Weibullanalys

Weibullanalys, or Weibull analysis, is a statistical method used in reliability engineering and life data analysis to model the time until a failure occurs. It uses the Weibull distribution to describe the probability of failure over time. The two-parameter form includes a shape parameter beta and a scale parameter eta; a three-parameter form may add a location parameter gamma to account for a threshold in the data.

The cumulative distribution function is F(t) = 1 - exp[-(t/eta)^beta], and the corresponding hazard rate is h(t) = (beta/eta) (t/eta)^(beta-1). The parameter beta governs how the failure rate changes over time: beta > 1 implies an increasing hazard, beta < 1 a decreasing hazard, and beta = 1 reduces to a constant hazard (the exponential case). The scale parameter eta relates to the characteristic life.

Data analyzed by Weibullanalys can be complete or right-censored, and estimates are often obtained by maximum likelihood estimation. Graphical tools include the Weibull plot, which transforms the data so that a straight line appears if the Weibull model fits; ln(-ln(1-F)) is plotted against ln t. For censored data, specialized estimators are used. Goodness-of-fit can be evaluated with tests such as Kolmogorov-Smirnov or Anderson-Darling, and confidence intervals for parameters can be constructed.

Applications of Weibullanalys include estimating reliability at future times, predicting failure rates, planning maintenance and spares, analyzing warranties, and informing design improvements. Limitations arise when data do not follow a Weibull form, when samples are small, or when outliers bias the results.