PART-I. (This part has no link with PART-11) Ponds Engineering and Fabricating Company (PEFC) produces a specific item to a reasonably high degree of precision. In an effort to create statistical process control charts for this item, eight units are randomly selected from the output every hour. The measurements (in centimetres) are recorded sequentially for the samples over the previous 6 hours of operation. The sample data collected for this process is shown below: 1 4 5 36.2 35.2 34.3 Sample 1 2 3 4 5 6 35.2 38.2 39.3 35.2 40.6 2 37.1 39.2 40 36.2 34.5 41.7 3 36.1 33.6 34.5 39.5 35.8 38.6 36.5 33.2 37.7 39.1 43.5 38.4 36.4 38.6 38.5 44.6 6 37.3 40.5 39.1 38.5 36.4 41.7 7 38.5 36.5 33.2 37.7 37.1 43.5 8 37.3 40.5 39.1 38.5 36.4 41.7 Average 36.50 37.55 36.71 ? 36.63 41.99 Range 4.2 ? 6.8 3.3 4.6 6 Three sigma control limits are applied in the statistical process control of this item. (I-a) Determine the upper and lower control limits of the X-bar chart. (i-b) Determine the upper and lower control limits of the R chart. PART- II. (This part has no link to PART-I) Chimney Commercial Pipes Fabricating Company (CCPFC) produces many different kinds of plastic pipes for commercial uses. Plastic pipe is used for plumbing in almost all new homes. If the pipes are too narrow or too wide, they will not connect appropriately with other parts of the plumbing system. The operations manager, Steve, wants to make sure that the production process is producing products (3-inch diameter pipe) within acceptable tolerance limits where diameter of pipe should be measured within 3 +0.10 inches. To test this, the operator takes several sample measurements and determines the mean of the process to be 2.9950 inches with a standard deviation of 0.0415 inches. (ll-a) Calculate the process capability index and interpret it. (ll-b) What percent of the current production is expected to be within the given tolerance limits