Table 1. Initial Coded Data Assignment Attachment I gives coded results of measurements on 25 subgroup of size 5. They relate to the outer diameter of a certain component of aircraft engines. The first task is to reconstruct the real data, in millimetres, form the coded values. This is done by multiplying each number in the table by hundred (100) and then adding a shift constant, provided by the instructor shift constant is 1.5 USE THE DECODED DATA to carry out the following tasks: Subgroup number 1 2 3 4 1. Set the scales of the X and R chart to obtain a reasonable-looking graph, which will also accommodate the controllimit lines. Chart the measurements and draw the broken-line graphs. Calculate the central and control limit lines; draw them on the X and R chart. 2. 3. Examine the chart for evidence of out-of-control points. If you find any points outside the control limits on either the X chart or the R chart, assume assignable causes, and eliminate them from the data. Establish X and Rvalues. Accept Xarx as the standard value for the process centre and Par to estimate the process capability. Calculate the capability index. . The specification limits are obtainable from their coded values (0.745 and 0.755), via the formulae: 1 0.751 0.750 0.749 0.748 0.753 0.755 0.754 0.748 0.751 0.751 0.752 0.750 0.748 0.749 0.752 0.752 0.756 0.749 0.752 0.754 0.750 0.750 0.750 0.754 0.749 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Sample Measurements 2 3 3 4 0.747 0.752 0.750 0.748 0.749 0.750 0.749 0.752 0.750 0.749 0.749 0.751 0.749 0.752 0.751 0.752 0.753 0.744 0.751 0.752 0.750 0.753 0.749 0.748 0.750 0.751 0.752 0.753 0.751 0.752 0.752 0.751 0.751 0.749 0.749 0.748 0.749 0.751 0.747 0.750 0.750 0.751 0.751 0.751 0.752 0.750 0.750 0.748 0.754 0.752 0.744 0.749 0.750 0.751 0.750 0.753 0.750 0.753 0.750 0.750 0.750 0.750 0.750 0.752 0.751 0.753 0.751 0.749 0.748 0.745 0.747 0.746 0.749 0.749 0.749 4. 5 5 0.751 0.752 0.748 0.748 0.751 0.749 0.750 0.748 0.751 0.751 0.751 0.751 0.750 0.751 0.751 0.750 0.747 0.749 0.754 0.751 0.748 0.750 0.748 0.755 0.750 5. 6. USL = 75.5+ shift constant LSL = 74.5+ shift constant 7. Hence determine the process capability ratio k. Does this look like a good process? Produce a frequency distribution of the in-control data points (i.e. the individual data points). Also calculate the skewness and kurtosis of this distribution. If the data seem approximately normally distributed, find the percentage of off-specification product that this process will yield. 8. Since X is only a statistic, the true process centre, H, may be different. Estimate a 95% confidence interval for LL. Table 1. Initial Coded Data Assignment Attachment I gives coded results of measurements on 25 subgroup of size 5. They relate to the outer diameter of a certain component of aircraft engines. The first task is to reconstruct the real data, in millimetres, form the coded values. This is done by multiplying each number in the table by hundred (100) and then adding a shift constant, provided by the instructor shift constant is 1.5 USE THE DECODED DATA to carry out the following tasks: Subgroup number 1 2 3 4 1. Set the scales of the X and R chart to obtain a reasonable-looking graph, which will also accommodate the controllimit lines. Chart the measurements and draw the broken-line graphs. Calculate the central and control limit lines; draw them on the X and R chart. 2. 3. Examine the chart for evidence of out-of-control points. If you find any points outside the control limits on either the X chart or the R chart, assume assignable causes, and eliminate them from the data. Establish X and Rvalues. Accept Xarx as the standard value for the process centre and Par to estimate the process capability. Calculate the capability index. . The specification limits are obtainable from their coded values (0.745 and 0.755), via the formulae: 1 0.751 0.750 0.749 0.748 0.753 0.755 0.754 0.748 0.751 0.751 0.752 0.750 0.748 0.749 0.752 0.752 0.756 0.749 0.752 0.754 0.750 0.750 0.750 0.754 0.749 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Sample Measurements 2 3 3 4 0.747 0.752 0.750 0.748 0.749 0.750 0.749 0.752 0.750 0.749 0.749 0.751 0.749 0.752 0.751 0.752 0.753 0.744 0.751 0.752 0.750 0.753 0.749 0.748 0.750 0.751 0.752 0.753 0.751 0.752 0.752 0.751 0.751 0.749 0.749 0.748 0.749 0.751 0.747 0.750 0.750 0.751 0.751 0.751 0.752 0.750 0.750 0.748 0.754 0.752 0.744 0.749 0.750 0.751 0.750 0.753 0.750 0.753 0.750 0.750 0.750 0.750 0.750 0.752 0.751 0.753 0.751 0.749 0.748 0.745 0.747 0.746 0.749 0.749 0.749 4. 5 5 0.751 0.752 0.748 0.748 0.751 0.749 0.750 0.748 0.751 0.751 0.751 0.751 0.750 0.751 0.751 0.750 0.747 0.749 0.754 0.751 0.748 0.750 0.748 0.755 0.750 5. 6. USL = 75.5+ shift constant LSL = 74.5+ shift constant 7. Hence determine the process capability ratio k. Does this look like a good process? Produce a frequency distribution of the in-control data points (i.e. the individual data points). Also calculate the skewness and kurtosis of this distribution. If the data seem approximately normally distributed, find the percentage of off-specification product that this process will yield. 8. Since X is only a statistic, the true process centre, H, may be different. Estimate a 95% confidence interval for LL