Section Summary

In this section we examined the expected time to failure of a particular type of light bulb. The data we saw are more or less representative of failure data for some types of electrical components. Such data may be modeled by describing the probability `F(a)` that a random component will fail between times `t=0` and `t=a`. In some cases, `F` has the form

The probability that a component will fail between `t=a` and `t=b` is `F(b) - F(a)`.

We modeled the expected lifetime of such a component by the familiar process of looking at a related discrete problem and then applying a subdivide-and-conquer analysis for the continuous problem. This led to the following formula for the expected lifetime:

where `f` is the derivative of `F` and `T` is a large number. In the next section we will examine this sort of integral in more detail.