ABSTRACT
In Chapter 3, we saw simple yet powerful methods for analyzing exponential data and planning life-test experiments. Questions about sample size selection, test duration, and con—dence bounds could all be answered using a few spreadsheet functions. However, these methods apply only under the constant failure rate assumption or the equivalent “lack of memory” property. As long as this assumption is nearly valid over the range of failure times we are concerned with, we can use the methods given. In contrast, what do we do when the failure rate is clearly decreasing (typical of early failure mechanisms) or increasing (typical of later life wear-out mechanisms)? This problem was tackled by Weibull (1951). He derived the generalization of the expo-
nential distribution that now bears his name. Since that time, the Weibull distribution has proven to be a successful model for many product failure mechanisms because it is a µexible distribution with a wide variety of possible failure rate curve shapes. In addition, the Weibull distribution can be derived as a so-called extreme value distribution, which suggests its theoretical applicability when failure is due to a “weakest link” of many possible sites where failure can occur. First we will derive the Weibull as an extension of the exponential. Then we will discuss
the extreme value theory. We shall learn that not only does the Weibull appear to “work” in many practical applications, but there is also an explanation to tell us why it applies and in what areas it is likely to be most successful.
