Portfolio created by Hein Htet |
Home Introduction Data Collection and Estimation System's Dynamics Human Factor Analysis Queue Theory Multifactorial Design Life-Cycle Audit Economic Analysis Conclusion and recommendation Bibliography

Introduction
There are 3 concepts that needed to be addressed in multifactorial design. They are Pareto Principle which include 80/20 rule and Pareto chart, the Bathtub Curve and Design of Experiments (DoE).
Pareto Principle (80/20 rule)
The core of the Pareto principle is that the 'vital few' among the problems hold the key, while the 'trivial many' only dissipate resources, focus and energy. The Pareto principle is based on 80/20 rule, which emphasizes that 80 percent of the problems come from 20 percent of causes (Bose 2011). Pareto discovered that 80% of the land in Italy was owned by 20% of the population. Later, he discovered that the Pareto principle was valid in other parts of life, such as gardening; 80% of his garden peas were produced by 20% of the pea pods (Parmenter 2007).
The steps involved in Pareto analysis;
(1) form a table of causes and frequency
(2) Arrange the rows in decreasing order of frequency
(3) Add a cumulative percentage column to the table
(4) Plot causes on x-axis and cumulative percentage on y-axis
(5) Join the points to form a curve
(6) plot bar graph with causes on x-axis and frequency on y-axis on the same graph
(7) draw a line at 80% of cumulative percentage on y-axis and then drop the line at the point of intersection with the curve on x-axis . The point on x-axis separates the important causes on the left and less important causes on the right. (Wikipedia 2013)
Application
The data required for this analysis is not able to obtain for our system and thus, we will go through this analysis by using some examples. The following example is taken from the youtube video of Dr. Eugene FM O'Loughlin's (2009).
The table 8 below shows the different types of complaints received at a hotel with frequency for reach type. Then we will rearrange the table with decreasing order of frequency. Cumulative frequency and percentage columns has added to the table as shown in table 9. I have omitted the other from the table as it is not useful reason. The Pareto chart is illustrated in figure 19. Then we draw a vertical line at 80% on the curve. The reasons to the left of the line are more important and that of right are less important. From the figure, we can see that room service, reservation and cleaning are the top complaints made by the customers.
When we look at the x-axis, the top 3 complaints contributes to 20% of all complaints made. Thus, the conclusion is 80% of customers' complaints were made by 20% of the reasons.

Table 8: Types of complaints received at a hotel | Table 9: Rearranged table of complaints with cumulative frequency and percentage.

Figure 19: The graph showing important reasons of causes according to 80/20 rule.
Bathtub Curve and Reliability-Centered maintenance (RCM)
The bathtub curve illustrates the nature of system failure. It is called Bathtub curve as the the curve looks like the cross sectional view of a bathtub as shown in figure 20.
The first section of the curve is characterized by decreasing failure rate. A system or component that has a decreasing failure rate is suffering from "infant mortality failures". These are premature failures caused by defective materials, inadequate materials, poor manufacturing, etc. In this case, reliability can be increased by resolving these issues or by burn-in; operating the device for a period of time long enough to weed our the infancy failures. The second portion of the curve is characterized by constant failure rate. Failures occurring at constant failure rate are independent of time. An item that has operated for one hour has the same probability of failure in the next 10 hours as an item that has operated for 1000 hours. This is known as lack of memory. Because of lack of memory, preventive maintenance is of no use. The third section of bathtub curve is characterized by increasing failure rat which represents components that wear out with age. In this case, system reliability can be increased by replacing components before they fail and by performing preventive maintenance. One thing to take note is that when modelling systems, only a portion of bathtub may be used. Many systems and components do not exhibit all 3 phases of bathtub curve (Dodson 2006).
The Bathtub curve is derived from the "Cumulative failure plot" as shown in figure 21. This plot shows the cumulative number of failures over time. For example, if you shipped 1,000 non repariable widgets and then kept track of total number of widgets that failed through the life of a product, the plot will look similar to figure 21 (Levin & Kalal 2003).
Figure 20: Bathtub Curve (Levin & Kalal, 2003)
Figure 21: Accumulated number of failure over time (Levin & Kalal, 2003)
Design of Experiment
Design of experiment is a kind of build-and-test approach in which some design factors are varied on at a time and test the design and record the outcomes until all the factors has been taken into consideration.
Application
According to our survey result as shown in figure 5 from "System's dynamics", only 17.1% of people use library computers while the other 82.9% only require a set of table and chair for them to study. We will go through high level application of theory here.
In order to do DOE, firstly, we have to make a design matrix with high and low level input factor as shown in table 10. In this case, the input factors are the number of study table and chair (STC) and number of computers. This is a 2 factor experiment which means there is a need to do 4 experiments. The value in the table indicates the number of sets of table and chair, and that of computers.
The next step is to run the experiment and record the results. For our case, the column 1 and 2 shows the number of sets for high level and low level. Column 3 shows the number of sets of both furniture and computers. Column 5 and 6 shows the number of sets of furniture and computers required for each experiment based on the survey data in figure 5 from "System's dynamics". The value is obtained by proportion to the survey data. for example, 17.1% of people use library computers according to survey data and thus 17.1% of total number of sets of facility in experiment for computers is 6. The same calculation has done for column 5 and 6.
column 7 and 8 shows the number of people waiting to see study space and computers. Negative value means supply is more than demand vice versa. Column 9 shows the total number of people waiting to use any facility at the library. Based on the table 11, experiment 3 has the lowest number of people waiting to use facility at library.
Column 10 and 11 shows the effect of increasing the number of sets of furniture and computers. The negative effect here means that supply is more than demand vice versa. When we increase the number of sets of furniture, we can supply more than demand. However, when we increase the number of computers at library, it will cause a lot of people to wait to use as there is not sufficient facility.
From this DOE, we can clearly see that the number of sets of furniture in the library will greatly affect the users.
Table 10: design matrix
Table 11 : DOE for library system

Computers at Menzies library
Create a free website with Weebly