What Is Graphical Analysis

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Generallyin any manufacturing or business process, Six Sigma teams deal with a vast amount of data, and it is impossible to convey the information effectively with the raw data. Thus, it is recommended to segregate and plot the data to analyze the problems.

The graphical analysis creates pictures of the data, which will help to understand the patterns and the correlation between process parameters. Often graphical analysis is the starting point for any problem-solving method.

Scatter diagrams, also known as Correlation Charts or XY Graphs, plot the relationship between two continuous variables. These can include the independent variable on the x-axis and the dependent variable on the y-axis.

A Histogram is the graphical representation of a frequency distribution. It is in the form of a rectangle with class intervals as the base and the corresponding frequencies as the height. Particularly, there are no gaps between any two successive rectangles.

The Normal Probability Plot is a graphical method to assess whether the data set follows a normal distribution or not. This includes identifying outliers, skewness, etc. Furthermore, the Normal Probability Plot is one example of a Quantile-Quantile (Q-Q) plot.

A Pareto Chart is also known as the 80-20 rule. It is a combination of a bar chart and a line chart. The actual data is in descending order and uses a bar chart and cumulative data in ascending order on a line graph.

A Bar Chart displays the frequency on one axis and the values of the categorical variable on the other axis. In a bar graph, bars of uniform widths are drawn with various heights. However, the height of the bars represents the frequency of the corresponding observation.

The project team uses various six sigma tools in the Define Phase like SIPOC (Supplier-Input-Process-Output-Customer), Process maps, value stream mapping, Project charter, SWOT analysis, and Voice of Customer.

The Six Sigma team uses graphical analysis tools. For example, they use a Bar Chart to understand a process trend, revenue loss, etc. Then, they use a Run chart to monitor customer complaints or defects over a period of time. Similarly, A Box Plot graphically represents the voice of the customer (pictorially depicts customer satisfaction with various attributes).

Graphical tools like the Pareto Chart are used to analyze the frequency of problems and identify the majority (80%) of issues. Similarly, the Process Capability Analysis is used to assess the ability of the process to perform according to the specification.

Often, the biggest challenge for Six Sigma teams is to understand the graph and make conclusions. In fact, it is difficult to understand the message from the graph right away. The Six Sigma team has to take time to interpret the graphs.

Graph analytics is the evaluation of information that has been organized as objects and their connections. The purpose of graph analytics is to understand how the objects relate or could relate. The objects are commonly referred to as nodes because they are points at which connections intersect. The collection of nodes and their connections is called a graph. (Graph analytics is also known as network analysis.)

A graph captures the strength of the relationship between nodes (such as how often you speak with your family or coworkers) and the direction of the relationship (are you always the one who starts text conversations with your best friend?). Not every node in a graph has to be of the same type; for example, a talent-related graph could include companies, people, and work skills all as nodes.

Graph analytics differs from numeric analysis by focusing on the relationships between nodes. An example of numeric analysis is calculating the average of a list of high temperatures. Graph analytics provides a way to organize and store the types of information where the value comes from the relationships. Researchers are interested in graph analytics because it allows them to determine how important a single node is to the whole group, detect communities within the group, and determine the shortest path between two nodes, among other characteristics.

Understanding graphs and how to evaluate them allows you to investigate relationships in topics as varied as internet searching, shipping optimization, and neuroscience. How does a credit card company detect fraudulent charges? They can analyze the relationship between people and purchases. What is the best route for a ride-hailing driver to take to transport multiple riders? Route-determining software can use the relationship between locations. How do your entertainment services decide what to recommend to you? They analyze the relationship between media you have enjoyed and all media available through the service.

The first discussion recorded in Europe that used analysis of a graph was Leonhard Euler's paper on the Seven Bridges of Knigsberg, published in 1736. Euler posed the question of how to travel between the islands and mainland of Knigsberg via its seven bridges using only each bridge once. This problem can be represented as a graph whose nodes stand in for the four pieces of land and the connections for the pathways between them.

While graph theory and topology developed from Euler's paper in the field of mathematics, most of the applications of graphs were in social sciences during the twentieth century. One notable example was psychologist Jacob Moreno, who used a type of graph he called a sociogram to represent social relations between school children, news of which garnered this 1933 headline from The New York Times: "Emotions Mapped by New Geography."

At the turn of the twenty-first century, both computational power and computer accessibility had sufficiently increased to allow biologists and physicists to apply graph analytics to the pressing big-data problems of their fields, such as molecular networks within a cell and the structure of the internet. The analysis of graphs spread from more academic questions into areas of inquiry such as social media in the twenty-first century.

Graph analytics is best suited to evaluate objects whose importance is in their relationships. More and more types of information are being thought of as nodes with relationships, including in industries like health care and fossil fuel distribution.

In the previous example, it is the existence of a relationship between nodes that allows the fraud detection software to determine that some part of a financial transaction is connected to a bad actor. But the relationships between nodes can tell more than simply that a relationship exists. In many graphs, the connections between nodes are assigned values and directions. When two internet pages link to each other, the connection between them can be stored as bi-directional. For two pages where only one links to the other, the connection would be one-way. The most common page-ranking algorithm, Google's PageRank, assigns values to the connections between nodes (in addition to direction). These values are calculated based on the number of connections a web page has as well as the importance of the web pages that link to it. Once these connection values exist, common graph analytics algorithms such as clustering and shortest-path calculations can be used to derive information from the graph.

Because graphs are the ideal way to represent information whose importance derives from its relationships, especially large datasets, the main benefit of graph analytics is characterization, evaluation, and prediction concerning the relationships represented by the graph.

One strength of graph analytics is the ease with which information can be added to a graph. Many of the most commonly used systems for working with connected data, such as relational database management systems, require a complete understanding of the data and its relationships before storage and investigation can occur. But adding new nodes and connections to a graph doesn't invalidate existing data processing or relationships. This means that you don't need to understand everything about your data to begin storing and investigating. This also means that maintenance of a graph database involves less risk because there is no need to modify data models as the dataset grows. Another strength of graph analytics is its use for predictive or discovery types of analysis. An example of this type of analysis is media recommendation engines, which examine both the existing relations between people and media as well as similarities between people based on their media choices to generate recommendations.

Graph analytics faces many of the same challenges as other connected data systems, such as computer processing time for querying the data. However, the characteristics of graphs themselves can also create longer query times or require more hardware because of the complexity of the type of graph and the randomness of the graph. (The randomness of a graph results from there being fewer constraints on a graph than other connected data systems when adding new data.)

Although graphs are the ideal way to store information whose value derives from its relationships, the storage and analysis of graphs has limitations based on the software and hardware architecture chosen to implement it.

Information can be modeled as a graph and stored in graph database software or it can be modeled using existing relational database techniques and manipulated in tabular form. One limitation to using a graph database is that relational databases are currently more widely in use and understood by computer professionals. Additionally, it may take more time to retrieve information from a graph database if you're also using it to store connected data that relates through more conventional relational database methodologies.

Another limitation of a graph database is the amount of time required to traverse through the graph to respond to a query. The time required depends on what fraction of the graph the query looks at in order to return its results. Recall the earlier discussion of credit card fraud detection. In that example, fraud was detected because representing the data as a graph made it simpler for the software to examine a larger set of nodes. However, the query to examine this larger set of nodes would take longer to return results than a query that restricted the amount of the graph it examined. As another example, a query asking for all the people connected to you through multiple layers of acquaintance would take longer than results for a query asking for all the people connected directly to you.

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