For a particular piece of equipment, the probability of failure during a given w

Question

For a particular piece of equipment, the probability of failure during a given week is as follows: Week of Operation Probability of Failure

Week of Operation

Probability of Failure

1

2

3

4

5

6

0.25

0.08

0.07

0.10

0.20

0.30

Management is considering a preventive maintenance program that would be implemented at the end of a given week of production. The production loss and downtime costs associated with an equipment failure are estimated to be $2,500 per failure. If it costs $500 to perform the preventive maintenance, when should the firm implement the preventive maintenance program? What is the total maintenance and failure cost associated with your recommendation, and how many failures can be expected each year? Assume 52 weeks of operation per year.

Week of Operation

Probability of Failure

1

2

3

4

5

6

0.25

0.08

0.07

0.10

0.20

0.30

Explanation / Answer

Cumulative probability table

Critical ratio = 500/(2500+500) = 0.17

This is less than cumulative probability of less than 0.25.

Therefore, optimal preventive maintenance schedule is every 1 week of operation.

Expected failure week = 1*0.25+2*0.08+3*0.07+4*0.1+5*0.2+6*0.3 = 3.82 week of operation

Expected number of failures each year = 52/3.82 = 13.6 failures

Week of operation Probability of failure Cumulative probability of failure 1 0.25 0.25 2 0.08 0.33 3 0.07 0.40 4 0.10 0.50 5 0.20 0.70 6 0.30 1.00

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