# W12_SSD_Selecting the Right Distribution

1. Problem Definition

A switchroom is one of the biggest non electrical components in a substation. Based on the information received on several tender submissions, a table which indicate the percentage of design work cost compare to total project cost is developed. The table is shown in Table 1. To properly use this set of data for estimating purpose, one need to identify what type of probability distribution may fit with the data. This distribution later may be used to calculate the contingency fund.

1. Alternative Identification

To fit a probability distribution with the data, software @Risk is used. One of this Excel add-in capabilities is to fit a distribution to a set of data. There are a lot of probability distributions to select. In this exercise, 3 probability distributions are compared. These 3 distributions are:

1. Normal distribution
2. Log Normal
3. Pert

The selection of these 3 distributions is because these 3 distributions are the type of distributions which commonly used in project analysis. The other type that commonly used includes triangular, uniform, and step.

1. Outcome for each Alternatives

Using Fit Distributions function in @Risk, the result is shown in the figure below: 1. Selection Criteria

There are several criteria on selecting the distribution, they are as follow:

1. having higher ranking in the fitting
2. visually look more fit compare to other
3. the distribution’s left leg does not have negative value. As in the real world situation, negative percentage is never happened.
1. Analysis and Comparison of the Alternative

The graph above shows the plotting of 3 types of distribution on the actual data. The actual data is represented by the blue bars. The normal distribution is represented by the red line, the pert distribution by the green line, and the log normal is represented by the purple line. At the right hand side of the graph, one can see the statistical value for each of the distribution.

On the above graph, the normal distribution is ranked higher compare to the other two using Akaike Information Criteria (AIC) methodology. But, the normal distribution has its peak off set from the highest blue bar. It also has its left leg crossing 0.00 at P9.1%.

The pert distribution is second best according to AIC ranking. It has its peak fit with the highest blue bar and it does not have negative leg. But, the distribution’s mode and minimum value is the same (0.05241). This situation is pretty rare in the real world.

The log normal distribution ranks last based on AIC ranking. Its mode is fit with tallest blue bar. The left leg value is higher than 0, and it seems to fit the actual pretty nicely.

1. Selection of the Preferred Alternatives

Based on the analysis above, the log normal distribution is selected as the preferred option. By using log normal distribution, the following statistical values apply:

1. mean = 0.018281
2. mode = 0.007658
3. standard deviation = 0.016936
1. Performance Monitoring and the Post Evaluation of Result

To use the distribution for estimating, the distribution should be multiplied to the switchroom total cost. The distribution basically replaces the % as single number with a distribution. If the total switchroom cost is \$500,000 then the estimate for the switchroom shop drawing is \$500,000 x (log normal distribution with mean= 0.018281 and standard deviation= 0.016936). The graph for this arrangement is as follow: From the graph we can see that the mode is \$3,925, which is less than P50 of the expected cost, the mean is \$9,145 which is equal to P67.5.

Currently the distribution plot is determined base on only 7 actual data. Once additional actual data become available, it will be good to update the graph, checking if the distribution still applicable.

References

Daroeso, S.S. (Dec 2013). Analysis and Parametric Estimating Formula for Switchroom Cost [PowerPoint slides]. Western Power.

1 Comment

Filed under Sadat SD, Week 12

### One response to “W12_SSD_Selecting the Right Distribution”

1. drpdg

EXCELLENT case study and analysis, Pak Sadat…..

Just watch your citations…… You did not cite Palisade Software correctly using APA format, which cost you one star…… https://owl.english.purdue.edu/owl/resource/560/10/

Keep up the good work and look forward to you catching up…..

BR,
Dr. PDG, Jakarta