Читать книгу Reliability Analysis, Safety Assessment and Optimization - Enrico Zio - Страница 27

A random variable T follows the Weibull distribution if and only if the pdf (shown in Figure 1.4) of T is

Figure 1.4 The pdf of the Weibull distribution with β=1.79, η=1.

(1.28)

where β>0 is the shape parameter and η>0 is the scale parameter of the distribution. The cdf of the Weibull distribution is

(1.29)

If T denotes the time to failure of an item with Weibull distribution, the reliability function will be

(1.30)

The hazard rate function is

(1.31)

The mean, μ, and variance, σ2, are

(1.32)