Applications of a New Power Normal Family : A Case Study on C_pk index
Takafumi Isogai · Institutional Repositories DataBase (IRDB) · 2010
We often come across problems that data sets are positive-valued and skewed, but we want to interpret them through usual means and variances because of their convenience. In this paper we shall examine a case where we have to evaluate usual Cpk, the Process Capability Index, for positively skewed data. The value of usual Cpk is biased. Thus, new versions of Cpk are introduced through a new power normal (Isogai, 1999) and related power normal families. Comparisons are made with normal, our new power normal and related families. Our new power normal family shows its stable performance, but Box-Cox power normal family (Box & Cox, 1964) does not.