The XYZ Company has just purchased a large machine for a new

The XYZ Company has just purchased a large machine for a new production process. The machine is powered by a motor that occasionally breaks down and requires a major overhaul. The breakdown always occur on the fourth, fifth, or sixth day that the motor is in use, and the probability distribution of breakdowns is as follows:

Day

Probability of a Breakdown

1, 2, 3

0

4

0.25

5

0.55

6

0.20

7 or more

0

Cost of a replacement cycle that begins with a breakdown is as follows:

Replace a Motor

$2,000

Lost production during replacement

$4,500

Overhaul a motor

$3,500

Total

$10,000

This company is now considering preventive maintenance option, which involves scheduling the moto to be removed and replaced for an overhaul at a certain time, even if a breakdown has not occurred. Cost of a replacement cycle that begins without a breakdown is as follows:

Replace a motor on overtime

$3,000

Lost production during replacement

0

Overhaul a motor before a breakdown

$3,000  

Total

$6,000

Based on the information above, this company is trying to use computer simulation to estimate the average cost per day of replacing motor after 5 days as the preventive maintenance option. Below is the spreadsheet that simulate the preventive maintenance. Fill in the yellow blanks.

Cycle

Random number

Time until breakdown

Scheduled time until replacement

Event that concludes cycle (breakdown or replacement)

Cumulative day

Cost

Cumulative Cost

1

0.0312

5

$10,000

2

0.2554

5

$20,000

3

0.9912

5

$26,000

4

0.0626

5

$36,000

30

0.3269

5

5

Breakdown

139

$10,000

$284,000

Average cost per day:

Day	Probability of a Breakdown
1, 2, 3	0
4	0.25
5	0.55
6	0.20
7 or more	0

Solution

Day Probability of a Breakdown Corresponding Random Numbers 1, 2, 3 0 4 0.25 0.0000 to 0.2499 5 0.55 0.2500 to 0.7999 6 0.2 0.8000 to 0.9999 7 or more 0 Cycle Random number Time until breakdown Scheduled time until replacement Event that concludes cycle (breakdown or replacement) Cumulative day Cost Cumulative Cost 1 0.0312 4 5 replacement 5 6000 $6,000 2 0.2554 5 5 breakdown 10 $10,000 $16,000 3 0.9912 6 5 replacement 15 6000 $22,000 4 0.0626 4 5 replacement 20 6000 $28,000 5 0.5446 5 5 breakdown 25 $10,000 $38,000 6 0.5024 5 5 breakdown 30 $10,000 $48,000 7 0.3518 5 5 breakdown 35 $10,000 $58,000 8 0.4369 5 5 breakdown 40 $10,000 $68,000 9 0.8892 6 5 replacement 45 6000 $74,000 10 0.0256 4 5 replacement 50 6000 $80,000 11 0.3407 5 5 breakdown 55 $10,000 $90,000 12 0.7896 5 5 breakdown 60 $10,000 $100,000 13 0.2086 4 5 replacement 65 6000 $106,000 14 0.5316 5 5 breakdown 70 $10,000 $116,000 15 0.89 6 5 replacement 75 6000 $122,000 16 0.0456 4 5 replacement 80 6000 $128,000 17 0.7986 5 5 breakdown 85 $10,000 $138,000 18 0.4536 5 5 breakdown 90 $10,000 $148,000 19 0.7198 5 5 breakdown 95 $10,000 $158,000 20 0.4589 5 5 breakdown 100 $10,000 $168,000 21 0.1256 4 5 replacement 105 6000 $174,000 22 0.6689 5 5 breakdown 110 $10,000 $184,000 23 0.2071 4 5 replacement 115 6000 $190,000 24 0.1474 4 5 replacement 120 6000 $196,000 25 0.4307 5 5 breakdown 125 $10,000 $206,000 26 0.8948 6 5 replacement 130 6000 $212,000 27 0.5111 5 5 breakdown 135 $10,000 $222,000 28 0.6564 5 5 breakdown 140 $10,000 $232,000 29 0.9692 6 5 replacement 145 6000 $238,000 30 0.3269 5 5 Breakdown 150 $10,000 $248,000