# Pareto Diagram

Analysis of numerical data plays an important role in decision-making. This data can be analysed in different ways, like a bar diagram, a histogram, a Pareto diagram, and a pie chart. A Pareto diagram is special type of statistical chart. The creator of the Pareto chart was an Italian economist, Vilfredo Pareto. It is problem-solving tool which decides the direction of efforts to satisfy the customer’s requirements. It is also known as even Pareto distribution or a Pareto graph. A Pareto chart is the combination of two graphs, namely, a bar chart and a line graph. A Pareto chart contains a vertical bar chart in descending order of relative frequency which starts from extreme left to right. The horizontal axis or x axis contains the independent variable.

TABLE 3.3

An Example of a Histogram

 Price range of pencils (in Rupees) 5-10 10-15 15-20 20-25 Number of pencils sold 10 15 25 20

FIGURE 3.1 Histogram.

The length of the bars in the Pareto chart represents the frequency. It is a prerequisite of graphical analysis. It is based on unequal distribution. In a Pareto chart, the most frequent data is at the extreme left and the least frequent data is on the other side. The basic principle of Pareto analysis is that in almost every process, 80% of the problems are incurred due to only 20% of the causes/reasons. Therefore, by focusing on the major causes, which are fewer in number, you can sort out the maximum number of problems. The purpose of the Pareto analysis is to know the most important and serious issue to focus on.

A Pareto chart is a special type of quality control chart that can be used in different situations. It is generally used to decide the priority of causes. It mainly has two objectives: the first one is to arrange the data in descending order, and the second one is to identify the improvement areas by prioritising the efforts. In a large database, it is very important to understand the most significant data on which to focus, which can generate the fruitful results.

## Utilisation of Pareto Diagram

• 1. Identification of the most significant problem.
• 2. Identification of the reason for the problem.
• 3. To prioritise actions.
• 4. To review the corrective measure that has been taken.
• 5. Allows explaining of important tasks.

• 1. It is an easy and efficient tool of quality control.
• 2. The Pareto chart provide the basis for the segregation of a problem and its root cause.

3. It helps to identify the minimum number of problems that creates the maximum number of problems.

It represents the most important problem easily.

It is one of the best visualisation tools.

## Limitations of Pareto Analysis

1. The Pareto principle is not a universal rule; it cannot be applicable in all

cases.

• 2. It is unable to provide root cause of problem; it only shows the major problems.
• 3. For large volumes of data, it is sometime difficult to draw the Pareto chart effectively.
• 4. A Pareto chart is only focused on past value or data. It is not useful for future or present/current scenario.

## How to a Construct Pareto Diagram

Step 1: Select the items for which the Pareto analysis is required.

Step 2: Draw the horizontal and vertical lines showing the x axis and the у axis.

Step 3: Divide the x axis and the у axis on a suitable scale as per the requirement.

Step 4: Draw the bars from the extreme left side of highest frequency and move to the right side w'ith decreasing frequency.

Step 5: Labels the bars. On the horizontal axis below each bar, label the bars so as to know which cause each bar represents, as shown in the graph below.

Step 6: Continue in this way to make all the bars.

Step 7: Make the dot for each and every item, corresponding to the frequency for each item. For every item, plot a dot on the graph. For this dot, start from the left, point on the bar or above it, corresponding to the value of frequencies for each of them.

Step8: Join all the dots by using a scale.

Step 9: Mention the title of the chart.

# Scatter Diagram

A scatter plot or scatter diagram is a mathematical diagram. It is also called as a scatter chart or scatter graph. It is one of the best tools for quality control. It uses Cartesian coordinates to represent a set of data. The data is shown as a compilation of points. In this, the point is located on the horizontal axis, and its value is on the vertical axis. It represents the relationship between the points. It shows the correlation between variables; if the point lies near the line or curve, the better will be the correlation. A scatter diagram is used to observe the connection between the two paired, interconnected data types. It gives a fair idea of how closely tw'o data points are related. It clearly identifies the critical point to focus on through which the problem can be controlled and sorted out. In a scatter plot, the controlled parameter is plotted on the x axis, and the measure of the dependent parameter is plotted on the у axis. If the collected data did not contain independent and dependent variables, then any data points can be plotted on any axis, and in this case the scatter plot will suggest the degree of correlation.

The scatter diagram is used to examine the relationship between the different data points. The scatter diagram can only be used for paired quantitative data. It is generally used with regression, modelling, and correlation techniques. It is used to identify the fundamental problems occurring in a process. It is used after the brainstorming technique and the fishbone diagram to determine the basic cause- and-effect diagram. Each and every point on a scatter diagram shows a relationship between dependent and independent variables. By the use of a scatter diagram, various types of correlation can be obtained between data points, like rising, falling, or null correlations. In a positive or rising correlation, the pattern of dot points is moving from lower left to upper right, and in negative or falling correlation it is from upper right to lower left direction. The best fit line, usually known as the trend line, is used to study the correlation between variables. Linear regression is used for linear correlation and it is able to generate the correct solution in a definite interval of time. A scatter plot is also able to show the nonlinear relationship between variables. Scatter diagrams are used to observe and identify the best possible interrelationship between the changes occurring in different group of variables, which is helpful in decision-making.

## Steps of Scatter Diagram

• 1. Collect the data in the process for which scatter diagram is to be plotted.
• 2. Put thet independent variable on the x axis and the dependent variable on the у axis. For each pair of data values, make a dot/point or a symbol.
• 3. Closely observe the pattern of points to understand the pattern and interrelationship between the points. This may be a curve or line. Then use a regression or correlation technique to find the best possible solution.

