Industrial Reliability: MTBF, MTTR and Availability Formulas

What reliability is #

Reliability is the probability that an asset performs the function it was designed for, over a defined period and under established operating conditions. Every part of that definition matters. Function: a pump delivering 70 percent of its flow has not failed as far as the manufacturer is concerned, but it has for the process. Period: reliability over one week and over one year are different numbers. Conditions: a motor run above its rated current does not have its catalog reliability. These indicators tell you whether a preventive maintenance plan is actually working or just being carried out.

On the plant floor, reliability comes down to one operational question: how long can I count on this equipment before it fails on me? Reliability engineering is the set of methods for answering it with data instead of intuition.

Reliability, availability and maintainability: three different things #

They get mixed up because they go together, but they measure different aspects:

• Reliability: how long it takes to fail. Indicator: MTBF.
• Maintainability: how long it takes to repair. Indicator: MTTR.
• Availability: what fraction of the time it is fit to operate. It combines the two above.

A compressor that fails every two weeks but is repaired in twenty minutes can have better availability than one that fails once a year and takes three days to come back. Confusing them leads to investing on the wrong side: buying redundancy when the problem was spare-parts logistics, or the other way around.

The formulas #

MTBF (mean time between failures) = total operating time / number of failures.

MTTR (mean time to repair) = total repair time / number of failures.

Availability = MTBF / (MTBF + MTTR).

Failure rate (λ) = 1 / MTBF. And reliability at time t, for random failures, is R(t) = e^-λt.

A worked example #

A packaging machine ran 720 hours in the month and had 6 failures that added up to 18 hours of repair.

• MTBF = (720 - 18) / 6 = 117 hours.
• MTTR = 18 / 6 = 3 hours.
• Availability = 117 / (117 + 3) = 97.5 percent.
• Failure rate = 1 / 117 = 0.0085 failures per hour.
• Probability of completing an 8-hour shift without a failure: R(8) = e^{-0.0085 × 8} = 93.4 percent.

That 93.4 percent is a number a production manager understands immediately: one in every fifteen shifts will have an unplanned stop. With that figure, the conversation about investing in monitoring or in spare parts stops being a debate of opinions.

Which failures count #

The most common mistake when calculating MTBF is counting everything that stops the machine. Only functional failures count: unscheduled events that prevent the function from being performed. Changeovers, cleaning, scheduled preventive work and material shortages are stops, but not failures; they go into OEE as availability losses, not into MTBF. If you do not separate them, MTBF ends up artificially low and the maintenance plan chases problems that are not its own.

The bathtub curve #

An asset's failure rate changes with its age. At first it is high because of manufacturing and installation defects (infant mortality); then it settles at a low, random value (useful life); at the end it rises with wear-out. The practical consequence: time-based preventive maintenance only makes sense in the wear-out zone. In the useful-life zone, where failures are random, intervening by the calendar does not lower the failure rate and sometimes raises it, because every intervention reintroduces infant mortality. This observation is the origin of RCM.

How to improve reliability #

1. Find where you are losing time

A Pareto of failures by asset and by failure mode usually shows that 20 percent of assets account for 80 percent of the lost hours. That is where the engineering goes. FMEA (failure mode and effects analysis) ranks each mode by severity, occurrence and detectability.

2. Assign the right strategy per failure mode

RCM decides, for each failure mode, whether a condition-based task, a scheduled replacement, a redesign or run-to-failure makes sense. Choosing the type of maintenance by criticality, not by habit, is the biggest lever on MTBF.

3. Measure condition instead of waiting for the failure

Where the failure mode gives signals (vibration, temperature, current, acoustics), condition monitoring turns a random failure into a planned intervention. MTBF goes up because the functional failure never happens; MTTR goes down because the spare part and the window were already lined up.

4. Reduce MTTR with information

Much of repair time is not repairing: it is diagnosing, finding the drawing, waiting for the spare part. An asset history with the readings leading up to the failure and the previous interventions shortens diagnosis; asset management with context is exactly that.

Reliability and asset management: ISO 55000 #

ISO 55000 defines asset management as the coordinated activity of an organization to realize value from its assets. Reliability is one of its core inputs: without MTBF and MTTR per asset there is no way to decide renewal, redundancy or maintenance level on a total-cost basis. We develop the approach in industrial asset management.

Common mistakes #

• Calculating a plant-wide MTBF instead of one per asset: the average hides the equipment that concentrates the failures.
• Using the manufacturer's MTBF instead of your own: the catalog figure assumes conditions the plant rarely meets.
• Measuring reliability without logging failures: if the work order has no failure mode and duration, the indicator does not exist.
• Confusing high availability with high reliability, and not investing in spare parts because the equipment is almost never down.

Where to start #

Pick the five assets that lost the most hours last quarter. For each one, log functional failures, duration and failure mode for a month, calculate MTBF and MTTR and chart the trend. That is enough to apply RCM to the first one on the list. The preventive maintenance plan Excel template has the fields to log it from day one. In iGromi OS the indicators are calculated automatically from the equipment signals and the closed work orders; deciding what to do with them is still the planner's call.

Frequently asked questions #

What is reliability in industrial maintenance?

It is the probability that a piece of equipment performs its function for a given period under defined operating conditions. It is expressed as a percentage or as mean time between failures (MTBF). Reliable equipment rarely fails; available equipment also gets repaired quickly.

How is MTBF calculated?

MTBF is the total operating time divided by the number of failures in that period. If a pump ran 2,000 hours and failed 4 times, its MTBF is 500 hours. Only failures that interrupt the function count, not scheduled stops.

What is the difference between reliability and availability?

Reliability measures how long equipment takes to fail (MTBF). Availability combines that with how long it takes to repair (MTTR): availability = MTBF / (MTBF + MTTR). Equipment can have low reliability but high availability if it is repaired in minutes.

What is maintainability?

It is how easily equipment is returned to service after a failure, measured by MTTR. It depends on design (access, modularity), logistics (spare parts, tools) and available information (history, diagnostics).