Fault Tree AND Gate Calculator

AND gate failure probability product only under independently established mutual independence/no common cause. Not a safe system assessment. Actual independently established compatible SI units/model context; conditional arithmetic, not code compliance, engineering design or safe operation approval.

Description

An AND-gate probability equals a product only when the supplied event model supports mutual independence.

An AND-gate probability equals a product only when the supplied event model supports mutual independence.^[1]

This tool multiplies caller-established probabilities without assessing dependence or system safety.

When to use Fault Tree AND Gate Calculator

Use this tool to calculate caller-established probabilities without assessing dependence or system safety.

How to use Fault Tree AND Gate Calculator and how it works

Prepare independentEventProbabilities, with the units, conventions and assumptions below.
Enter the required fields and run Fault Tree AND Gate Calculator.
Read result.value using the output definitions below.
Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.

Input field	Meaning	Value type	Requirement
independentEventProbabilities	Independent Event Probabilities. Use the units and matching context stated in the calculation below.	array of number	Required; other constraints below

Supply a nonempty array of independent basic-event probabilities, each from zero to one inclusive. Return their product as the AND-gate probability. The tool does not estimate probabilities or account for dependent events.

ANDprobability=product(p_i)

Apply the input ordering, units and branch conditions stated above.

Output field	Meaning	Value type
result	Object containing the calculated or selected fields below.	object
result.value	Dimensionless AND-gate probability under the independent-event assumption.	number

json

{
  "input": {
    "independentEventProbabilities": [
      0.5,
      0.2
    ]
  },
  "output": {
    "result": {
      "value": 0.1
    }
  }
}

Limitations and assumptions

The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.

All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.

Alternative or Complementary methods

Use Risk Priority Number Calculator for a complementary operation: An FMEA risk priority number multiplies ordinal severity, occurrence and detection codes under a chosen scoring convention.

Use Fault Tree OR Gate Calculator for a complementary operation: An OR-gate probability can combine event probabilities by the complement-product rule when mutual independence holds.

References

Fault Tree AND Gate Calculator — tool.io

Similar or alternative tools

Risk Priority Number Calculator
An FMEA risk priority number multiplies ordinal severity, occurrence and detection codes under a chosen scoring convention.
Fault Tree OR Gate Calculator
An OR-gate probability can combine event probabilities by the complement-product rule when mutual independence holds.