IT QUALITY AND PROJECT MANAGEMENT

IT QUALITY AND PROJECT MANAGEMENT



IT QUALITY AND PROJECT MANAGEMENT

PART I

Task I

The network diagram

Activity

Duration

Start Date

End Date

Proceedings

A

4 days

07/10/2009

12/10/2009



B

4 days

13/10/2009

16/10/2009

1

C

1 day

13/10/2009

13/10/2009

1

D

1 day

13/10/2009

13/10/2009

1

E

1 day

13/10/2009

13/10/2009

1

F

5 days

19/10/2009

23/10/2009

2,3,4,5

G

6 days

26/10/2009

02/11/2009

6

H

2 days

26/10/2009

27/10/2009

6

I

2 days

26/10/2009

27/10/2009

6

Gantt Chart and Network Diagram are presented in attached project file

Task II

See attached Excel Sheet

Task III

See attached pptx file

Part II

Using the inverse transformation method for a general discrete distribution is essentially a table lookup. To generate random numbers from an empirical distribution, we can use either the LOOKUP, VLOOKUP, or HLOOKUP functions provided by Excel. The vector form of LOOKUP function is discussed here. The syntax of the vector form is

=LOOKUP(lookup_value, lookup_vector, result_vector)

The values in the lookup vector must be in ascending order. LOOKUP compares the lookup_value to each cell in the lookup_vector until it finds a cell larger than the lookup_value. It then moves up one cell and returns the content of the corresponding cell in the result_vector as the answer. For example, assume the relative frequency of sales in unit per month for laser printers is as shown in Table 1.

Table 1

Unit Sales of Laser Printers

Unit Sales Per Month

Relative Frequency

350

0.1

450

0.1

550

0.5

650

0.3

To generate monthly unit sales, say, for six months in cells E2 through E7 from the above empirical distribution, at first, convert Table 1 into a cumulative-relative-frequency table as shown in Columns A and B of Table 2. Then, type =LOOKUP(RAND(),$B$2:$B$5, $A$2:$A$5) in cell E2. Finally, position the mouse pointer over the fill handle and drag it to cell E7 to extend the LOOKUP function from cell E2 to the range E3:E7. Suppose the numbers generated by RAND() are 0.22, 0.04, 0.39, 0.78, 0.23, and 0.16, the unit sales generated will be 550, 350, 550, 650, 550, and 450, respectively.

Table 2

Illustration of Empirical Random Number Generation

Triangular Distribution

The cumulative distribution function (CDF) of a triangular distribution with lower limit a, mode c and upper limit b is

The inverse of F is then

Thus, a triangular-distributed random number can be generated by the Excel formula

=IF(r<=(c-a)/(b-a), a+SQRT(r*(b-a)*(c-a)),b-SQRT((1-r)*(b-a)*(b-c))

where r can be generated by the RAND() function. Storing the value from the RAND() function in the variable r is important because the RAND() function returns a new value each time it is called. 

The Triangular Distribution may be used when the knowledge about a population is limited but the minimum, maximum and mode are known. 

Exponential Distribution

The CDF of an exponentially distributed random variable is

F(x) = 1 - e-ßx for x > 0

where 1/ß equals the mean of the exponential random variable. The inverse of F is then

F-1(r) = -ln(1-r)/ß

Therefore, the Excel formula for generating an exponentially distributed random number is simply

= -LN(1-RAND())/beta

Because RAND() is uniformly distributed, 1-RAND() is also uniformly distributed, and the above Excel formula can be further simplified as

= -LN(RAND())/beta

The distribution of time that elapses before the occurrence of some event often follows an exponential distribution.

Normal Distribution

The closed-form functional representation of the inverse of the CDF for the normal distribution does not exist. Fortunately, Excel has a built-in function NORMINV(probability,mean,std_dev) which returns the inverse of the normal cumulative distribution for the specified mean ...