Carillon Technologies Limited  Charts and Graphs

Types of Graphs and Charts

• Line graphs (Line graphs, Run charts, Control charts)
• Column and bar graphs (Histograms, Pareto diagrams)
• Area graphs (Pie graphs)
• Relationship graphs (Scatter plots and trendlines

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Introduction

The analysis of data is best handled by the use of graphics and charts.

Nearly all Statistical Process Control or Corrective Action Steps require the use of simple graphs or charts.

The purpose of this module is to introduce the basic types and methodology for making graphs and charts.

• Summarizes the data collected.
• Helps in problem solving
• Illustrates a point
• Describes the data in an interesting manner

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Line Graphs

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Links

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Parts of a Line Graph

The line graph illustrates how a part or process characteristic changes over time.

Line graphs are the simplest graph to construct and use.

All line graphs consist of the following four parts:

#1. The X axis is usually used to record the time-frame or sequence of the data being plotted. #2. The Y axis is usually used to note the measured value or effect. #3. The origin, or zero point, is the point where the two axes meet. #4. The scale determines how the data appear on the graph.

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Creating a Line Graph

Steps

#1 Collect and List Data

• The first step is to collect accurate and complete data. This data can be organized using checksheets.
• See the data used in the construction of a cornflake length histogram.

Step # 2 Convert the Data

• The data may be recorded in a variety of forms including, decimal, fractional, uncoded, coded.
• To use the data properly, it must be transformed into a form suitable for graphing.

Step #3 Determine the Data's Range

To fit the data to the graph paper, one must determine the range of the data for both axes.Using the cornflake example the range in diameters of the first thirty 30 samples of cornflakes from the check sheets is:

• The range of the data is 32mm -21mm = 11mm
• The number of samples is 30.

Step # 4 Scaling the Graph When determining scales for the graph, it is important that the information being displayed uses about 50 to 75% of the available scale. Thus, if the range of the cornflake data is 11 mm, the scale should have a spread of about 15 mm and room for 40 samples of data.

Step #5 Label Axes and Title Graph Every graph should have a full title. The full title can be located at the top or the bottom of the graph. Each axis should be clearly labeled with its numerical values or categories and with appropriate descriptions. Step#6 Plot and Connect Data Points Each data point is located and plotted at its X and Y coordinates. Connect the data points to make a line graph.

Converting a Line Graph to a Run Chart

Definition: A run chart is a line graph that compares process measurements collected over time to process specifications.

Procedure: To convert a simple line graph into a run chart:

Step #7 Calculate the average

• This is accomplished by adding up all of the measured values and dividing this sum by the number of values collected.
• Plot this average value on the graph.
• For example, the average for the cornflakes is 26.4mm

Step # 8 Plot the specification limits on the graph.

Step # 9 Analyze the graph for possible effects.

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A completed cornflake diameter run chart

Run Chart Analysis

Trends
Cycles
Shift in the Average

A shift is indicated when one of the following observations apply:

• 7 out of 7 readings plot above the average
• 7 out of 7 readings plot below the average
• 10 out of 11 readings plot above the average
• 10 out of 11 readings plot below the average

Example Problems (links under construction)

	Printing: Black Color Density
	Infection Rate in Hospital
	Accident Rate in Industrial Plant
	Dimension of Machined Gear
	Monthly Sales at Small Plant
	Variance from Promished Deliver Times
	Variation from Quarter to Quarter for Student Enrollment

Study these run charts.

What conclusions can be made about the processes?

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