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Quality Engineering Report I
N5_N7
The diameters of small shafts being cut on two lathes, N5 and N7, are measured from the thimble of a 0"-1" micrometer. There are 10 subgroups for each lathe and 6 samples per subgroup. The process specification is 0.258 +/- 0.005. The grouped data analysis and statistical process control analysis will be done on the data and the lathes will be compared.
Quality Engineering Report 1: Text
N5 Analysis
The diameters of the small shafts cut on lathe N5 are shown to the left. The maximum is 0.266 and the minimum is 0.254. Using the grouped data analysis method the range is 0.012, the average is 0.259, and the standard deviation is 0.003. These can be used to calculate and initial process capability of 0.659 and a centered process capability of 0.847. Since neither process capability is above 1 we can assume that there is a problem within the process.
The histogram was constructed using an interval of 0.002. The bell curve is centered appropriately rather than skewed and is distributed enough so that the kurtosis of it is not impossibly tight.
The Xbar chart shows the average of each subgroup (blue line) compared to the total average (red line), the upper control limit (green line), and the lower control limit (purple line). Using the constant 0.483, the upper control limit is 0.263 and the lower control limit is 0.256. None of the subgroup averages exceed the upper and lower control limits so there is no blatant assignable causes. However, since subgroup 4 is very close to the upper control limit it can be considered an assignable cause.
The range chart compares the range of each subgroup (blue line) to the average of the subgroup ranges (green line) and the upper control limit for the range (red line). Using a constant of 2.004, the upper control limit is 0.013. By examining this chart we can see there is a large drop from subgroup to subgroup 5 and then a large increase from subgroup 8 to subgroup 9. This can indicate that there is an issue in the process and these subgroups can be considered assignable causes.
By using the data collected thus far more accurate process capabilities can be calculated. The initial process capability is 0.408 and the centered process capability is 0.414. Like the process capabilities found in the grouped data analysis we can see that the process is not capable of handling the specification and will not produce usable product.
Since we have determined the process cannot handle the specification we can look at the assignable causes found on the individuals chart to identify the where the process must improve. It can be seen that samples in subgroups 1,4, and 9 exceeded the upper tolerance limit. It is also worth noting that samples in subgroups 2, 3, and 6 are on the upper tolerance limit line. These areas of the process should be analyzed for problems since they are producing products that are outside of the specification.
Quality Engineering Report 1: Features
N7 Analysis
The diameters of the small shafts cut on lathe N7 are shown to the left. The maximum is 0.267 and the minimum is 0.253. Using the grouped data analysis method the range is 0.014, the average is 0.259, and the standard deviation is 0.003. These can be used to calculate and initial process capability of 0.533 and a centered process capability of 0.846. Similarly to N5 neither process capability is above 1 and we again can assume that there is a problem within the process.
The histogram was constructed using an interval of 0.002. The bell curve is not centered correctly. The data is skewed towards the smaller diameters and thus there must be an issue within the process. The data started to rise appropriately but there is a sudden drop after the 0.258 interval where it levels out before dropping again. For a process to work well the bell curve should be decently symmetrical and stay within the upper and lower specifications.
The Xbar chart shows the average of each subgroup (blue line) compared to the total average (red line), the upper control limit (green line), and the lower control limit (purple line). Using the constant 0.483, the upper control limit is 0.261 and the lower control limit is 0.257. There are several assignable causes present in this graph which is not only noted by where subgroups exceed the control limits but also the large magnitude to which Xbar increase. Subgroups 1 and 2 are both below the lower control limit and subgroup 3 is on the lower control limit line. Subgroups 9 and 10 are above the upper control and subgroup 7 is on the upper control limit line. These 6 subgroups from the 10 are all assignable causes thus we can assume there is a severe problem in the process.
The range chart compares the range of each subgroup (blue line) to the average of the subgroup ranges (green line) and the upper control limit for the range (red line). Using a constant of 2.004, the upper control limit is 0.008. While fluctuations on this chart is normal the magnitude to which it fluctuates between several of these subgroups are fairly large and can be considered assignable causes.
By using the data collected thus far more accurate process capabilities can be calculated. The initial process capability is 0.408 and the centered process capability is 0.216. Like the process capabilities found in the grouped data analysis we can see that the process is not capable of handling the specification and will not produce usable product.
Since we have determined the process cannot handle the specification we can look at the assignable causes found on the individuals chart to identify the where the process must improve. Subgroups 1 and 2 both have a sample on the lower tolerance line. Subgroup 8 has one sample and subgroups 9 and 10 both have two samples on the upper tolerance line. Subgroup 7 has one sample and subgroup 10 has three samples above the upper tolerance. Another issue that needs to be taken into account is that each subgroups samples increase in diameter since the last group. An effective process would show fluctuations in the size but in this case they seem to steady increase. Not only do the areas where samples are out of specification need to be analyzed but also why there is a an increase in sample diameter as time goes on.
Quality Engineering Report 1: Features
It can be seen just by looking at the histograms that N5 will be the more capable and stable process. N5's histogram is balanced well so we need a more in depth analysis to see if the process is capable pf meeting requirements. In contrast, N7's histogram is skewed in one direction indicating that there is a problem in the process that needs to be addressed. The process capabilities in each lathes grouped data analysis are very close in value thus making it hard to tell which lathe is more stable and capable. However, there is a about a 0.126 advantage in favor of N5 in the initial process capability calculation. In contrast N7 has about 0.029 advantage in the centered process capability.Â
After analyzing all of the data it can be seen that while neither lathe can be considered capable. However, N5 is the better lathe to use since it had a better statistical process control capability and is more stable than N7.
Quality Engineering Report 1: Text
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