7. A malfunction in a machine creates a loss which has a normal distribution wit

Question

7. A malfunction in a machine creates a loss which has a normal distribution with average $10,000 and standard deviation $1,000. Suppose that normally, there is a probability 20% that a malfunction does occur on any given week. A technician can be called to perform a preventive maintenance once every week, reducing this probability to 2%. (a) Suppose that as a result of the current policies, a maintenance can only be performed on 10% of the weeks. Find the average cost due to malfunctions. (b) Now, if it costs $200 per week to increase the frequency of maintenance to 40% of the weeks, should this increase be implemented?

Explanation / Answer

Now the malfunction creates a loss that has an average of 10000 dollars and std. dev of 1000$ and thereis a 20% chance that malfunction does occur in a week

(a) Now if a maintainance can be performed only on 10% of the weeks then considering thereare 50 weeks ina year and so maintainance can be done only on 10% of 50 = 5 weeks in a year, the average costs die to malfunctions will be 45 * 10000 = $4,500,000 for the whole year

(b) If it costs 200$ per week to increase the frequency of maintainance to 40% then total weeks that maintainance can be done is 0.4 * 50 = 20 weeks this leaves 50 -20 =30 weeks so cost of maintainance = 30 * 10000 = 3,000,000$ so considering a cost of 200$ per week extra we get cost of 200*20 = 4000$ extra,.

This still creates a saving of more than $1,000,000 and hence this increase should be implemented

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