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Histograms with Two or More Peaks

Q: When I make a histogram of my data, it seems to have two distinct peaks or "humps." What could be causing this?

Histogram of Bimodal Data

A: A histogram with two peaks is called "bimodal" since it has two values or data ranges that appear most often in the data. In a process that is repeated over time, we typically expect the data to appear in the familiar, bell-shaped curve of the normal distribution. Thus, the bimodal histogram can signal something out of the ordinary. Histograms can also be multi-modal and the following discussion can be applied to these shapes, too.

A bimodal histogram shape often reflects the presence of two different processes being "mixed" in the displayed data. For example, the data could contain information from two different machines, two shifts, weekdays and weekends, two offices, etc. Control charts based on mixed data often have overly wide control limits relative to the individual processes. These wide limits can seriously decrease the ability of the chart to signal shifts and changes in the individual processes over time.

The best solution for mixed data is to separate the data based on the individual processes, and then make separate histograms and/or control charts for each process. Process management efforts can then be directed to each process individually to (1) determine the cause or causes of the differences between the processes, (2) monitor and control each process, and (3) improve one or both of the processes.

Alternatively, a bimodal histogram shape for a process that can change over time could indicate that the mean of the process has been shifted over the period covered by the data. For example, this could occur if the observations spanned a time period that included a significant process or "phase" change, such as machine calibration, tool change, new service method, new supplier, etc.

The best approach to analyzing data representing the different phases is to make separate histograms representing each phase. Control charts should also segregate the data, so that the control limits can be based on the data in the appropriate phases only. The position of the center line and/or the width of the control limits in the individual phases is an indication of whether there have been any phase-related changes in process performance. Statware's family of process management products can base control limits on the data from the individual phases.