Chapter 19: A High-Maturity Perspective

u- Charts

The u-chart is based on the assumption that your data are based on a count of discrete events occurring within well-defined , finite regions /areas, and that these events are independent. The u-chart assumes a Poisson process. You may want to consider a u-chart when dealing with defects (counts) within a group of pages (region/area); for example, number of errors per page or the number of defects per 1000 lines of code.

The u-chart differs from the XmR chart in that the upper and lower control limits of the u-chart change over time. The « in u-chart is the weighted average of the count (« = ˆ‘ countj/ ˆ‘ sizej). The upper control limit is calculated by adding « to three times the square root of the « divided by the last size (sizej). The lower control limit is calculated by subtracting « from three times the square root of the « divided by the last size (sizej).

Now go back and look at our example of inconsistent data gathered from peer reviews. We said, "Suppose a peer review is done on a program comprising 8000 lines of code, and eight errors are found. Another peer review is done on a program comprising eight lines of code, and six errors are found. The second peer review found fewer errors. Does that mean that the person who coded the second program is a better coder than the person who coded the first program? Of course not. You also need to consider the complexity of the programs, the length of the programs, the type of language, etc." A u-chart is sometimes used for just this example because it takes into consideration the size of the program reviewed by charting the defect density and not just the number of defects. However, we still do not recommend using a u-chart in this case. It is too easy to misinterpret the results, and too easy to use the wrong data to construct the charts.

OK, so if this all sounds too complicated and you do not like the idea of your limits changing with each observation, then just go ahead and use the XmR chart with your count-based data. The XmR chart's behavior will resemble the c-chart and the u-chart because these are special cases of the individual chart.