Six Sigma Tool Navigator: The Master Guide for Teams

2017-07-07 02:10:07

AKA

Polygon Analysis

Classification

Analyzing/Trending (AT)

Tool description

A polygon is a line graph that displays the central tendency, process variability, and relative frequency of collected data. Typically taken from a frequency distribution, a polygon is very effective in providing a visual representation of how actual measurements of a characteristic vary around a target or specification value.

Typical application

To determine if the process variability within a data distribution is within specification limits.

To show problematic process variations from a desired result or value.

To reflect shifts in process capability.

To verify changes in the process after improvements have been made.

Problem-solving phase

→	Select and define problem or opportunity
→	Identify and analyze causes or potential change
	Develop and plan possible solutions or change
→	Implement and evaluate solution or change
→	Measure and report solution or change results
	Recognize and reward team efforts

Typically used by

1	Research/statistics
	Creativity/innovation
	Engineering
4	Project management
3	Manufacturing
5	Marketing/sales
	Administration/documentation
	Servicing/support
2	Customer/quality metrics
	Change management

links to other tools

before

Checksheets

Frequency Distribution (FD)

Events Log

Observation

Dot Diagram

after

Pareto Chart

Multivariable Chart

Presentation

Pie Chart

Stratification

Notes and key points

Preparation for Grouping of Data

Determine the range(s) of the distribution

For smaller data sets, N = < 100: number of class intervals (C.I.) between 5–10

For larger data sets, N = > 100: number of class intervals (C.I.) between 10–20.

Width of the class interval to be 2, 3, 5, 10, 20, for smaller numbers. (Add zeros for larger data sets.)

Select numbers of class intervals:

Check to see if the lowest data point in the data set is dividisble an equal number of times by the C.I. width. If not, select the next lower data point that is.

Step-by-step procedure

STEP 1 Count the number (N of data points or observations (see example Completed Rework Hours) and sequence them from low to high.

STEP 3 Calculate range (R):

STEP 4 Determine the number of class intervals (C.I.) and width:

STEP 5 List resulting class intervals (C.I.):

C.I.	f
9–11	2
12–14	4
15–17	7
18–20	5
21–23	4
24–26	4
27–29	3
30–32	1
Note: 9 was used as the lowest score since 10 was not divisible by the C.I. of 3 without a remainder.

STEP 6 Construct a polygon. Apply the 3:4 ratio rule: The height of the vertical axis (Y) must be 75 percent of the length of the horizontal axis (X).

Complete the polygon by plotting dots at the height (frequency) and the midpoint of each Class Interval. Connect all dots with straight lines.

STEP 7 Lable both axes and date the polygon.