WEIBULL.DIST()/WEIBULL()

SyntaxWEIBULL.DIST(x;alpha;beta;cumulative)

Definition. This function returns the probabilities of a Weibull-distributed random variable. Use this distribution in a reliability analysis (for example, to calculate a device’s mean time to failure).

Arguments

Note

If x, alpha, or beta isn’t a numeric expression, the WEIBULL.DIST() function returns the #VALUE! error.

If x is less than 0, the function returns the #NUM! error.

If alpha or beta is less than or equal to 0, the WEIBULL.DIST() function returns the #NUM! error.

Background. The Weibull distribution is also a statistical distribution. Among other things, the Weibull distribution is used to examine the life cycle of devices based on the fatigue of brittle material or the mean time to failure of electronic parts.

The Weibull distribution is named after Waloddi Weibull (1887–1979). The Weibull analysis is considered a classic reliability analysis or classic life cycle chart and is commonly used in the auto industry. The so called “Weibull net” shows the typical life cycle and the failure probability for parts and other components.

In general, a Weibull distribution is an exponential distribution. The Weibull distribution is used for different purposes:

See Also

You will find more information about exponential distributions in the description of EXPON.DIST().

The WEIBULL.DIST() function calculates the density and the distribution function of the Weibull distribution.

To calculate the density function, specify the logical value FALSE for the cumulative argument. The density function is the first derivation of the distribution function based on a random variable (such as the time for the failure density function). In other words, the differential change of the relative frequency per scale unit is calculated.

To calculate the distribution function, specify the logical value TRUE for the cumulative argument. The distribution function F(x) indicates the relative cumulative frequency of events.

The distribution function F(x) indicates the probability that the random variable y doesn’t exceed value x (see Figure 12-154).

A Weibull distribution with the arguments x, alpha=5, beta=2, and cumulative = FALSE.

Figure 12-154. A Weibull distribution with the arguments x, alpha=5, beta=2, and cumulative = FALSE.

The equation for the distribution function of a Weibull distribution is:

F(x, α, β) = 1 – e–(x/β)α

The equation for the density function of a Weibull distribution is:

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If alpha = 1, WEIBULL.DIST() returns the exponential distribution with:

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The failure ratio depends on the parameter β:

Example. Use the following values to calculate WEIBULL.DIST():

Figure 12-155 shows the calculation of WEIBULL.DIST().

Calculating WEIBULL.DIST().

Figure 12-155. Calculating WEIBULL.DIST().

The WEIBULL.DIST() function returns the following results using the parameters shown in Figure 12-155:

See Also

EXPON.DIST()