管理チャートでのローリング平均の計算方法

The new Control Chart uses a different calculation for the rolling average, than the old Control Chart. On this page, we compare different methods for calculating the rolling average, and show how the work item based calculation (Example 3) is better.

下の例でローリング平均（青線）がどう描かれるか見てみましょう。３つの例はどれも同じデータを使用しています。：

例 1: 時間をもとにした枠を使用し、各日を平均の中心とする表示方法 

この例では、ローリング平均は日ごとに計算され、グラフに示されます。以前の管理図では、この計算方法を使用しています。

ローリング平均は、次のような方法でその日ごとに計算されます。

• チャート全体の期間に基づき、時間枠 (たとえば 2 日間) を決定します。

• Use the work items in the window to calculate the average cycle time.

時間枠が1週間のもの (1日間のウィンドウ)

時間枠が2週間のもの (2日間のウィンドウ)

This approach has a number of problems. In these charts, you can see that the last work item is clearly an outlier. However, as it is too far apart from other work items, the rolling average line simply jumps up, particularly in the one-week timeframe. The rolling average line also bends at unexpected places on the chart.

The one-week timeframe also shows no standard deviation (light blue shaded area) around the outlier, although it is a bit better when zoomed out to a two-week timeframe. However, the two-week timeframe shows other problems — the rolling average rises and even fluctuates before the very first work item.

Example 2: Window based on time, centered on each work item

In this example, the rolling average is calculated and mapped for each work item on the chart.

At each work item, the average is calculated by doing the following:

• グラフ全体の期間をもとに、時間枠（たとえば、 2 日間）を決定します。

• Use the work items in the window to calculate the average cycle time.

時間枠が一週間のもの (1日間のウィンドウ)

時間枠が二週間のもの (2日間のウィンドウ)

このチャートは左のチャートと同じですが、表示範囲が 2 週間に広がっています。すなわち、元の 1 週間のチャートにその前の 1 週間が付け加わっています。

This approach is better than the approach in Example 1. By centering around the work items points, the variation in the moving average line is easier to understand — each completed work item causes a change. The moving average also starts at the first point, instead of moving up from zero.

しかし、まだ外れ値の処理がうまくできていないことに注意してください。ローリング平均はやはり飛び上がり、標準偏差が表示されていません。

Example 3: Window based on a number of the total work items, centered on each work item

In this example, the rolling average is calculated and mapped for each work item on the chart. This calculation is used in the new Control Chart and is described in more detail in Control Chart.

At each work item, the average is calculated by doing the following:

• Take a set number of work items (e.g. five work items), based on the total number of work items in the chart.

• Use the work items in the window to calculate the average cycle time.

期間 1 週間

期間2週間

This approach improves upon both Example 1 and Example 2. The window is not time-based, but is based on the number of work items — in the charts above, it includes two work items ahead and two work items behind.

The rolling average starts at the first data point and the variations are easy to understand. In addition, it handles the outlier better. The rolling average is a more steady line towards the right of the chart, and clearly shows the last work item as an outlier with the appropriate standard deviation.