Worst-Case Tolerance Stack Calculator

Signed asymmetric independent interval tolerance envelope, not an unweighted symmetric tolerance sum. Caller independently establishes units, regime, calibration and applicability; this does not establish design-code compliance, authenticity, operational safety, treatment efficacy or a validated forecast.

Description

Worst-case tolerance stacking propagates each signed sensitivity over its allowed deviation interval.

Worst-case tolerance stacking propagates each signed sensitivity over its allowed deviation interval.^[1]

Sign matters because a negative sensitivity reverses which endpoint contributes to each bound. Use this tool to calculate worst-Case Tolerance Stack from the supplied measurements and assumptions.

When to use Worst-Case Tolerance Stack Calculator

Use this tool to calculate worst-Case Tolerance Stack from the supplied measurements and assumptions. Establish the SI units or caller unit basis, load signs, measurement interval, model conditions and independently chosen coefficients or references.

How to use Worst-Case Tolerance Stack Calculator and understand its results

Establish the SI units or caller unit basis, load signs, measurement interval, model conditions and independently chosen coefficients or references.
Enter nominalDimensions, signedSensitivityCoefficients, lowerDimensionDeviations, upperDimensionDeviations, using the field meanings and rules below, then run the tool.
Read nominalStack, worstCaseStackLower, worstCaseStackUpper. Interpret the fields using their units, signs and evidence conventions below.
If input validation fails, correct the reported field and run again. Before applying the result, check reference scope, model assumptions and any missing evidence or placeholder values.

Input field	Meaning	Value type	Requirement
nominalDimensions	Nominal dimensions	list of number	Required
signedSensitivityCoefficients	Signed sensitivity coefficients	list of number	Required
lowerDimensionDeviations	Lower dimension deviations	list of number	Required
upperDimensionDeviations	Upper dimension deviations	list of number	Required

Enter nonempty aligned nominal dimensions, finite signed sensitivities and deviation endpoints with lower≤0≤upper. Nominal result is Σnominal×sensitivity. Sum the minimum and maximum signed endpoint contributions separately to obtain absolute stack bounds. No probability distribution or independence assumption is used.

nominal=Σn_i×s_i; lower=nominal+Σmin(s_i×lo_i,s_i×hi_i); upper=nominal+Σmax(s_i×lo_i,s_i×hi_i)

Use the exact units, boundary rules, ordering and missing-evidence conventions above.

Output field	Meaning	Value type
nominalStack	Nominal Stack; follow the units, sign, ordering and evidence convention stated above	number
worstCaseStackLower	Worst Case Stack Lower; follow the units, sign, ordering and evidence convention stated above	number
worstCaseStackUpper	Worst Case Stack Upper; follow the units, sign, ordering and evidence convention stated above	number

json

{
  "input": {
    "nominalDimensions": [
      10,
      20
    ],
    "signedSensitivityCoefficients": [
      1,
      -1
    ],
    "lowerDimensionDeviations": [
      -1,
      -2
    ],
    "upperDimensionDeviations": [
      2,
      3
    ]
  },
  "output": {
    "nominalStack": -10,
    "worstCaseStackLower": -14,
    "worstCaseStackUpper": -6
  }
}

Limitations and assumptions

Sign matters because a negative sensitivity reverses which endpoint contributes to each bound. Interpretation depends on the units, sampling scope and exact model described above.

All listed fields require explicit values. Unexpected fields, incorrect types, nonfinite numbers and sparse evidence arrays fail validation; the specific bounds and alignment requirements are stated above. Extremely large inputs or outputs can also be rejected. An input error is distinct from a successful result reporting false, no matches or missing evidence.

Alternative or Complementary methods

Use RSS Tolerance Stack Calculator for this related task: Root-sum-square stacking combines independent standard-deviation contributions.

Use Interference Fit Pressure Calculator when its separate inputs and assumptions fit the question: An interference-fit model relates diametral interference to combined diametral compliance.

References

Worst-Case Tolerance Stack Calculator — tool.io

Similar or alternative tools

RSS Tolerance Stack Calculator
Root-sum-square stacking combines independent standard-deviation contributions.
Interference Fit Pressure Calculator
An interference-fit model relates diametral interference to combined diametral compliance.