The probability of an asset operating at acceptable level of service without mai
ID: 3221337 • Letter: T
Question
The probability of an asset operating at acceptable level of service without maintenance is given as follows: Year 1 = 0.80 Year 2 = 0.65 Year 3 = 0.35 Year 4 = 0.25 The user cost associated with any asset operating at unacceptable level of service = $12, 500, 000 per year. The annual cost of maintaining an asset to continue operating at acceptable level of service = $4, 500, 000. Determine the recommended maintenance frequency (maximum number of years of deferred maintenance) of assets in order to minimize the expected cost.Explanation / Answer
Give probability of acceptable level of service is
Year 1=0.80
Year 2=0.65
Year 3=0.35
Year 4=0.25
Calculations are show in tha table
probability.
of
acceptable level of
service
Cost of
Operatig at unacceptable service
0.80*12=9.6
1*4,500,000
=$4,500,000
1*4,500,000
=$4,500,000
2*4,500,000
=$9,000,000
3*4,500,000
=$13,500,000
As the above table, in the first year, the asset will continue to operate at an acceptable level of service for 9.6 months and thus will need maintenance once. For the second month also once
For the third year, the asset will require maintenance after 4.2 months and after 8.4 months.
For the fourth year, the asset will require maintenance after 3, 6 and 9 months. But the cost of three maintenance will be high compared to the cost operating at unacceptable level of service.
So minimum cost will be =( 4500000 + 4500000 + 9000000 + 12500000) = $30500000
And the total maintenance required will be = 1+1 +2 = 4
Yearprobability.
of
acceptable level of
service
Monhs No. maitanance Cost of maintanaceCost of
Operatig at unacceptable service
Minumum oo Dore 1 0.800.80*12=9.6
11*4,500,000
=$4,500,000
$12,500,000 $4,500,000 2 0.65 0.65*12=7.8 11*4,500,000
=$4,500,000
$12,500,000 $4,500,000 3 0.35 0.35*12=4.2 22*4,500,000
=$9,000,000
$12,500,000 $9,000,000 4 025 0.25*12=3.0 33*4,500,000
=$13,500,000
$12,500,000 $13,500,000Related Questions
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