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Exponential Distribution Formula:
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The Probability of Failure Calculator estimates the likelihood of system or component failure over time using the exponential distribution model. This model is commonly used in reliability engineering and risk analysis to predict failure probabilities based on constant failure rates.
The calculator uses the exponential distribution formula:
Where:
Explanation: The exponential distribution assumes a constant failure rate over time, making it suitable for electronic components and systems during their useful life period.
Details: Calculating failure probabilities is essential for reliability engineering, maintenance planning, risk assessment, and safety analysis across various industries including aerospace, automotive, and manufacturing.
Tips: Enter the failure rate (λ) in failures per unit time and the time period (t) in the same time units. Both values must be positive numbers greater than zero.
Q1: When is the exponential distribution appropriate?
A: The exponential distribution is suitable for systems with constant failure rates, typically during the useful life period after initial failures and before wear-out failures.
Q2: What are typical failure rate values?
A: Failure rates vary widely by component type, ranging from 10⁻⁹ failures/hour for highly reliable components to 10⁻³ failures/hour for less reliable ones.
Q3: How does this relate to reliability?
A: Reliability (R) is the complement of failure probability: R = 1 - P_f = e^(-λt), representing the probability of successful operation.
Q4: What are the limitations of this model?
A: The exponential distribution assumes constant failure rates and may not accurately model systems with aging, wear-out, or infant mortality characteristics.
Q5: Can this be used for complex systems?
A: For complex systems with multiple components, system reliability analysis using series/parallel configurations may be required in addition to component failure probabilities.