Hotelling T² control chart based on bivariate ranked set schemes

Abstract

Univariate control charts under ranked set schemes are used to continuously monitor two or more related characteristic independently. In this article we have offered Hotelling T² control chart based on different bivariate ranked set schemes for monitoring two related characteristic simultaneously instead of independently. In this regard, we have proposed control chart statistic and control limits under bivariate ranked set schemes for handling two characteristics. Furthermore, we have computed empirical run length distribution and its properties to see the effect or role of different factors. We have found that proposed Hotelling T² control chart under ranked set schemes perform outstanding as compared to classical Hotelling T² control chart under simple random sampling in general. Moreover, proposed Hotelling T² control chart under double ranked set schemes is declared more efficient relative to single ranked set schemes. Among single and double ranked set schemes, proposed control chart under median ranked set schemes have uniformly high detection ability. Another feature of proposed control chart is to become special cases of the existing control charts when specific value of correlation between study variables and concomitant variable as well as sample size are considered. A real life example has included in which irrigation water monitored through the proposed control chart.

KEYWORDS:

• Average run length
• control chart
• emperical cumulative distribution function
• Hotelling T2
• median of run length
• ranked set schemes
• run length distribution

Acknowledgment

I am specially thankful to my beloved wife for providing me lots of support to accomplish this research work successfully.