Importance-Performance Grid

Histograms, as discussed last time, are bar charts that are used to show the frequency distribution of a set of measures. This month we will conclude our short tour with an investigation into different shapes of Histogram that might be found and the interpretation that may be concluded.

The most common shape of Histogram that is found both in nature and in business is the Normal, or Gaussian distribution. The bell-shape of such distributions, as in the diagram below, follows a mathematically defined curve that enables predictions to be calculated about probable future measures.

Beyond predictive uses, the Histogram is often used to provide information about potential problems in the process. Note the word ‘potential’ – as with any other measure, the interpretation seldom provides conclusive evidence, but it will often give a strong hint as to where you should investigate next. The table below indicates a number of the different shapes you might find and useful interpretations that can be drawn from them.

Histogram shape	Symptom	Interpretation
	Low with gaps	Bar range too narrow (check horizontal scale) or too few measurements (check vertical scale) or version of plateau distribution.
	High with few bars	Bar range too wide (check horizontal scale) or too few measurements (check vertical scale). Could be extreme version of truncated distribution.
	Skewed (this is positive; negative skew has tail to right)	Natural distribution (more variation in one direction - often found in item count and time distributions) or incomplete data being used.
	Exponential	Distribution is not bell-shaped (extreme version of skewed) or truncated data (could be the tail of a bell-shaped curve).
	Dual-peaked (bimodal)	Measurement is of two processes. This is very common, e.g. data from two periods, process changed mid-stream.
	Isolated-peaked	Two processes being measured (well-separated bimodal distribution).
	Cog-toothed (or comb)	Faulty measurement, rounding error or version of plateau distribution.
	Plateau	Combination of multiple bell-shaped curves, extreme version of bimodal distribution (multiple processes) or faulty measurement.
	Edge-peaked	Modified data - often caused by shifting data that was out of specification back inside specification limits.
	Truncated	Incompletely reported data or measured after inspection has rejected items outside specification limits.

Thus, for example, if an electronics manufacturer received a number of 0.1 ohm resistors and measured the resistance of sample of them, they might find the following Histogram. This should indicate to them that, although the resistors are within specification, they have been selected from a lot where the average resistance is closer to 0.995 ohms. Although a good electronic design should cope with this variance, the manufacturer may look more closely at other components from the same supplier, and explore other suppliers who might give a more centralized supply of components.

This article first appeared in Quality World, the journal of the Institute for Quality Assurance

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Histograms part 2: interpreting them