Abstract
It is generally assumed that data are distributed as normal random variables. Therefore, the data are analyzed based on normal distribution. However, in practice, there are many situations that data are distributed as non-normal random variables. The data for material destruction phenomenon is one example. In this case, the data for destruction is explained clearer by the extreme value distribution based on the weakest link theory rather than normal distribution. It is illustrated that the various data based on the weakest link theory, such as data for the strength of industrial materials, mechanical and electronic parts and lifetime of products, are distributed as an extreme value distribution. By the way, the control chart is widely known as a statistical process control tools. Until now, there have been many studies about control charts for normal random variables, but few studies for non-normal random variables. Here, Johnson has proposed a method for transforming non-normal random variables into normal random variables. In this study, we consider the control chart for the double exponential random variables by using Johnson's transformation method, propose a design procedure and then verify the property of the proposed control chart.
