Information & Training. | SPC and Statistical Methods for Process Improvement.
Types of Histograms
When you construct a histogram, you will normally expect to obtain a bell shaped curve. In such situations the majority of measurements recorded from a process being analysed, will be centrally located. Further from the centre, there will be fewer and fewer measurements recorded. This distribution is so common that when a distribution does not follow along the lines of such a “Normal Distribution”, then you need to be asking why is the data not normally distributed? What are the various types of histograms frequently seen?
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Bimodal Histogram.
Can also be called a Multi-modal. This type of histogram has two or more peaks. In the bimodal or multi-modal distribution there are two or more clusters of higher frequency numbers arising. This arises when the data comes from two or more distributions, for example if you are using two different machines in the one production line, two sources of the same raw material, different shifts etc..
In order to fully understand and interpret the bi-modal histogram, the sources of the two (or more) distributions needs to be identified and individual histograms should then be plotted.
A bimodal histogram can also arise, where the data for the histogram is taken over a period of time. In this situation, a change may have arisen within the process to cause the mean of the data to change, resulting in the two data peaks. In such a situation the process should be investigated over the period of time related to the data being collected to determine what could have changed within the process, for example, was the data collected over two shifts with different process operators. Could the environmental conditions have changed (a warm day versus a cold day), were different items of test equipment used to record measurements, etc..
Types of Histograms – Histograms with missing sets of data.
Where a set of data looks to be missing, then the reviewer needs to ask is there a specific reason, such as a prejudice in the data collection. Maybe the data comes from an inspection point, where a minor change results in a Pass/Reject result, and there is a tendency to Pass, so data is missing from just outside the fail limit and a higher than normal frequency of data is seen just inside the specification Pass limit.
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Positively & Negatively Skewed Histogram.
Is there sorting of data? In the positively skewed histogram are there efforts in place to reduce the measured values? In the negatively skewed histogram are there opposite effects in place to increase the measured values?
Skewed data often occur due to lower or upper bounds on the data. That is, data that have a lower bound are often skewed right while data that have an upper bound are often skewed left.
Another possible cause is in the early stages of a new process or product where there are a high level of early stage failures, which fall off over time. An alternative is a process measured over time, where there is a high level of reliability within the process, however coming to “end of life” situations, failures start to arise. These two scenarios can lead to Positively and Negatively skewed histograms.
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Types of Histograms – A Uniform histogram.
A uniform histogram may be a distribution with a range of modes, i.e. multi-modal. In this situation there may be a range of independent influences on the histogram plotted.
This distribution may be a reflection of inaccurately calculating the cell widths. The reviewer needs to look at the data and assess if different cell sizes would impact the histogram.
The distribution may demonstrate that there are equal probabilities of the data in each cell arising, for example in a “toss of the dice” or lottery situation, there will be equal probabilities. The histogram may be showing that probabilities are in fact truly equal.
The uniform histogram may indicate that a process is not in control, e.g. a tool on a machine is wearing out, so will result in the process going out of specification in time. The measurements taken could demonstrate that the same process outputs are arising ever when inputs are changing.
Histograms with an outlier.
Outliers may arise due to a range of factors such as an inaccurate reading, data entry error or other such type of error, start-up effect, an equipment failure, input change, e.g. electrical surge, etc..
The outlier may arise due to data grouping, i.e. on the upper end of a spectrum of measurements, there may be a category for “all other data”. In this situation, too many data points may be included into this category. The solution may be to review the cell widths.
Outliers need to be investigated as they may represent unique groupings of conditions, or intermittent changes in process performance.
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Types of Histograms – Comb Histogram.
In the comb distribution, the cells alternate between short and long, each with their own bell curve. This effect can arise where data is being rounded off, i.e. readings less than “.5” are rounded down to “0”, readings above “.5” and rounded up to “1”. In all continuous data situations, there will be an element of rounding either by the person performing the measurement, or automatically by items of test equipment, where rounding will be inherent within the test software. The solution is to ensure that the cell boundaries are suitably set so as to eliminate this effect.
Information & Training.
SPC & Statistical Methods for Process Improvement.
- Process Capability. Variability Reduction. Statistical Process Control.
- Pre-Control. R&R Studies.
- Process capability indices Cp, Cpk, Cpm, Capability ratio.
- Performance indices Pp and Ppk.
- Variable Control Charts.
- Attribute Charts.
- Pareto Charts.
- Individual – X Charts.
- Histograms / Process Capability Analysis.
- Scatter Diagrams.
- Etc. … Etc. …
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