Tabtrainer Minitab: SPC Charts for Attribute Quality Data

In this lesson, we dive into a practical business case from the final assembly line of the Smartboard Company. Across early, late, and night shifts, all skateboard components are assembled into finished products. Before shipment, each skateboard undergoes an automatic surface inspection to detect scratches that may have occurred during assembly.

Historically, the boards were categorized using attribute data into “good” (no surface defects) and “bad” (surface defects present). Damaged boards required costly rework or were scrapped. To improve quality, the inspection system now records not only whether defects are present, but also the number of boards with defects and the total number of defects per shift.

In this unit, we apply attribute control charts to monitor process stability:

The p-Chart is used to track the proportion of defective boards per shift.

The u-Chart is applied to monitor the number of surface defects per board (defects per unit).

You will also learn how to perform diagnostics on these control charts to identify special causes of variation and assess whether the process is under statistical control. This case provides essential skills for anyone aiming to apply Six Sigma or SPC tools in real production environments.

In this lesson, we shift our focus from binomially distributed quality data—analyzed previously using p-Charts and np-Charts—to Poisson-distributed process data, which requires a different statistical approach. Instead of monitoring whether a skateboard is defective, we now examine the number of defects per unit and per subgroup, such as the number of surface scratches occurring during final assembly at Smartboard Company.

Previously, we learned that binomial distribution applies when classifying outcomes into two categories, such as “good” and “bad.” This allowed us to track the proportion of defective items with a p-Chart, or the absolute number of defective items with an np-Chart.

In this practical business case, however, we no longer count defective skateboards—but instead count defects per skateboard, which follow the Poisson distribution, familiar from our earlier Measurement System Analysis.

To analyze process stability in this context, we apply:

• The U-Chart, where U stands for "unit" – displaying defects per unit (e.g., scratches per skateboard) by dividing total defects by subgroup size.

• The C-Chart, where C stands for "count" – showing the absolute number of defects per subgroup. This chart is used when all subgroups are of equal size.

• The Laney U′-Chart, an adjusted version of the U-Chart, used when diagnostics reveal that the data exhibits overdispersion or underdispersion compared to the expected Poisson variation.

These charts allow us to evaluate whether the process is stable in terms of defect frequency. However, they only yield accurate control limits and valid interpretations if the underlying assumptions of the Poisson distribution are met.

In this lesson, we perform a full diagnostic analysis to determine whether our dataset meets the conditions required for valid Poisson-based control charting. Specifically, we use the U-Chart Diagnostic Tool to evaluate whether the variation in the number of surface scratches follows the expected random behavior of a Poisson distribution.

We begin by navigating to Statistics > Control Charts > Attribute Charts > U Chart Diagnostic and apply the test using. This generates a Poisson probability plot, similar in function to those used in binomial or normal distributions. The red line in the plot represents the theoretical distribution; the blue points show our actual data. A perfect alignment would indicate a 100% agreement between our observed and theoretical data.

We also explain the decision criteria:

• If the observed variation exceeds the upper confidence limit (e.g., above 126.3%), this indicates overdispersion. In such cases, a Laney U′-Chart should be used to adjust for the excess variability.

• Conversely, if the observed variation is far below the expected range, we might have underdispersion, requiring separate interpretation—though in such cases, a standard U chart often remains acceptable.

By the end of this lesson, you will be able to:

• Conduct U chart diagnostics using Poisson probability plots.

• Interpret agreement rates and confidence intervals.

• Decide whether to apply a standard U chart or a Laney U′-chart based on statistical evidence.

In this lesson, we apply a U-Chart to analyze the defect rate of surface scratches per unit in the final assembly of skateboards. Using real process data, you will learn how to construct, interpret, and evaluate the chart, and how to detect process instabilities through defined control tests.

You will learn how to:

• Interpret each data point as the number of scratches divided by subgroup size.

• Understand how control limits narrow or widen depending on subgroup size.

• Calculate mean defect rate (U-bar) and mean subgroup size (N-bar) using descriptive statistics.

• Derive the upper and lower control limits using AIAG formulas.

• Identify process violations, such as Test 1 violations where points lie beyond three standard deviations from the centerline.

• Recognize contextual process causes, like the observed anomalies around New Year’s Day.

• Examine the AIAG's 75% rule, which determines whether smoothed control limits can be applied.

You’ll learn why:

• Control limits based on mixed data can lead to misinterpretation.

• Splitting the chart is essential for valid control analysis post-improvement.

By the end of this lesson, you’ll understand how to:

• Properly construct a U chart with varying subgroup sizes,

• Apply AIAG criteria for control limits,

• Diagnose special cause variation using control tests,

• And correctly segment control charts when process improvements are introduced.

In this lesson, we demonstrate how critical it is to properly split a control chart into distinct stages when your process has undergone significant changes. Using our existing dataset on surface scratches in final assembly, we first revisit the U chart without stage separation and then correctly create a two-stage U chart for valid process control:

We apply the correct method by splitting the data into two distinct stages. This creates a stage-separated U chart, distinguishing between the original process and the optimized process.

By comparing:

• The original U chart (before July),

• The incorrect full-process U chart

• The correct split-stage U chart,

we clearly observe:

• A drop in average defects

• A reduction in process variation

• The disappearance of false alarms, which previously occurred due to mixed control limits.

You’ll learn how to:

• Correctly implement stage-splitting in control charts,

• Avoid misinterpretation of process stability,

• Use U charts for both varying and constant subgroup sizes,

• And validate real process improvements with statistical evidence.

By the end of this lesson, participants will be able to:

• Understand when and why to use a C chart instead of a U chart—specifically in cases where subgroup sizes are constant.

• Apply a C chart in Minitab using a dataset with uniform subgroup sizes, and correctly activate all necessary control tests.

• Distinguish between absolute defect counts (C chart) and relative defect rates (U chart) through direct comparison of chart outputs.

• Recognize that the C chart plots actual defect values, while the U chart expresses them in relation to subgroup size (e.g., scratches per unit).

• Calculate mean defect count (C-bar) and determine upper and lower control limits using AIAG standard formulas.

• Use Minitab’s descriptive statistics tool to determine C-bar from column C3 and confirm the computed control limits.

• Interpret data points in the C chart, including their exact values, and compare them to the corresponding points in the U chart.

• Appreciate the visual simplicity of the C chart, with fixed control limits, in contrast to the varying limits in the U chart.