Reliability Analysis
Reliability engineering deals with the ability of a system or component to perform its required functions under given conditions for a specified period of time. These calculators help you analyze and predict system reliability.
Where:
- R(t) = Reliability at time t (probability of success)
- λ = Failure rate (failures per unit time)
- t = Mission time (time period of interest)
- MTBF = Mean Time Between Failures = 1/λ
Calculation Scenario
Select what you want to calculate:
Calculate Reliability
Calculate the reliability (probability of success) given the failure rate and mission time.
Result
Reliability R(t):
Probability of failure:
Calculate Failure Rate
Calculate the failure rate (λ) given the reliability and mission time.
Result
Failure Rate (λ): failures per unit time
MTBF: time units
Calculate MTBF
Calculate the Mean Time Between Failures (MTBF) given total operating time and number of failures.
Result
MTBF: time units
Failure Rate (λ): failures per unit time
Calculate System Reliability
Calculate the overall system reliability for series or parallel configurations.
Result
System Reliability:
System Failure Rate (λ):
System MTBF:
Calculate Mission Time
Calculate the maximum mission time to achieve a target reliability given the failure rate.
Result
Maximum Mission Time: time units
Practical Examples
Component Reliability
A component has a failure rate of 0.0002 failures per hour. What is its reliability for a 1000-hour mission?
R(1000) = e^(-0.0002 × 1000) = e^(-0.2) ≈ 0.8187 (81.87%)
Series System
A system has three components in series with reliabilities 0.95, 0.92, and 0.98. The system reliability is:
R_system = 0.95 × 0.92 × 0.98 ≈ 0.857 (85.7%)
Parallel System
A system has two identical components in parallel, each with reliability 0.90. The system reliability is:
R_system = 1 - (1 - 0.90) × (1 - 0.90) = 1 - 0.01 = 0.99 (99%)
MTBF Calculation
A machine operates for 10,000 hours with 4 failures. The MTBF is:
MTBF = 10,000 hours / 4 failures = 2,500 hours