This is just an Excerpt from a larger document, click here to view the entire document.Statistical Assumptions and their Implications
Every statistical model has its own "assumptions" that have to be verified and met, to provide valid results. In the Exponential case, the CI for the mean life of a device requires two "assumptions": that the lives of the tested devices are (1) independent, and (2) Exponentially distributed. These two statistical assumptions must be met (and verified) for the corresponding CI to cover the true mean with the prescribed probability. But if the data do not follow the assumed distribution, the CI coverage probability (or its confidence) may be totally different than the one prescribed.
Fortunately, the assumptions for all distribution models (e.g., Normal, Exponential, Weibull, Lognormal, etc.) have practical and useful implications. Hence, having some background information about a device may help us assess its life distribution.
A case in question occurs with the assumption that the distribution of the lives of a device is Exponential. An implication of the Exponential is that the device failure rate is constant. In practice, the presence of a constant failure rate may be confirmed from observing the times between failures of a process where failures occur at random times.
In general, if we observe any process composed of events that occur at random times (say lightning strikes, coal mine accidents, earthquakes, fires, etc.), the times between these events will be Exponentially distributed. The probability of occurrence of the next event is independent of the occurrence time of the past event. As a result, phrases such as "old is as good as new" have a valid meaning. [It is important to note that although failures may occur at random times, they do not occur for "no reason". Every failure has an underlying cause.]
In what follows, we will use statistical properties derived from Exponential distribution implications to validate the Exponential assumption.
