EXAMPLE 5.14

Weibull density curves. Figure 5.13 shows the density curves of three members of the Weibull family. Each describes a different type of distribution for the time to failure of a product.

  1. 1. The top curve in Figure 5.13 is a model for infant mortality. This describes products that often fail immediately, prior to delivery to the customer. However, if the product does not fail right away, it will likely last a long time. For products like this, a manufacturer might test them and ship only the ones that do not fail immediately.

  2. 2. The middle curve in Figure 5.13 is a model for early failure. These products do not fail immediately, but many fail early in their lives after they are in the hands of customers. This is disastrous—the product or the process that makes it must be changed at once.

  3. 3. The bottom curve in Figure 5.13 is a model for old-age wear-out. Most of these products fail only when they begin to wear out, and then many fail at about the same age.