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

机译:使用X图表和经济学的制药行业观察值之间的相关性级别

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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.
机译:传统上,假设观测值是独立且相同分布的(IID)。但是,在实际操作中,这些观察结果可能是相关的。本文介绍了新的X图表;基于卡方理论之和,并设计用于抵消自相关。本文提出了针对不同相关度(Φ)的四个样本量(n)的新X图表的最优方案。糖浆的数量(以毫升为单位)样品取自制药业;位于印度的位置,并计算观测值之间的相关程度。计算糖浆量的观察值之间的相关程度,并与建议的新X图表针对样本大小(n)为4的最佳方案相匹配。发现行业数据之间存在0.50_的相关水平。对于给定的参数集,新的X图表的经济绩效还根据每小时的预期成本(EC)进行衡量。每小时EC用于计算过程平均值的变化。可以看到,对于四个样本量的新X图表,比在工业上使用的Shewhart X图表更经济;存在自相关的地方。

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