 # Project Management Mathematics I- Monitoring & Control

• Cause-and-effect diagram
• Control charts
• Histogram
• Flowchart
• Pareto chart
• Checksheets
• Scatter diagram

## Cause and effect diagram

It is also known as fishbone diagram which are very helpful to find the root cause of the defect. The causes are found by looking at the problem statement and asking “why” until the actionable root cause has been identified or until the reasonable possibilities on each fishbone have been exhausted. This Ishikawa diagram helps stimulate thinking and organizes thoughts. This diagram depicts every potential cause and sub cause of a problem and the effect that each proposed solution will have on the problem. In the above diagram: poor training, old equipment, funds are the causes and “Excessive downtime” is the effect.

## Control charts

Control charts measure the results of processes over time and display the results in a graphical form. These charts are a way to determine whether process variances are in or out of control. A control chart is based on sample variance measurements. From the samples chosen and measured, the mean and standard deviation are determined. Let’s assume from a sample you have determined the measurement where mean is 300 and the standard deviation equals 44.72. Three standard deviations on either side of the mean become your upper and lower control points on this chart. In this case 3 standard deviations is equal to 300 +- (134.16).Therefore, if all control points fall within plus or minus three standard deviations on either side of the mean, the process is in control. If points fall outside the acceptable limits, the process is not in control and corrective action is needed. UCL and LCL are Upper control limit and lower control limit respectively. USL and LSL are upper specification limit and lower specification limit.

The relationship between mean and  SD is out of course, but if there is a sample of n items with values x1,x2,x3,x4 and so on

The SD and mean(X) can be calculated using the formula given below

X=(X1+X2+X3+…Xn) / n

SD = [(1/n) * ((X – X1) ^ 2 + (X- X2) ^ 2 +…. + (X -Xn) ^ 2)] ^ (1 /2)

## Histogram

Histogram is used for illustrating the relationship in the context of two variables. Histograms are typically bar charts that depict the distribution of variables over time. This represents the distribution by mean. If the histogram is normal, the graph takes the shape of a bell curve. If it is not normal, it may take different shapes based on the condition of the distribution. Histogram can be used to measure something against time i.e. the graph is plotted on x-axis and y-axis.

Consider the following example: The following histogram shows number of hits on the company’s website in different time of the day. The .x. axis shows the number of users or customers active on the website and the .y. axis shows the time of the day. ## Flowchart

The flow chart can be used to understand a complex process in order to find the relationships and dependencies between events. Flow charts can be used for any field and to illustrate events involving processes of any complexity. They typically show activities, decision points, and the flow or order of steps in a process. Flowcharts are diagrams that show the logical steps that must be performed in order to accomplish an objective. They can also show how the individual elements of a system interrelate. Flowcharting can help identify where quality problems might occur on the project and how problems happen. There is specific software tools developed for drawing flow charts, such as Microsoft Visio.

## Pareto chart

You have probably heard of the 80/20 rule. Pareto observed that 80 percent of the wealth and land ownership in Italy was held by 20 percent of the population. Over the years, others have shown that the 80/20 rule applies across many disciplines and areas. So it is good practice to identify and focus on the category of defects which are large in number, as 80 percent of the defects are due to 20 % of the cause. It is a special form of vertical bar chart and used to identify the first few major sources responsible for the problem.

In the figure below the total no. of defects are plotted against the reasons for those defects. The problems are rank-ordered according to their frequency and percentage of defects. The rank-ordering of these problems shows you where corrective action should be taken first. ## Checksheets

A check sheet is basically used for gathering and organizing data. When this is done with the help of software packages such as Microsoft Excel, you can derive further analysis graphs and automate through macros available. Therefore, it is always a good idea to use a software check sheet for information gathering and organizing needs. One can always use a paper based check sheet when the information gathered is only used for backup or storing purposes other than further processing. ## Scatter diagram

Scatter diagrams use two variables; one is called an independent variable, the input, and other dependent variable, which is an output. Scatter diagrams display the relationship between these two elements as points on a graph. This relationship is typically analyzed to prove or disprove cause-and-effect relationships.

As an example, maybe your scatter diagram plots the total number of downtime and space issues. The length of time (in days) they have performed this task is plotted as the independent variable on the X axis, and the dates when space issues were faced, which is expressed as a score—the dependent variable—is plotted on the Y axis. The scatter diagram can then help to determine whether the reason for downtime was space issue, and thus can be proved. Scatter diagrams can also help you look for and analyze root causes of problems.

1. Which of the following are the diagrams rank-order factors for corrective action by frequency of occurrence? They are also a type of histogram.
• A. Control charts
• B. Process flowcharts
• C. Scatter diagrams
• D. Pareto charts

2. Your project team has identified several potential risks on your current project that could have a significant impact if they occurred. The team examined the root cause of the risks by identifying the reasons of the risks. What type of diagram will the team use to display this information?
• A. Fishbone diagram
• C. Control charts
• D. Process flowchart

Correct Answer: A. Cause and effect diagrams or fishbone diagrams are used for finding the root cause of the problem.

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