Tool 136: Polygon


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

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links to other tools

before

  • Checksheets

  • Frequency Distribution (FD)

  • Events Log

  • Observation

  • Dot Diagram

after

  • Pareto Chart

  • Multivariable Chart

  • Presentation

  • Pie Chart

  • Stratification

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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.

Example of tool application

click to expand




Six Sigma Tool Navigator(c) The Master Guide for Teams
Six Sigma Tool Navigator: The Master Guide for Teams
ISBN: 1563272954
EAN: 2147483647
Year: 2005
Pages: 326

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