Six Sigma Tools: How to Understand Variation

Histogram

A distribution showing the frequency of occurrences between high and low range of data.

A Histogram is a graphical representation of individual value in a data set, according to frequency of occurrence.

It is constructed from the data collected in a frequency table, a chart that divide range of the data into several equal sections to compare the frequency of occurrence in each section.

The Histogram drawn from the frequency table resembles a bar graph, composed of columns.

The width of each column represents the an interval, or group of observations within a range, while height represents the number of observations falling given interval.

Use of Histogram

· Assessing the material strength

· Evaluating process

· Indicating the necessary for corrective action

· Measuring effect of corrective action

· Determining the machine capabilities

· Portraying life characteristics

· Comparing products.

· Communicate information about variation in a process.

· Make decision on the focus of improvement efforts.

· Comparing Operators

· Comparing materials.

· Comparing vendors

Limitations

The simple Histogram is help in making an analysis, but its use limited because

· It requires many measurements

· It does not take time into consideration

· It does not separate two types of variation

· Variation due to chance

· Variation due to assignable factors

It does not show trends.

After constructing the histogram, if we draw the specification limit, the histogram will then quickly answer the following questions :

· Is the product consistent with previous checks

· Is the product well centered.

· Does it appears that the product is meeting engineering specifications

Key Concept

· Data always have variation

· Variation have patterns

· Patterns can be seen easily when summarized pictorially.

· Important characteristics of pattern are

o Its Center

o Its Width

o Its Shape

Units of Measurement of Histogram

· Time

· Weight

· Size

· Frequency of Certain Occurrence

No. of Observation Required

Do not construct histogram if the number of observations are less than 50.

In special circumstances, the number of readings, due to stratification of data, may be reduced to less than 50, in such circumstances only, construct a histogram with number of reading less than 50

Construction Using Microsoft Excel

· Enter the data in Microsoft Excel

· Find smallest value of data set, S. Use syntax MIN ( Data Array )

· Find largest value of data set, S. Use syntax MAX ( Data Array )

· Find the temporary bin width, TBW = ( L-S )/( No. of the cells chosen )

· Round off TBW, and get bin width, BW

· Design Bin

· Enter starting value less than S in the cell

· Enter a value S + BW in a cell below the cell of starting value.

· Block both cells, and holding corner, drag till a cell value more than L appears.

· Click Tools / Data Analysis / Histogram

· In the template for histogram