# How To Calculate the MTBF of a System

Written by doug leenhouts
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Quality engineers are often tasked with calculating the mean time before failure, or MTBF, of their products and systems. This rate is determined by the failure rates of every individual part in the product. Failure rates are most often expressed in terms of hours, with reliability increasing as failure rates decrease. It is common to assume that products in the field, especially electronics and computers, are run continuously as to avoid subtracting any downtime from the equation.

Skill level:
Moderate

## Instructions

1. 1

Establish the length of time you will use to test the product or system. 1,760 hours is usually sufficient, as that is the number of hours in one month.

2. 2

Measure the number of failures that occur during this time frame. To more accurately assess and improve system reliability, record which part failed during each product failure.

3. 3

Sum up the number of failures, and divide the total number of hours by the number of failures. For example, if there are 3 failures in one month of testing, the MTBF is calculated as (1,760/3) = 586.67 hours.

4. 4

Determine the probability that a product will last a certain number of hours by using the equation P(t) = exp(-t/MTBF). The probability that a product with an MTBF of 1 year (21,120 hours) will last 1 month is exp(-1,760/21,120) = 0.92 or 92 per cent.

#### Tips and warnings

• Reducing the individual component failure rates increases the system's MTBF.

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