Individuals Chart Report that can also Provide a Process Capability Statement

An individuals chart that can provide a process capability statement too is a 30,000-foot-level metric report-out. At the enterprise level, 30,000-foot-level report-outs can be used in an Integrated Enterprise Excellence (IEE) Business Management System.

An individuals control chart (XmR chart, I-chart) can be used for time-series tracking of a process to determine if the process is in statistical control and can be considered stable. When a process is considered stable, it experiences only common-cause variability. When a process is not in control, special-cause conditions can be causing non-stability.

In a process, effort should be taken to understand and resolve, when appropriate, special-cause conditions. A process that only experiences common-cause conditions does not imply that the process does not have any issues. A process can be stable but be unable to provide a consistent level of quality or performance. Assessments for process stability and capability can be provided through 30,000-foot-level reports with predictive measurements.

A moving range chart can be included with an individuals control chart report-out, producing a pair of charts (i.e., XmR control chart or ImR control chart). However, since the primary purpose of the MR chart is only to identify larger than normal short-term swings in the data, this chart will not be included in the described report-outs so that the overall reporting and evaluation process can be simplified.

Individuals Control Chart (XmR chart, I-chart) Reporting Illustration

Content of this webpage is from Chapter 10 of Integrated Enterprise Excellence Volume III – Improvement Project Execution: A Management and Black Belt Guide for Going Beyond Lean Six Sigma and the Balanced Scorecard, Forrest W. Breyfogle III.


The data in Table 1 will be used to illustrate the mechanics of creating of an individuals control chart. We will consider that these data were collected using an infrequently subgrouping/sampling plan that is consistent with application of a 30,000-foot-level charting methodology.1 (For more information about 30,000-foot-level reporting and its benefits see Performance Metric Reporting Issues: 30,000-foot-level Resolution.)

Individuals Control Chart (XmR chart, I-chart) Reporting Time Series Data

Table 1: Time-series Data


An individuals control chart has an upper control limit (UCL) and lower control limit (LCL), which are calculated from the raw time-series data.  Charting parameters for the individual values chart are:

Formula 01

The 2.66 factor is 3/d2, where 3 is for three standard deviations and d2 is from Table J1 for a sample size of 2 (i.e., 3/1.128 = 2.66). This relationship can be used when the moving range is selected to expand beyond the adjacent samples. For this situation, the value for d2 would be adjusted accordingly.

For the Table 1 data set, the MRs are determined from the relationship

Formula 02

The process mean and moving range mean are calculated and used to determine the individual-measurement control chart parameters of

Formula 03

An individuals control chart of the Table 1 data with these calculated UCL and LCL is shown in Figure 1.

Individuals Control Chart (XmR chart, I-chart) Reporting

Figure 1: Individuals Control Chart


From this figure the process is concluded to be in control and have a recent region of stability. This conclusion is made since there are no trends relative to or data points outside the statistically determined upper and lower control limits (UCL and LCL).

Since the process has a recent region of stability, one can conclude that the process is predictable. The up and down variability shown over time is from common-cause variability.  Organizations should not react to individual common-cause values, which can lead to much firefighting; i.e., reacting to special-cause variability as though it were common-cause variability.

A probability plot can be useful to determine how a process that has a continuous response is performing relative to customer needs, where these desires are often conveyed through specification values.  This data is further analyzed for determining process capability (process performance) in the paper Probability Plotting: Quantifying Process Performance.

A 30,000-foot-level Report-out of the Data

An individuals control chart can be combined with a probability plot in one chart to create a 30,000-foot-level report-out.  When there is no specification, typically an estimated median and 80% frequency of occurrence response is recorded at the bottom of the graph.


individuals chart with probability plot


An IEE business management system provides the framework for linkage of 30,000-foot-level output responses throughout and organization with the processes that created them.  An IEE system addresses the business scorecard issues that are described in a 1-minute video


individuals chart video




Contact Us to set up a time to discuss with Forrest Breyfogle how your organization might gain much from an Integrated Enterprise Excellence (IEE) Business Process Management System and how an individuals chart report can also provide a process capability statement.