The process control methods based on the statistical analysis apply the analysis method or mathematical model under the assumption that the process characteristic is normally distributed. However, the distribution of data collected by the automatic measurement system in real time is often not followed by normal distribution. As the statistical analysis tools, the process capability index (PCI) has been used a lot as a measure of process capability analysis in the production site. However, PCI has been usually used without checking the normality test for the process data. Even though the normality assumption is violated, if the analysis method under the assumption of the normal distribution is performed, this will be an incorrect result and take a wrong action. When the normality assumption is violated, we can transform the non-normal data into the normal data by using an appropriate normal transformation method. There are various methods of the normal transformation. In this paper, we consider the Box-Cox transformation among them. Hence, the purpose of the study is to expand the analysis method for the multivariate process capability index using Box-Cox transformation. This study proposes the multivariate process capability index to be able to use according to both methodologies whether data is normally distributed or not. Through the computational examples, we compare and discuss the multivariate process capability index between before and after Box-Cox transformation when the process data is not normally distributed.

Network externalities are essentially dynamic in that the value consumers feel about a product is affected by the size of the existing customer base that uses that product. However, existing studies on network externalities analyzed the effects of network externalities in a static way, not dynamic. In this study, unlike previous studies, the impact of network externalities on price competition in a vertically differentiated market is dynamically analyzed. To this end, a two-period duopoly game model was used to reflect the dynamic aspects of network externalities. Based on the game model, the Nash equilibria for price, sales volume, and revenue were derived and numerically analyzed. The results can be summarized as follows. First, if high-end product has strong market power, the high-end product vendor takes almost all benefits of the network externality. Second, when high-end product has strong market power, the low-end product will take over most of the initial sales volume increase. Third, when market power of high-end product is not strong, it can be seen that the effects of network externalities on the high and low-end products are generally proportional to the difference in quality. Lastly, if there exists a strong network externality, it is shown that the presence of low-end product can be more profitable for high-end product vendor. In other words, high-end product vendor has incentive to disclose some technologies for the market entrance of low-end product, even if it has exclusive rights to the technologies. In that case, however, it is shown that the difference in quality should be maintained significantly.