Correlation level among the observations for a pharmaceutical industry using X chart with economics

Traditionally, it is assumed that the observations are independent and identically distributed (IID). However, in actual practice, the observations may be correlated. The paper presents the new X chart; based on sum of chi-squares theory and designed to counter the autocorrelation. Optimal schemes of new X chart for sample size (n) of four at different levels of correlation (Φ) are presented in this paper. Samples of quantity (in ml.) of the syrup are taken from a pharmaceutical industry; located in India and the level of correlation among the observations is calculated. The levels of correlation among the observations of the quantity of the syrup are computed and matched with the suggested optimal schemes of new X chart for sample size (n) of four. It is found that the level of correlation of 0.50 exists among the data of the industry. The economic performance of the new X chart is also measured in terms of the expected cost (EC) per hour for the given set of parameters. The EC per hour is calculated for the shifts in the process mean. It is observed that the new X chart for sample size of four is more economical than Shewhart X chart to use in the industries where autocorrelation exists.