# How to calculate MTBF

MTBF (Mean Time Between Failure) is an important parameter for various analyses:

• Reliability / Availability analysis – probability of mission failure or system downtime
• Safety – occurrence probability of a safety event
• Spare parts provisioning – required spare parts to ensure system availability
• Warranty – probability of failure before warranty expires

The mean number of failures is used for these analyses.

Tenders for utilities, defense, aerospace, rail and telecom systems often include an MTBF requirement that the designer must achieve.

Initially the designer allocates failure rates to sub-system assemblies.

When a detailed design exists, more accurate MTBF calculation must be conducted to verify compliance with the requirement.

Finally, during field testing an MTBF demonstration takes place by accumulating field failure data.

## How MTBF is calculated:

If you have field failure data, divide the total operation hours by the total number of failures. This is the field MTBF.

You can also calculate field MTBF to specific confidence levels.

Note: This MTBF is only valid for similar operation conditions.

If you do not have field data, MTBF prediction methods must be used.

MTBF is usually calculated from bottom to top of a product / system breakdown tree.
The calculation steps are as follows:

1. Calculate the MTBF of “end items” at the bottom of the breakdown tree.
2. Use the lower level MTBF to calculate MTBF at the next higher level.
3. Repeat the process until the whole tree is calculated.

“End item” MTBF can be obtained from various sources:

• Statistical analysis of field failure data
• Standard prediction methods (MIL HDBK 217, Telcordia 3, SN29500, FIDES, etc…)
• OEM datasheets
• Failure databases such as NPRD, and OREDA

Note: Equipment MTBF value represents the expected rate of failure at a specific operation profile, under specific environmental conditions. Conversion factors may be required to adapt the MTBF value for different conditions.

Prediction methods usually provide “end item” MTBF according to the following MTBF formula:

MTBF=1/(λ0·ΠS·ΠD·ΠE·Π)

 Parameter 내용 λ0 Item base failure rate ΠS Stress factor, e.g., accounting for the ratio of actual power applied to a resistor and the resistor rated power ΠD Duty Cycle ΠE Environment factor e.g., ground / mobile / naval / airborne / space Π티 Temperature factor, usually in the form of an Arrhenius equation, accounting for an activation energy

Additional Π factors that are appear in prediction methods account for manufacturing and screening quality, electronic component packaging, humidity, and more.

Higher level MTBF is calculated as a function of lower-level item’s MTBF:

MTBFparent=1/∑나는(1/MTBF나는)

Where MTBF나는 is the MTBF of the ith direct child.
The above equation accounts for failure of any child item, this is good for:

• Worse case assumption
• Serial reliability model
• Maintenance calculations

If you wish to account for redundancies, you need to calculate MTBCF (Mean Time Between Critical Failures). RBD(신뢰성 블록 다이어그램) (RBD) can be used for MTBCF analysis.

## How to calculate MTBF – Example:

Specific base failure rates and factors are defined in the prediction standards.

There are two methods for calculating MTBF of electronic products according to MIL HDBK 217 F2:

• Parts Count – assuming default ΠS = Π = ΠD= 1
• Parts Stress – accounting for ΠS , Π and ΠD

Parts count can be calculated using BQR’s online application: BQR-Digital:

Parts count can be calculated using BQR’s ECAD Pug-InfiXtress desktop software:

## How to improve MTBF:

If you calculated MTBF according to parts count method, you can probably get a better MTBF value by calculating according to the parts-stress method. While this requires to input the component stresses, actual engineering value can be obtained from such analysis. For example: an over-stressed component will exhibit very low MTBF. By looking at a pareto view of the failure contributors – over-stressed components may be identified.

Better yet – conduct a component derating analysis and then utilize the data for MTBF prediction.

BQR’s fiXtress Pro provides an easy platform for conducting component derating and MTBF prediction.