process capability, rejection rate or probability is calculated.
- No normal distribution or independent-variable assumption is silently imposed.
- No RSS output is presented beside the deterministic interval.
Scope exclusions
- 2D/3D vector loops, angular effects, datum mobility, geometric tolerances and contact geometry.
- Thermal expansion, deformation, preload, wear, surface texture and operating-state changes unless already incorporated into controlled term limits.
- Assembly fit/function, clearance acceptance, interference risk or safety decisions.
- Measurement uncertainty and ISO 14253 conformity decision rules.
- Statistical tolerancing, process distributions, covariance and Monte Carlo analysis.
Standards lifecycle and boundary
| Document | Verified public status | Relevance |
|---|---|---|
| ISO 14405-1:2025, edition 3 | Published; replaces withdrawn ISO 14405-1:2016. | Indication of linear sizes and specification operators. This worksheet does not infer an operator; limits must already be controlled. |
| ISO 2768-2:1989 | Withdrawn 2021-02-04; revised by ISO 22081:2021. | Do not present this withdrawn geometrical-general-tolerance document as current. No class table is reproduced here. |
| ISO 22081:2021, edition 1 | Published; confirmed in 2026. | General geometrical and general size specifications under its stated scope. It does not create a universal tolerance-stack probability formula. |
| NIST TN 1297, section 5 | Official open metrology guidance. | Clarifies that RSS combines standard-uncertainty/standard-deviation components and covariances as appropriate; it is not cited as an ISO tolerance-stack rule. |
Exact normative interpretation still requires licensed controlled copies of the applicable standards and the complete product specification.
Official source records
- ISO 14405-1:2025 official record — edition, status, scope and lifecycle; accessed 2026-07-15.
- ISO 2768-2:1989 official withdrawn record — withdrawal and replacement; accessed 2026-07-15.
- ISO 22081:2021 official record — current scope and confirmation; accessed 2026-07-15.
- NIST TN 1297, section 5 — what RSS combines; accessed 2026-07-15.
Nikolai Shelkovenko
Nikolai Shelkovenko is a vibration analysis engineer and the founder and CEO of Vibromera. For more than 15 years he has balanced rotating equipment in the field rather than on a test bench: mulchers, industrial fans, crushers, centrifuges, shafts and spindles. That work is what the Balanset instruments grew out of — they were designed as a tool a specialist can carry to the machine and use alone, on site, not as laboratory equipment. Vibromera was founded in 2017 and has been based in Porto, Portugal, since 2023. Development, assembly and support of the Balanset line all happen here. The flagship instrument is the Balanset-1A, a portable analyser for single- and two-plane balancing and for vibration diagnostics. Nikolai is personally involved in customer support, in working through difficult balancing cases and in the development of the software. He works with customers worldwide, in any language.
