Equipment reliability: the odds of not failing in the next few hours

Availability looks back: how much of the time the equipment was ready to run. Reliability looks ahead: what are the odds it runs the next few hours without failing. It's the math behind a question every technician has heard: "Will it make it to the end of the season?"

Both numbers come from the same place: MTBF and MTTR. If you don't know how to calculate those two yet, start with how to calculate MTBF and MTTR and come back here.

Inherent availability: the rearview mirror

Inherent availability shows the share of time the equipment was ready to run, counting only stops caused by failures:

Availability = MTBF ÷ (MTBF + MTTR)

Example: a compressor with an MTBF of 240 hours and an MTTR of 4 hours has an availability of 240 ÷ 244 = 98.4%. In other words, out of every 100 hours, it was down due to failure for just over 1.5.

It's called "inherent" because it only deducts failures. Stops for preventive work, setup or lack of scheduled production don't count. When those stops count too, it becomes a different metric, and that's where OEE comes in. The availability calculator does this math for you.

Reliability: the windshield

Reliability is a probability: the chance that equipment runs for a time t without failing. When failures happen at random, with no link to the part's age, it's calculated like this:

R(t) = e^{−t ÷ MTBF}

The "e" is Euler's number (2.718...), which any scientific calculator or spreadsheet has. In Excel or Google Sheets, the formula is =EXP(-t/MTBF).

Take a compressor with an MTBF of 400 hours:

Period ahead	Math	Chance of not failing
One shift (8 h)	e−8/400	98%
One week (168 h)	e−168/400	66%
400 h (equal to MTBF)	e−1	37%
One month (720 h)	e−720/400	17%

Working it backwards: how long can I trust it?

Day to day, the question is usually the reverse: for how long does this equipment have, say, a 90% chance of not failing? Just solve for t:

t = −MTBF × ln(R)

For the same compressor, with R = 90%: t = −400 × ln(0.90) = 400 × 0.105 = 42 hours. If a critical 3-day operation depends on that compressor alone, the chance of getting through without a failure is well below 90%. Time to think about a backup.

Equipment in series and in parallel

Almost nothing works alone. A pumping line has a motor, a pump, a control panel, valves. The reliability of the whole depends on how the parts are connected.

In series (if one stops, everything stops): multiply the reliabilities. A motor, a pump and a panel, each with a 95% chance of getting through the week without failing, give 0.95 × 0.95 × 0.95 = 86% for the set. Every extra item in the series pulls the total down.

In parallel (a backup takes over if the other one stops): calculate the chance of both failing and subtract it from 100%. Two pumps, each at 90%: 1 − (0.10 × 0.10) = 99%. That's why standby pumps, backup generators and standby compressors exist: a single backup turns 90% into 99%.

This reasoning explains why, in a pumping system or a substation, the backup is treated as a critical item. The idle backup needs preventive maintenance too: if it doesn't start when called on, parallel turns into series.

When the formula doesn't apply

The exponential formula assumes the chance of failure is the same at any point in the item's life. That holds reasonably well for random failures, such as electronic components, voltage surges and many faults in complex systems. It doesn't hold for:

• Wear: belts, bearings, brake pads, tires and seals become more likely to fail with use. For them, age matters, and preventive replacement based on time or condition makes sense.
• Early-life failures: assembly errors, parts with factory defects, startup after an overhaul. The chance of failure is higher right at the beginning.
• Short history: with two or three recorded failures, MTBF is a guess. The more well-recorded failures, the better the estimate.
• Mixed failure modes: if the MTBF lumps together bearing failures, electrical faults and operator errors, the average doesn't describe any of them well.

For wear, there are better models, such as the Weibull distribution, which take age into account. But to start thinking about risk in numbers, the exponential already lifts the conversation above "I think it'll hold".

In practice

• Use availability to show the month's results.
• Use reliability to make decisions: do you need a backup? Is it worth doing the preventive task before the critical operation? How much spare parts stock should you keep?
• Calculate by equipment and by failure mode whenever you can. A plant-wide average doesn't help you decide anything.
• It all depends on a well-measured MTBF: failures recorded with the asset tag, time and cause.

In taskfield, MTBF, MTTR and availability are calculated per asset from corrective work orders, and each piece of equipment's failure history is one tap away in the technician's app.