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Statistical Process Control 5 Part 8

Tham khảo tài liệu 'statistical process control 5 part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 232 Cumulative sum cusum charts Figure 9.3 Slope of cusum chart for a change of 2SE in sample mean lines at 3SE Chapter 6 . We shall use this convention in the design of cusum charts for variables not in the setting of control limits but in the calculation of vertical and horizontal scales. When we examine a cusum chart we would wish that a major change -such as a change of 2SE in sample mean - shows clearly yet not so obtusely that the cusum graph is oscillating wildly following normal variation. This requirement may be met by arranging the scales such that a shift in sample mean of 2SE is represented on the chart by ca 45 slope. This is shown in Figure 9.3. It requires that the distance along the horizontal axis which represents one sample plot is approximately the same as that along the vertical axis representing 2SE. An example should clarify the explanation. In Chapter 6 we examined a process manufacturing steel rods. Data on rod lengths taken from 25 samples of size four had the following characteristics Grand or Process Mean Length X 150.1mm Mean Sample Range R 10.8 mm. We may use our simple formula from Chapter 6 to provide an estimate of the process standard deviation ơ Ơ R dn where dn is Hartley s Constant 2.059 for sample size n 4 Hence Ơ 10.8 2.059 5.25 mm. This value may in turn be used to calculate the standard error of the means Cumulative sum cusum charts 233 SE ơ pt SE 5.25 4 2.625 and 2SE 2 X 2.625 5.25 mm. We are now in a position to set the vertical and horizontal scales for the cusum chart. Assume that we wish to plot a sample result every 1 cm along the horizontal scale abscissa - the distance between each sample plot is 1 cm. To obtain a cusum slope of ca 45 for a change of 2SE in sample mean 1 cm on the vertical axis ordinate should correspond to the value of 2SE or thereabouts. In the steel rod process 2SE 5.25 mm. No one would be happy plotting a graph which required a scale 1 cm 5.25 mm so it is necessary to round up or down. Which shall