According to the PMBOK® Guide, specifically within the Control Quality process, a Control chart is the primary tool used to determine whether a process is stable or has predictable performance.

Control charts are graphic displays of process data over time and against established control limits, which have a centerline (the mean), an upper control limit (UCL), and a lower control limit (LCL).

Stability and Predictability: If the process data points stay within the control limits and do not exhibit non-random patterns, the process is considered " in control " and stable.

The Rule of Seven: A process is considered out of control if a single point exceeds a control limit or if seven consecutive points fall on one side of the mean, even if they are within the limits. This indicates a shift in the process that requires investigation.

Application: These are used in both manufacturing and management to monitor repetitive activities to ensure the results remain within acceptable statistical boundaries.

A. Matrix diagram: This is a quality management and planning tool used to perform data analysis within the organizational structure created in the matrix. it is used to show the strength of relationships between factors, causes, and objectives, not process stability.

B. Histogram: A histogram is a special form of bar chart used to describe the central tendency, dispersion, and shape of a statistical distribution. While it shows the frequency of occurrences, it does not show trends over time or process stability.

D. Flowchart: Also known as process maps, flowcharts display the sequence of steps and the branching possibilities that exist for a process that transforms one or more inputs into one or more outputs. They are used for identifying where quality problems might occur but not for measuring statistical stability.

In PMI standards, the Control Chart helps distinguish between Common Cause Variation (inherent to the process) and Special Cause Variation (caused by specific, unusual events). Identifying special causes is the first step in bringing a process back into a stable, predictable state.