1. The mean time between failures and mean time to repair in a certain department of the factory are 400 hr and 8 hr, respectively.The department operates 25 machines during one 8 hr shift/day, 5 day/wk, 52 wk/yr. Each time a machine breaks down, it costs the company. $200hr (per machine) in lost revenue. A proposal has been submitted to install a preventive maintenance program in this department. In this program, preventive maintenance would be performed on the machines during the evening so that there will be no interruptions to production during the regular shift.The effect of this program is expected to be that the average MTBF will double, and half of the emergency repair time normally accomplished during the day shift will be performed during the evening shift. The cost of the maintenance crew will be $1500wk. However, a reduction of maintenance personnel on the day shift will result in a savings during the regular shift of $700wk. (a) Compute the availability of machines in the department both before and after the preventive maintenance program is installed. (b) Determine how many total hours per year the 25 machines in the department are under repair both before and after the preventive maintenance program is installed. In this part and in part (c), ignore effects of queueing of the machines that might have to wait for a maintenance crew. (c) Will the preventive maintenance program pay for itself in terms of savings in the cost of lost revenues?

2. There are nine machines in the automatic lathe section of a certain machine shop.The setup time on an automatic lathe averages 6 hr.The average batch size for parts processed through the section is 90.The average operation time=8.0 min. Under shop rules, an operator is permitted to be assigned to run up to three machines.Accordingly, there are three operators in the section for the nine lathes. In addition to the lathe operators, there are two setup workers who perform machine setups exclusively. These setup workers are kept busy the full shift.The section runs one 8 hr shift/day, 6 day/wk. However, an average of 15% of the production time is lost due to machine breakdowns. Scrap losses are negligible.The production control manager claims that the capacity of the section should be 1836 piece/wk. However, the actual output averages only 1440 unit/wk.What is the problem? Recommend a solution.