MTBF Formula (Table of Contents)
MTBF Formula
MTBF is the usual term mainly used in the field of manufacturing industries. It is the average time taken between the two failures. That is the start of last uptime to start of follow up failure. This is predominantly used to access system reliability and compare different system designs. In the current world, this is used in software industries as well for a similar type of prediction.
A formula for MTBF (Mean Time Between Failure) is –
Where,
 TOT = Total Operational Time which is calculated by using the below formula
TOT = ∑ (Start of Downtime after last Failure – Start of Uptime after last Failure)
 F = Number of Failures
And Failure Rate is just the reciprocal of MTBF. This can be written mathematically like below.
FR = 1 / MTBF
These measures are generally very helpful in finding a failure rate which can be a preventive measure of many systems. High MTBF value means that the system is too good for operational.
Examples of MTBF Formula (With Excel Template)
Let’s take an example to understand the calculation of MTBF formula in a better manner.
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MTBF Formula – Example #1
The overall operating hours of a system is 10 hours per day. But there are two failures with the downtime of 1 hour and 2 hours. Calculate the MTBF and Failure rate.
Solution:
Total Down Time is calculated as:
 Total Down Time = 1 +2
 Total Down Time = 3 hours
Since there are 2 failures of 1 and 2 hours, overall downtime for this system is 3 hours.
TOT is calculated using the formula given below
TOT = ∑ (Start of Downtime after last Failure – Start of Uptime after last Failure)
 TOT = 10 – 3
 TOT = 7 hours
Hence the overall operational time is 7 hours.
MTBF is calculated using the formula given below
MTBF = ∑ (TOT) / F
 MTBF = 7 / 2
 MTBF = 3.5 hours
Hence the system will be down for every 3.5 hours that will result in a loss to the organization.
Failure Rate is calculated using the formula given below
Failure Rate = 1 / MTBF
 Failure Rate = 1 / 3.5
 Failure Rate = 0.28571
Failure rate per hour would be 0.28571.
MTBF Formula – Example #2
There is a Bank bazaar website. Its availability is 24 hours per day. However, the site is not available during 121 PM IST and also another incident during 33.30 am IST. What would be the MTBF for this website?
Solution:
Total Down Time is calculated as:
 Total Down Time = 1 +0.5
 Total Down Time = 1.5 hours
Since there are 2 failures of 1 and 0.5 hours, overall downtime for this system is 1.5 hours.
TOT is calculated using the formula given below
TOT = ∑ (Start of Downtime after last Failure – Start of Uptime after last Failure)
 TOT = 24 – 1.5
 TOT = 22.5 hours
Hence the overall operational time can be calculated is 22.5 hours.
MTBF is calculated using the formula given below
MTBF = ∑ (TOT) / F
 MTBF = 22.5 / 2
 MTBF = 11.25 hours
Hence the system will be down for every 11.25 hours that will result in a loss to the organization.
Failure Rate is calculated using the formula given below
Failure Rate = 1 / MTBF
 Failure Rate = 1 / 11.25
 Failure Rate = 0.08889
Failure rate per hour would be 0.08889.
Hence the system is more stable!!
Explanation
Below is the step by step approach for attaining MTBF Formula.
Step 1: Note down the value of TOT which denotes Total Operational Time. It can be calculated by deducting the start of Uptime after the last failure from the start of Downtime after the last failure. Simply it can be said the productive operational hours of a system without considering the failure duration.
T = ∑ (Start of Downtime after last failure – Start of Uptime after last failure)
Step 2: Note down the value of F. It is the number of failures occurred in a system.
Step 3: Finally MTBF can be calculated using the above formula.
MTBF = TOT / F
Step 4: Failure Rate is just the reciprocal value of MTBF. Thus the formula is,
FR = 1 / MTBF
Relevance and Uses of MTBF Formula
MTBF value simply tells about a product’s survival time. It is very important in Hardware product Industries rather than consumers. It is simply the number of failures occurring per hour. Consumers mostly go with a pricedriven approach hence do not mind much about MTBF. When it comes to industries, based on MTBF values only systems with different designs are compared. This value tells about Reliability, stability, and performance of a system. Because a system’s performance relies on its stability. How often it gets a failure and how productive it is. Low MTBF always denotes that the system is not stable and not much operational. And for critical products such as Airplanes, safety equipment assets, inverters, generators, etc., performance and stability are very important. In this case, MTBF is the indicator of Performance expected from a specific system and also a metric for reliability and acts as a tool at the stage of design and production of hardware. This metric is simply known as average life expectancy. The wrong predictions of a product’s stability lead to poor designs and performance of systems. This says how often a product to be maintained to avoid breakdowns. An also MTBF is a current status indicator of performance in plant maintenance as a preventive maintenance schedule.
MTBF Formula Calculator
You can use the following MTBF Calculator
Σ(TOT)  
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MTBF Formula  
MTBF Formula  = 


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