Source: https://guthlabs.ai/docs/instruments/mtbf-mttr-reliability-calculator/mechanism/

instrument mechanism / verified-clean

# MTBF / MTTR / Reliability Calculator mechanism

The inspectable method record for MTBF / MTTR / Reliability Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The core availability, series, and parallel formulas are standard under the stated independence and steady-state assumptions. The specification needs an explicit downtime-per-year formula, a precise MTBF definition, validation rules for nonpositive inputs and empty topologies, and an honest distinction between availability and reliability before it can receive PASS.

- A=MTBF/(MTBF+MTTR) is the standard steady-state availability formula when MTBF means mean operating time between failures and MTTR means mean repair time, with both expressed in the same time units.

- The series formula is correct for components that are all required to operate and whose availabilities can be treated as independent.

- The parallel formula is correct for independent redundant components where the system operates when at least one component operates.

- The specification claims a downtime-per-year equivalent output but provides no formula for it; an explicit formula such as downtime_per_year=(1-A_sys)*hours_per_year is required.

- The name includes Reliability, but the listed formulas compute availability, not time-dependent reliability. A standard constant-failure-rate reliability formula would be R(t)=exp(-t/MTBF), under additional assumptions.

- MTBF is ambiguous unless defined as mean uptime between failures; if MTBF includes repair time in a failure-to-failure interval, the stated availability formula is not valid as written.

## Units and conventions

- MTBF and MTTR must use identical time units before addition or division.

- The test vectors use 8760 hours per year; leap years and calendar-specific downtime are not modeled.

- The downtime-per-year equivalent is assumed to be (1-A_sys)*8760 hours.

- Availability is interpreted as long-run steady-state availability for repairable systems.

- Series and parallel component availabilities are assumed statistically independent, with no common-cause failures, shared repair dependencies, or switching failures.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "MTBF_hours": 1000,
    "MTTR_hours": 10,
    "topology": "single",
    "component_count": 1
  },
  "expected_outputs": {
    "component_availability": 0.9900990099,
    "system_availability": 0.9900990099,
    "downtime_per_year_hours": 86.7326732673
  },
  "working": "A=MTBF/(MTBF+MTTR)=1000/(1000+10)=1000/1010=100/101=0.9900990099. Downtime/year=(1-A)*8760=(1-100/101)*8760=(1/101)*8760=8760/101=86.7326732673 hours."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The MTBF = 0 and MTTR = 0 input produces the undefined expression 0/0 and must be rejected. The calculator also has an explicit annual-downtime convention sensitivity when the input time unit is days.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/mtbf-mttr-reliability-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/mtbf-mttr-reliability-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/mtbf-mttr-reliability-calculator/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche5/tranche5-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`