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Problem 13. The new shearing machine is set to cut off a piece of steel from a long bar for various reasons the machine at times cuts off a piece that is too long or too shon. These unacceptable pieces are automatically dropped in a box and the operator of the shearing machine is to count these defectives after 100 pieces are sheared off. The record after the first day of operation is : Number Sheared off Number Defectives 100 100 100 100 100 Set out upper and lower control limits. 5 6 7 4 8 Problem 11. A manufacturing firm is considering a policy of replacing certain key electrical components belonging to one group of machines on a group replacement basis instead of making repairs as needed. There are approximately 100 parts of one type that have the mortality distribution shown below. The cost of replacing parts on individual basis is estimated to be Rs. 10 per part whereas that on group basis comes to Rs. 3 per part. Compare the average weekly cost of the two replacement alternatives : Week Probability of failure during week 1 2 3 4 5 0.3 0.1 0.1 0.2 0.3