Posted on by Judy

The fire department has a number of failures with its oxygen masks and is evaluating the possibility of outsourcing preventive maintenance to the manufacturer. Because of the risk associated with a failure, the cost of each failure is estimated at $2000. The current maintenance policy (with station employees performing maintenance) has yielded the following history: Number of breakdowns 0 1 2 3 4 5 Number of years in which breakdowns occurred 4 3 1 5 5 0 This manufacturer will guarantee repairs on any and all failures as part of a service contract. The cost of this service is $5000 per year. a. What is the expected number of breakdowns per year with station employees performing maintenance? b. What is the cost of the current maintenance policy? c. What is the more economical policy?

a) Construct probability table.
Number of breakdowns Number of years in which breakdowns occurred Frequency
0 4 22.22%
1 3 16.67%
2 1 5.56%
3 5 27.78%
4 5 27.78%
5 0 0%
18
(a) Expected number of breakdowns per year = 0*22.22%+1*16.67%+2*5.56%+3*27.78%+4*27.78%+5*0% = 2.22
(b) The cost of current maintenance policy is $ 5000 per year.
(c) Expected cost of failure = Expected number of failures per year * Cost of each failure = 2.22*2000 = $ 4444 per year
We see that the expected cost of failures is less than the cost of current maintenance policy. Therefore, the more economic policy is to get corrective maintenance based on actual failures, rather than having a service contract for $ 5000. In this case, the expected cost will be $ 4444 per year.
 
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