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

Authors: D.R. Prajapati

Addresses: Department of Mechanical Engineering, PEC University of Technology, Chandigarh – 160012, India

Abstract: 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.

Keywords: correlation level; sample size; average run length; ARL; pharmaceutical industry; x-bar charts; economic design; control charts; statistical process control; SPC; India; autocorrelation.

DOI: 10.1504/IJPQM.2016.079777

International Journal of Productivity and Quality Management, 2016 Vol.19 No.3, pp.277 - 300

Received: 27 Jan 2015
Accepted: 01 Mar 2015

Published online: 24 Sep 2016 *

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