# MTBF Calculation

The following short paper is a primer for MTBF.

## MTBF Meaning:

MTBF stands for Mean Time Between Failure.
Failure rate in [1/Hours] is defined as 1/MTBF.
MTBF is an important parameter for critical equipment. Equipment MTBF is the cornerstone for many analyses:

• System Reliability and Availability
• System Safety
• Spare Parts provisioning
• Comparing design alternatives
• Comparing COTS

## MTBF Formula:

A simple formula for assessing equipment MTBF from field or test data is:

Equation 1: MTBF=Total operation hours / Total number of failures

Equation 1 is relevant for cases where field data exists.
If field data is not available, there are other sources for MTBF:
• Original Equipment Manufacturer (OEM) data
• MTBF prediction standards
• Failure rate databases such as RADC, NPRD and OREDA

## MTBF calculation for electronic components:

Several standards exist for MTBF prediction of electronic systems:

 Standard Description MIL-HDBK  217F / G RELIABILITY PREDICTION OF ELECTRONIC EQUIPMENT MIL-HDBK  217F2 with ANSI/VITA 51.1 RELIABILITY PREDICTION OF ELECTRONIC EQUIPMENT FIDES Reliability Methodology for Electronic Systems IEC 62380 Universal model for reliability prediction of electronics components, PCBs and equipment Telcordia Reliability Prediction Procedure for Electronic Equipment HDBK GJB299 Reliability Prediction Handbook for Electronic Equipment SN 29500 Failure rate, component, expected value, dependability HRD 5 Handbook of Reliability Data for Electronic Components

Table 1: Standards for MTBF calculation for electronic components

Different standards are used in different industries.
The most popular standards are: MIL-HDBK 217F2/G which used mainly in the defense industry, and
Telcordia for telecom and commercial equipment.

## MTTF vs MTBF:

MTTF stands for “Mean Time To (first) Failure” whereas MTBF is the “Mean Time Between failures”.
If the equipment in question is not repairable then MTTF=MTBF.
If the equipment in question is repairable then usually MTTF>MTBF. The reason for this is that after repair, equipment is usually not as good as new, therefore time to the next failure is shorten than MTTF.

## MTBCF vs MTBF:

MTBCF stands for “Mean Time Between Critical Failures”. A critical failure is a failure that prevents the equipment from carrying out its intended functionality, and is used for mission critical systems.
MTBF is “Mean Time Between ANY Failure”, and is also used for calculating the expected number of maintenance actions that will have to be done.
Not every failure is critical, therefore MTBCF>=MTBF.
Critical systems often have redundancies. As more redundant equipment is added, MTBCF increases, but the rate of having a non critical failure increases i.e. MTBF decreases and more maintenance events are expected.

MTBCF is calculated using methods such as Reliability Block Diagram and Markov chain.

MTBF is not always enough:
Equipment failure is characterized by a failure distribution f(t). The failure distribution defines MTBF but it holds a lot of additional information.
Example:
A popular distribution is the exponential function. The exponential failure distribution has a constant failure rate. During 1 MTBF the probability of equipment to fail is 63.21%.
Following is the reliability curve for an equipment with MTBF = 1 hour:

You may calculate MTBF for various failure distributions using BQR’s Free calculator.