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Completely and thoroughly explain how Control Charts could be used by a company that makes Eyeglass...

Completely and thoroughly explain how Control Charts could be used by a company that makes Eyeglass Lenses to improve the manufacturing processes they use to make eyeglass lenses.

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The company can use the variable  as well as attribute charts to improve the manufacturing process in following manner.

(a) Company can identify certain crucial properties of the eyeglass lenses such as the thickness of the lens utilising the running data, collected in form of samples taken at regular intervals such as once every shift of 8 hours. If there are 8 machines, one sample from each would make it 8 per shift. If this exercise continues for 10 days, we have sets of 8 samples each. The average as well as range ( difference between the highest value and the lowest value in a set of 8) can be noted. Now the average of the averages ( xbarbar) and average of ranges ( rbar) can be calculated. The Xbar and R chart can be prepared with help of statistical methods and can be used to find if both the values ( xbar and R) are within conrol limits. The pattern of variation of data can be used to find if the process has an assignable cause or it is just random variation.

(c) The attributes can also be used to  construct the charts ( p chart, c chart ), These attributes are inform of number of defects or fraction of defects which can be calculated from a sample of taken at random and finding out number of defects in it. Ten or twenty or more of such samples of 100 each can be used to find out the average fraction defective and construct the charts to find out if the process is under control limits or not. If the process is found to produce more defects, it can be rectified accordingly.

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