The p-chart is used to monitor a process over time based on proportions. The process is described by a metric that indicates the proportion of certain events in a total quantity. It shows whether this proportion is within the expected range or if noticeable changes occur in the process. This can be, for example, the rejection rate in production, the sales quota in sales, or the proportion of delayed deliveries. The goal is to detect changes early, systematically analyze possible causes, build process knowledge, and avoid unnecessary interventions.
In the filling of tomato sauce, it is checked per shift how many jars have a crooked or incomplete label. The goal is to determine whether the proportion of non-conforming units remains stable over time.
Interpretation of the results:
There are no points outside the control limits and no noticeable patterns are visible. The proportion of defective labels fluctuates randomly around the centerline. The process can thus be assessed as stable.
Explanations of the graphic:
- The points show the proportion of non-conforming units per subgroup in chronological order.
- The centerline corresponds to the average proportion of non-conforming units.
- The control limits are calculated for each subgroup from sample size and average proportion. With varying sample sizes, they often appear stepped.
Preparation
- Define a clear binary classification, for example, “non-compliant” and “compliant.”
- Ensure that for each data row, both the total number of units considered (sample size) and the number of non-compliant or compliant units are available.
- Check whether the subgroup size changes over time and whether this is technically reasonable.
- Determine whether the chart should be created based on current data or with a historical reference.
- Define which tests for exception conditions should be used to detect noticeable patterns.
Usage in AlphadiTab
- Select the tool “p-chart” in the Control Phase.
- For defective units, specify “non-compliant units,” for sample size, specify “tested units.”
- Generate the control chart via “Create New.”
- Conduct the defined tests in the Nelson Rules tab.
Interpretation
- Check whether points lie outside the control limits.
- Check whether non-random patterns such as trends, shifts, or cyclical patterns are recognizable.
- Assess whether known special causes are present or whether a sustainable process change must be suspected.
- Only decide whether intervention in the process is necessary after clarifying the causes.
The p-chart shows whether the process is statistically stable. Whether target values or specifications are met must be evaluated separately from a technical perspective.
Historical values
If historical reference values are known, they can be used as a fixed basis. The centerline and control limits then remain constant.
Sections
Sections are useful if the process has deliberately changed, e.g., after a supplier change or a process adjustment. Separate centerlines and control limits are calculated for each section.
Non-random patterns are detected with the tests:
Temporal Order
The subgroups must be in the order in which they were created.
Only in this way can shifts, trends, and other patterns be reliably detected.
Number of first-resolved inquiries
In IT service, it is evaluated daily how high the number of inquiries is that are resolved at the first contact. The np-chart helps to assess whether this number remains stable over time or if anomalies such as trends or shifts occur.
Interpretation
There are several points outside the control limits. The process is unstable and should be examined more closely.
→ Several points outside the limits – process unstable, check causes.
Number of offers with missing mandatory information
In sales, it is checked monthly how many offers are missing mandatory information. This allows tracking whether the number of incomplete offers remains consistently stable.
Interpretation
The numbers are unusually close together. Such a low dispersion is often not random for a real process and may indicate standardized rework, too coarse classification, or a peculiarity in the inspection system. Additionally, nine points are on the same side of the centerline.
→ Noticeably low dispersion + 9 points on one side – question inspection system/classification.
Number of Shipments with Transport Damage
In the logistics sector, it is evaluated per tour how many shipments arrive with visible transport damage. The goal is to identify extraordinary stresses early.
Interpretation
An outlier is recognizable; the 13th tour is affected. A rear-end collision was reported by the driver for this tour. The deviation can thus be explained by a known special cause and does not indicate a permanent change in the process.
→ Outlier due to known special cause (accident) – no new basic pattern.
Number of Goods Receipts with Blocking Note
In purchasing, the number of goods receipts with a blocking note is monitored. During the observation period, there was a switch from Supplier A to Supplier B, so two sections are useful.
Interpretation
After the supplier change, the number of goods receipts with a blocking note is at a noticeably higher level. The separate consideration of the sections shows that the process level has changed. The change should be evaluated in the context of the supplier change.
→ Level shift after supplier change – evaluate sections separately.
Number of Positions with Critical Forecast Error
In production planning, each planning cycle evaluates how many positions exceed a defined forecast error threshold. The np-chart shows whether the number of problematic positions changes over time.
Interpretation
Over the period, an increasing trend in the number of incorrect forecasts is noticeable. Since the values also decrease again in between, no trend is signaled according to the Nelson rules. However, the development should still be observed professionally.
pᵢ: Proportion of nonconforming units in the i-th subgroup.
Subgroup: Associated sample, e.g., a shift, a tour, a day, or a lot.
Centerline: Average proportion of nonconforming units as the central process level.
Control limits (UCL / LCL): Limits within which the random fluctuation of a stable process is expected.
Historical reference value p: Specified proportion of nonconforming units from a stable comparison period.
Sections: Separate phases of the process, each with its own centerline and limits.
Nelson rules / tests: Statistical rules for detecting non-random patterns.
With the historical fix, p̄ is replaced by the given reference value p.