MTBF / MTTR / Reliability Calculator mechanism

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

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