1. What is the Reliability Function?

The reliability function R(t) represents the probability that a system or component will function without failure up to time t, given a constant failure rate λ. This follows the exponential distribution commonly used in reliability engineering.

2. How Does the Calculator Work?

The calculator uses the reliability function:

Where:

• \( R(t) \) — Reliability at time t (unitless probability)
• \( \lambda \) — Constant failure rate (failures per unit time)
• \( t \) — Time duration
• \( e \) — Euler's number (approximately 2.71828)

Explanation: The exponential reliability function assumes a constant failure rate over time, making it suitable for electronic components and systems during their useful life period.

3. Importance of Reliability Calculation

Details: Reliability calculations are essential for system design, maintenance planning, warranty analysis, and risk assessment in engineering and manufacturing industries.

4. Using the Calculator

Tips: Enter failure rate in failures per unit time and time in the same time units. Both values must be positive (time can be zero).

5. Frequently Asked Questions (FAQ)

Q1: What does a reliability of 0.9 mean?
A: A reliability of 0.9 means there is a 90% probability that the system will function without failure up to the specified time.

Q2: When is the exponential distribution appropriate?
A: It's appropriate for systems with constant failure rates, typically during the useful life period after early failures and before wear-out failures.

Q3: How is failure rate related to MTBF?
A: For constant failure rates, Mean Time Between Failures (MTBF) is the reciprocal of failure rate: MTBF = 1/λ.

Q4: Can reliability exceed 1?
A: No, reliability is a probability and ranges from 0 to 1, where 1 represents perfect reliability and 0 represents certain failure.

Q5: What are typical failure rate units?
A: Common units include failures per hour, failures per million hours (FIT), or failures per operating cycle, depending on the application.