Reliability & MTBF Estimator
Reliability engineering is the sub-discipline of systems engineering that emphasizes the ability of equipment to function, without failure, for a specified period of time under stated conditions. This estimator provides core metrics used by maintenance professionals to quantify system performance and plan lifecycle interventions.
MTBF vs MTTR
MTBF (Mean Time Between Failures) measures reliability. It is the average time a system operates before a failure occurs.MTTR (Mean Time To Repair) measures maintainability. It is the average time required to repair a failed system and return it to service.
The Availability Math
System Availability is the probability that a system is "up" and able to perform its function at any given time. It is a function of both reliability and maintainability:A = MTBF / (MTBF + MTTR)
Interactive Estimator
Enter your operational data below to calculate mission-critical reliability metrics. The generated chart visualizes the probability of failure-free operation over the selected time horizon.
System Parameters
MTBF is calculated as Time / Failures. Availability includes MTTR impact.
Reliability Function $R(t)$
Probability of maintaining mission-ready state over time.
Availability Benchmarks
- Three Nines (99.9%)8.77 hrs/year
- Four Nines (99.99%)52.6 mins/year
- Five Nines (99.999%)5.26 mins/year
Engineering Notes
MTBF assumes a constant failure rate (Exponential Distribution), which is typical for the "useful life" section of the Bathtub Curve. For wearable components, use Weibull analysis.
Technical Standards & References
Theoretical Background
The Failure Rate ($\lambda$)
In reliability engineering, the failure rate is the frequency with which an engineered system or component fails, expressed, for example, in failures per hour. It is conceptually the inverse of MTBF:
Reliability Function $R(t)$
The Reliability Function $R(t)$, also known as the survival function, represents the probability that a system will succeed (not fail) through time $t$. Under the assumption of a constant failure rate (the "flat" portion of the bathtub curve), it is expressed as:
Where:
- $e$ is Euler's number ($\approx 2.71828$)
- $\lambda$ is the failure rate
- $t$ is the operating time for which reliability is being estimated
The Bathtub Curve Insight
While the constant failure rate model is widely used, real-world systems often transition through three stages: **Infant Mortality** (high early failure), **Useful Life** (constant random failure), and **Wear-out Phase** (increasing failure rate due to degradation). This tool is optimized for the **Useful Life** region.