# Gráficos para subgrupos

Subgroup control charts are used to investigate the quality of a process within subsamples. Draw them in Excel using the XLSTAT statistical software.

## What is a subgroup control chart

A **subgroup chart** is a type of control chart that focus on the quality characteristic measurement within one subgroup.

It is used to supervise production quality, in the case where you have a group of measurements for each point in time. The measurements need to be quantitative data. This tool is useful to recap the mean and the variability of the measured production quality.

## Subgroup chart in XLSTAT

Integrated in this tool, you will find Box-Cox transformations, calculation of process capability and the application of rules for special causes and Westgard rules (an alternative set of rules to identify special causes) to complete your analysis. The subgroup charts tool offers you the following chart types alone or in combination:

- An X bar chart is useful to follow the mean of a production process. Mean shifts are easily visible in the diagrams.
- An R chart (Range chart) is useful to analyze the variability of the production. A large difference in production, caused for example by the use of different production lines, will be easily visible.
- S and S’² charts are also used to analyze the variability of production. The S chart draws the standard deviation of the process and the S’² chart draws the variance (which is the square of the standard deviation).

*Note: During the interpretation of the different indicators for the process capability please pay attention to the fact that some indicators suppose normality or at least symmetry of the distribution of the measured values. By the use of a normality test, you can verify these premises (see the Normality Tests in XLSTAT-Base).*

## Results for subgroup charts in XLSTAT

### Box-Cox transformation

Estimates of the parameters of the model: This table is available only if the Lambda parameter has been optimized. It displays the estimator for Lambda. Series before and after transformation: This table displays the series before and after transformation. If Lambda has been optimized, the transformed series corresponds to the residuals of the model. If it hasn’t then the transformed series is the direct application of the Box-Cox transformation

### X bar/ R/ S/ S² table

This table contains information about the center line and the upper and lower control limits of the selected chart. There will be one column for each phase.

### Process capabilities

Process capabilities tables are displayed if the "process capability" option has been selected. There is one table for each phase. A table contains the following indicators for the process capability and if possible the corresponding confidence intervals: Cp, Cpl, Cpu, Cpk, Pp, Ppl, Ppu, Ppk, Cpm, Cpm (Boyle), Cp 5.5, Cpk 5.5, Cpmk, and Cs (Wright). For Cp, Cpl, and Cpu, information about the process performance is supplied and for Cp a status information is given to facilitate the interpretation. **Interpretation of the Cp**

- Cp values have the following status based on Ekvall and Juran (1974):
- "not adequate" if Cp < 1
- "adequate" if 1 ≤ Cp ≤ 1.33
- "more than adequate" if Cp > 1.33

- Based on Montgomery (2001), Cp needs to have the following minimal values for the process performance to be as expected:
- 1.33 for existing processes
- 1.50 for new processes or for existing processes when the variable is critical
- 1.67 for new processes when the variable is critical

- Based on Montgomery (2001), Cpu and Cpl need to have the following minimal values for process performance to be as expected:
- 1.25 for existing processes
- 1.45 for new processes or for existing processes when the variable is critical
- 1.60 for new processes when the variable is critical

**Capabilities chart** This chart contains information about the specification and control limits. A line between the lower and upper limits represents the interval with an additional vertical mark for the center line. The different control limits of each phase are drawn separately.

### Normality tests

For each of the four tests, the statistics relating to the test are displayed including, in particular, the p-value which is afterwards used in interpreting the test by comparing with the chosen significance threshold. If requested, a Q-Q plot is then displayed.

### Subgroup charts in XLSTAT

The following results are displayed separately for each requested chart. Charts can be selected alone or in combination with the X bar chart.

- Observation details: This table displays detailed information for each subgroup. For each subgroup the corresponding phase, the size, the mean, the minimum and the maximum values, the center line, and the lower and upper control limits are displayed. If the information about the zones A, B and C are activated, then the lower and upper control limits of the zones A and B are displayed as well.
- Rule details: If the rules options are activated, a detailed table about the rules will be displayed. For each subgroup, there is one row for each rule that applies. "Yes" indicates that the corresponding rule was fired for the corresponding subgroup and "No" indicates that the rule does not apply.
- X bar/ R/ S/ S² chart: If the charts are activated, then a chart containing the information of the two tables above is displayed. Each subgroup is displayed. The center line and the lower and upper control limits are displayed as well. If the corresponding options have been activated, the lower and upper control limits for the zones A and B are included and there are labels for the subgroups for which rules were fired. A legend with the activated rules and the corresponding rule number is displayed below the chart.
- Histograms: The histograms are displayed. If desired, you can change the color of the lines, scales, titles as with any Excel chart.
- Run chart: The chart of the last data points is displayed.

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