Gráfico de control subgrupos: tutorial Excel

This tutorial shows how to compute and interpret a subgroup control chart on quantitative data in Excel using XLSTAT software.

Dataset for the analysis of a subgroup chart

The data are from [Pyzdek Th. (2003); The Six Sigma Handbook, McGraw Hill, New York] and correspond to 25 inspections each having 5 measurements of a production process.

Goal of this tutorial

The control charts are an efficient method to decide if a process is statistically under control or not. There is a variety of different control charts that can be used for different aims.

The subgroup charts tool offers you the following chart types alone or in combination: - X bar: An X bar chart is useful to follow the mean of a production process. Mean shifts are easily visible in the diagrams.

• R: An R chart (Range diagram) is useful to analyze the variability of the production. Large differences in production, caused using different production lines, will be easily visible.
• S, S²: S and S² charts are also used to analyze the variability of production. The S chart draws the standard deviation of the process and the S² chart draws the variance (which is the square of the standard deviation).

Note 1: If you want to investigate smaller mean shifts, then you can also use CUSUM group charts which are often preferred in comparison to the subgroup control charts, because they can detect smaller mean shifts.

Note 2: If you have only one measurement for each point in time, then please use the control charts for individuals.

Note 3: If you have measurements as qualitative values (for instance ok, not ok, conform not conform), then use the control charts for attributes.

During this tutorial an X-bar chart together with an R chart are generated.

Setting up the dialog box for generating a subgroup chart

After launching XLSTAT, click the Statistical Process Control button on the ribbon and select subgroup charts. The dialog box pops up. In the General tab, select the chart type, choose the combination X-Bar – R chart, and the data. In the Options tab, you can activate the options Process capabilities to display the process key figures. The given values for the USL, LSL and the target are entered.

Then click on the OK button, the computations start.

Interpret the results of the subgroup chart

The first results that are displayed are the estimated mean and the standard deviation. Then, the process capability figures together with a chart and the X-bar control limits are displayed. It’s interesting to see that the Cp indicator tells the process is "not adequate". The process is not capable according to the specifications. The following chart represent the X-bar control chart including the different control limits and central lines.

The central line (CL), the lower (LCL) and upper (UCL) control limits, and the lower and upper zone limits for the B and C areas are displayed for each group. Like the X-bar chart, the data of the R chart are always inside the control limits and no special causes are present. Both control charts let us conclude that the process is “statistically under control”.

The next table contains the details for the special cause rules. Only "No" can be read in the table. The data has a good quality with respect to this issue. Summing up the conclusions made above, you can discover the different things suggested by the X bar control chart. The group means values are always between the lower and upper control limits.

Further it is interesting to know, if the data follows a normal distribution and therefore the common rules for control charts and process capabilities can be applied. In the next section the results of 4 different normality tests and a Q-Q plot are displayed. All the 4 tests conclude that the Hypothesis H0 of normal distribution can be accepted. In the Q-Q plot we see that the data are close to the first bisector line. We suppose that the data are normally distributed. Finally, the run chart is displayed. It contains all individual measurements to judge the range and trends. We see that the measurements inside a group have a wide range, lying between 91 and 110. Therefore, the group means representing these measurements must be used carefully. This is the reason why the Cp value of the process indicates a process that has not a good performance. This is caused by the values of the specifications.