JET copies case study

JET copies case study

1. MS Excel model for number of days required to repair the copier.

Let assume that the required number of days for repairing the copier machine is random and the random number is donated by RN and it generates any value between 0 and 1 as follows:

When random value RN is greater than 0 but less than 0.2, then it takes 1 day to repair the machine.

When random value RN is greater than 0.2 but less than 0.65, then it takes 2 days to repair the machine.

When random value RN is greater than 0.65 but less than 0.9, then it takes 3 days to repair the machine.

When random value RN is greater than 0.9 but less than or equals to 1, then it takes 4 day to repair the machine.

The excel model is illustrated in the table below:

Breakdowns

RN

Repair Time (days)

1

0.62

2

2

0.67

3

3

0.66

3

4

0.85

3

5

0.72

3

6

0.06

1

7

0.66

3

8

0.62

2

9

0.21

2

10

0.43

2

11

0.64

2

12

0.02

1

13

0.30

2

14

0.52

2

The average number of time to repair the copier is obtained by dividing the total repair time by breakdowns. The average repair time for the breakdown obtained is 2.21 days.

2. Excel model for interval between successive breakdowns

To develop the Excel model that tell the intervals between successive breakdowns can be done by assuming that the random number varies between 0 to 6 weeks time, and the probability is increasing with the passage of time. This can be approximated with the function given below:

F(x) = x/18, for 0 = x = 6, where x is number of weeks between breakdowns of machine. In this way the distribution function will be as follows:

F(x) = X2/36 for 0 = x = 6

Let assume another random number RN1 that is any random value between 0 and 1 then:

RN1 - x2/36

X = 6*sqrt(RN1)

Excel model for the interval between successive breakdowns is given below:

Breakdowns

RN1

Time Between Breakdown, x (weeks)

Cumulative x

1

0.96

5.89

2.19

2

0.59

4.62

6.81

3

0.35

3.56

10.37

4

0.36

3.61

13.98

5

0.06

1.47

15.45

6

0.29

3.23

18.67

7

0.52

4.34

23.01

8

0.06

1.42

24.43

9

0.00

0.29

24.72

10

0.46

4.05

28.77

11

0.84

5.49

34.26

12

0.91

5.71

39.98

13

0.17

2.49

42.46

14

0.67

4.90

47.36

15

0.54

4.43

51.79

Average ...