It is found that the process outputs from most of the industries are correlated and the performance of X-bar chart deteriorates when the level of correlation increases. The purpose of this paper is to compute the level of correlation among the observations of the weights of tablets of a pharmaceutical industry by using modified X-bar chart.
The design of the modified X-bar chart is based upon the sum of χ2s, using warning limits and the performance of the chart is measured in terms of average run lengths (ARLs). The ARLs at various sets of parameters of the modified X-bar chart are computed; using MATLAB software at the given mean and standard deviation.
The performance of the modified X-bar chart is computed for sample sizes of four. ARLs of optimal schemes of X-bar chart for sample size of four are computed. Various optimal schemes of modified X-bar chart for sample size (n) of four at the levels of correlation (Φ) of 0.00, 0.25, 0.50, 0.75 and 1.00 are presented in this paper. Samples of weights of the tablets are taken from a pharmaceutical industry and computed the level of correlation among the observations of the weights of the tablets. It is found that the observations are closely resembled with the simulated observations for the level of correlation of 0.75 in this case study. The performance of modified X-bar chart for sample size (n) of four at the levels of correlation (Φ) of 0.50 and 0.75 is also compared with the conventional (Shewhart) X-bar chart and it is concluded that the modified X-bar chart performs better than Shewhart X-bar chart.
All the schemes are optimized by assuming the normal distribution. But this assumption may also be relaxed to design theses schemes for autocorrelated data. The optimal schemes for modified X-bar chart can also be used for other industries; where the manufacturing time of products is small. This scheme may also be used for any sample sizes suitable for the industries
The optimal scheme of modified X-bar chart for sample size (n) of four is used according to the computed level of correlation in the observations. The simple design of modified X-bar chart makes it more useful at the shop floor level for many industries where correlation exists. The correlation among the process outputs of any industry can be find out and corresponding to that level of correlation, the suggested control chart parameters can be used.
The design of modified X-bar chart uses very less numbers of parameters so it can be used at the shop floor level with ease. The rejection level of products in the industries can be reduced by designing the better control chart schemes which will also reduce the loss to the society as suggested by Taguchi (1985).
Although; it is the extension of previous work but it can be applied to various manufacturing and service industries; where the data are correlated and normally distributed.
Prajapati, D.R. and Singh, S. (2016), "Determination of level of correlation for products of pharmaceutical industry by using modified
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