# Simultaneous Confidence Interval for the Weibull Parameters

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This Demonstration shows the construction of the simultaneous confidence interval (CI) for the Weibull parameters (shape) and (scale) maximum likelihood estimators (MLE). In reliability analysis, the Weibull parameters MLE derive from failure and suspension time data of independently operating systems.

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Contributed by: Michail Bozoudis (January 2016)

Suggested by: Michail Boutsikas

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Assuming that failure times follow a two-parameter Weibull distribution, the maximum likelihood method is applied to estimate the Weibull parameters and .

Given a time dataset that refers to failures and suspensions, the likelihood function for the Weibull parameters is:

,

Reference

[1] R. B. Abernethy, *The New Weibull Handbook*, 5th ed., North Palm Beach: R. B. Abernethy, 2006.

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