Q control charts for negative binomial distribution

As we known, Q charts are SPC charts for approximate normal distribution. This paper proposes new kinds of Q charts for negative binomial random variable. First, define two transformations of approximate standard normal distribution for a negative binomial parameter p which it is known or unknown. Then, Q charts are constructed by transformed data, these Q charts are useful for monitoring process in real time from the beginning of sampling, especially, for p unknown in advance. In order to compare the goodness of the Q charts with conventional Shewhart charts with 3-sigma limits, an example is given. The results have shown that these Q charts are more efficient than classical Shewhart charts. Finally, some review are given.