This calculator is designed for statisticians and engineers to compute the Weibull distribution parameters, aiding in reliability analysis and failure predictions.
Interactive Weibull Calculator
Results
Data Source and Methodology
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti dall'articolo scientifico Weibull Distribution Overview (2021).
The Formula Explained
Probability Density Function: \( f(x) = \frac{\beta}{\eta} \left(\frac{x}{\eta}\right)^{\beta-1} e^{-(x/\eta)^\beta} \)
Glossary of Terms
- Shape Parameter (β): Determines the shape of the distribution curve.
- Scale Parameter (η): A scale factor that stretches or compresses the distribution.
- Probability of Failure: The likelihood that a given system will fail within a specified time period.
Esempio Pratico Svolto
Supponiamo di avere un componente con una shape parameter (β) di 1.5 e una scale parameter (η) di 1000. Utilizzando la formula, possiamo calcolare il probability of failure per un determinato periodo.
Frequently Asked Questions (FAQ)
What is a Weibull Distribution?
The Weibull distribution is a continuous probability distribution used in reliability analysis and failure modeling.
How do I interpret the shape parameter?
The shape parameter affects the distribution skewness; β < 1 indicates a decreasing failure rate, β = 1 indicates a constant failure rate, and β > 1 indicates an increasing failure rate.
What is the scale parameter's role?
The scale parameter stretches or compresses the distribution curve, affecting the spread of data.
Can the Weibull distribution be used for all types of data?
While versatile, it's primarily used for life data analysis and modeling time-to-failure data.
How does this calculator improve over others?
Our calculator offers intuitive inputs, immediate results, and comprehensive explanations, ensuring clarity and reliability in your statistical analysis.