MTBF and MTTR calculator

How MTBF and MTTR are calculated

Mean time between failures (MTBF) says how long repairable equipment runs, on average, between two failures; mean time to repair (MTTR) how long it takes to get it running again. Together they give the inherent availability and the failure rate, the figures behind the availability loss of OEE and behind maintenance planning.

Formulas

• MTBF = operating time / number of failures. Operating time is the time the equipment was running or ready to run: from a log, the scheduled time of each machine minus its repair time.
• MTTR = total repair time / number of repairs (equal to the failures in a log). Repair time here runs from the stop to the restart, so it includes waiting for a technician or parts.
• Failure rate λ = failures / operating time = 1 / MTBF, shown per 1000 hours.
• Inherent availability Ai = MTBF / (MTBF + MTTR): the share of time up, counting only failures and their repair (no planned maintenance, no logistics delays beyond what the repair times contain).
• Confidence interval of MTBF, with T the operating time, r the failures and α = 1 − confidence: time-terminated (the records end on a date) 2T / χ²(1 − α/2; 2r + 2) ≤ MTBF ≤ 2T / χ²(α/2; 2r); failure-terminated (the records end at a failure) 2T / χ²(1 − α/2; 2r) for the lower bound. A one-sided lower bound uses α instead of α/2. With no failures only the lower bound exists.
• Reliability over a mission of t hours: R(t) = exp(−t / MTBF), the chance of running t hours without a failure; the same at the lower bound gives a cautious value.
• Assumption: the interval and R(t) assume a constant failure rate, so that times between failures are exponential and failures form a Poisson process. MTBF and MTTR themselves are plain averages and need no assumption.
• Several machines: each gets its own row; “All machines” adds the operating times and failures. That fleet MTBF describes one machine only if all of them fail at about the same rate.

Worked example (the tool's example)

1. Three CNC machines were scheduled for 480 h each in March. The log has 12 failures: 4 on CNC-1, 2 on CNC-2, 6 on CNC-3.
2. CNC-1 was down 90 + 55 + 165 + 40 = 350 min = 5.83 h, so it operated 474.17 h: MTBF = 474.17 / 4 = 118.5 h and MTTR = 5.83 / 4 = 1.46 h.
3. All machines: 1422.17 operating hours and 17.83 repair hours for 12 failures: MTBF = 118.5 h, MTTR = 1.49 h, Ai = 118.5 / (118.5 + 1.49) = 98.76 %.
4. 90 % interval, time-terminated: 2 × 1422.17 / χ²(0.95; 26) = 2844.33 / 38.885 = 73.1 h to 2 × 1422.17 / χ²(0.05; 24) = 2844.33 / 13.848 = 205.4 h. Twelve failures leave a wide range.
5. Reliability over an 8-hour shift: R(8) = exp(−8 / 118.5) = 0.935; at the lower bound 73.1 h it is 0.896.

Common mistakes

• Using calendar time instead of operating time: idle weekends inflate MTBF.
• Reading MTBF as a failure-free period: with a constant rate 63 % of the units fail before the MTBF.
• Quoting an MTBF from a handful of failures without its interval.
• Counting planned maintenance or changeovers as failures, or leaving out short stops that were really failures.
• Applying exp(−t / MTBF) to wear-out failures (bearings, tools, belts): use a Weibull analysis of the failure times instead.
• Adding MTBF values of machines in series: for a line, add the failure rates (λ line = Σ λ) and invert.

Input and files

• Timestamps: 2026-03-02 14:05 (ISO, also with T and seconds), 2026.03.02 14:05, 02.03.2026 14:05 (day first) or 3/2/2026 14:05 (month first, as Excel shows dates in English). No time zone or daylight saving shift is applied. Without Start and End columns, the number column is the repair duration (minutes or hours, as chosen).
• The Failures column (by header name only) lets a row stand for several failures with their total repair time. Numbers may use a decimal comma or point.
• Files: CSV, TSV and TXT are read as if pasted (UTF-8, UTF-16, otherwise Windows-1257). XLSX: choose the sheet and the columns or a cell range; formula cells use the value Excel last saved, dates are kept as text. Files up to 20 MB are read in this browser only and never uploaded.
• XLSX files are read with SheetJS Community Edition 0.20.3, Apache License 2.0 (license), loaded only when an Excel file is opened or created.

Questions

Is MTBF the time a machine runs before it fails?

No. MTBF is an average over many failures, not a guaranteed failure-free time. With a constant failure rate only about 37 % of the units are still running at a time equal to the MTBF; most fail before it.

Should the repair time be taken off the operating time?

Yes. MTBF counts the time the equipment was running or ready to run, so time spent down for repair is not part of it. The calculator subtracts each machine’s repair time from its scheduled time.

Why use 2r + 2 degrees of freedom for the lower bound?

When the records end at a fixed date rather than at a failure (a time-terminated test), the next failure has not happened yet, so the lower bound allows for one more failure: chi-square with 2r + 2 degrees of freedom. A test stopped at a failure (failure-terminated) uses 2r.

When is R(t) = exp(−t / MTBF) wrong?

When the failure rate is not constant: early-life failures make the rate fall, wear-out makes it rise. Plot the failure times or fit a Weibull distribution; a Weibull shape clearly different from 1 means the exponential formulas understate or overstate the risk.

Related tools

• Weibull reliability: check whether the failure rate is constant, and B10 life and reliability when it is not.
• OEE calculator: what the downtime costs in availability, next to performance and quality.
• Pareto chart: rank the failure causes or the machines by downtime.
• Capacity planning: available hours per machine with an efficiency factor.