# Process Flow Chart

A flow chart is a chart that shows how a number of essential processes interact with each other for completion of the process. It is the pictorial representation of all the steps required to complete a process in a sequential manner. This is knowrn as one of the best techniques of quality control and is widely used in industries. It contains the sequence of operation or flow of material in a process, i.e. the input and output of the machines. It includes the time required for completion of the process. This is a fundamental quality control tool that can be used in a wide variety of purposes in manufacturing or in service sectors. It is used to understand the basic knowledge of process and can be used as a process improvement technique. It is used in the planning phase of the product development process, for better understanding of processes and communicating the process to other department of the company. To draw the flow chart, it is required to identify key persons and key processes involved in the process. Nowadays, a flow chart is drawn by computer software.

## How to Construct the Flow Chart

Step 1: The very first step to draw the flow chart is to understand the process. This requires the identification of all the sub-processes of the flow of material involved in a process. It includes the supplier and customers also.

Step 2: Arrange the processes involved in a sequential manner for completion of the process.

Step 3: Review the flow chart with some experienced person who has expertise in the field.

A flow chart can be classified as per the sequence of operations performed by a person or as per the movement/flow of material to complete a process. It is generally obtained by thoroughly inspecting the process and sequence of its operations. The following are the symbols used to draw the flow chart in quality control (Table 3.4).

# Cause-and-Effect Diagram

A cause-and-effect diagram is also known as a fishbone diagram. In the year 1950, Ishikawa and associates first developed this tool in Japan, to explain the causes that affected the production of steel. It identifies all the probable reasons/causes of an effect or problem. It provides a basis for a brainstorming session and has a power to categorise ideas in to useful solutions. It gives a systematic representation of the causes and their effect on a problem. To solve the problem scientifically, there must be a clear understanding of the reasons that creates the problems and the consequences of those problems. In a plant, people, machines, materials, money facilities, the conditions of the machines, the operators’ skill in performing the process, etc. are the main reasons that create problems and a decrease in production, low productivity of workers, and low turnover are the major effects that occur due to

TABLE 3.4

Flow Process Chart for Material

 Activates Operations Distance moved (Meters) Time (Minutes) Remarks (if any) Casting laying in foundry store Moved to gas cutting machine 8 3 By trolley Wait, cutting machine being set 5 Risers cut 20 Wait for trolley 10 Move to inspection dept. 6 2 Inspection before machining 15 By trolley Moved to machine shop 0 3

Job - Material casting ready for machining. Chart begins - Casting lying in foundry. Chart ends - Casting ready for machining.

these problems. The cause-and-effect diagram shows the interrelations among these different causes with their possible consequences. To obtain better results in a process, it is required to identify the various causes and try to develop results so that corrective measures can be put in place. This is basically a problem-solving tool and it can be applied in various fields, like manufacturing or services. This diagram is able to provide all causes that affect a certain event. This diagram is widely used in product design and to identify all the possible causes/factors that affect the process (Figure 3.2 and Table 3.5).

## How to Construct a Fishbone Diagram

Step 1: Define the problem statement, also known as the effect of a process.

Step 2: Conduct a brainstorming session to identify all the possible causes of a problem. The focus here is people, machines, materials, inspection and testing, maintenance, safety, services, or the after-sales service.

Step 3: Try to categorise all the possible causes.

Step 4: Again, try to identify all the sub-causes of the main cause by using the question ‘Why?’ and developing a high level of understanding of all causes.

Step 5: Draw the causes and all possible sub-causes in a diagram.

FIGURE 3.2 General layout of cause-and-effect diagram.

TABLE 3.5

The Important Possible Causes That Affect the Process

 S. NO. Manufacturing Sector Service Sector 1 Machines Product=Service ■ Price 2 Method Place 3 Material People Skills 4 Manpower Productivity 5 Inspection and Testing Quality 6 Money - power Surroundings 7 Maintenance Systems 8 Environment Suppliers 9 Management support Top Management Commitment

# Run Chart

A run chart is one basic tool of quality control. A run chart is a simple and useful process improvement tool. A process can be defined as a sequence of operations that transforms input into output, and to change from input to output requires some time called ‘processing time,’ or the actual operation time. If a change happens in a process during its operation, its output affected. A run chart is used to understand the effect of this change in a process. It does not require huge calculations; it simply plots the observed value on the vertical axis. With respect to what quantities this change affects, this is plotted on the horizontal axis. It is a graphical tool to capture the important process variables in a definite interval of time. These charts are used to identify the trends, patterns, and cycles of the process during a certain period of time. They are used to supervise significant process variables over a period of time. These charts show the quality and workload of a process. In this chart, on the horizontal axis are independent variables like time and duration, and on vertical axis, the required parameter is used. It is most suitable for the analysis of trends of the product or process. It is used to observe the changes in the process. It is drawn during a shift in a production plant to check the performance of the plant over a period of time. The difference between a run chart and a control chart is that a run chart does not show the control limits, while this is necessary in a control chart. It can easily observe the causes of variation in a process. In general, the patterns observed in a process are as follows:

a. Ideal pattern or state of the product.

b. Threshold pattern or state of the product.

c. Brink of chaos pattern or state of the product.

d. State of chaos pattern or state of the product.

If a process operates during an ideal state, it shows stability and target performance over a period of time. This type of process produces the output that will be as per the customer’s requirement. In the threshold state of the product, the process did not consistently fulfil the customer’s expectation, but still the process is in a predictable state. The occurrence of a chaos state shows the pattern just opposite to the threshold state, as it is unpredictable, but still able to fulfil the customer’s expectations. In the fourth state of pattern, the process is unpredictable as well as not performing as per the customer’s requirement.