In a U-chart versus a C-chart, which control chart tracks defects per unit when sample sizes vary?

• A. U-chart tracks defects per unit with varying sample size.
• B. C-chart tracks counts of defects with fixed sample size.
• C. P-chart tracks proportions of defects per unit.
• D. X-bar chart tracks averages of defects.

Answer: (A)

The important idea is measuring a rate when the amount sampled changes. A U-chart does exactly that by plotting defects per unit and using the actual sample size for each point. By defining the rate as defects divided by units (u = defects/units) and computing a bar rate ū from all samples, the control limits become functions of the varying sample sizes (LCL = ū − 3√(ū/n_i), UCL = ū + 3√(ū/n_i)). This normalization allows fair comparison of defect density across samples of different sizes, so the chart can detect true shifts in defect rate rather than changes merely due to sample size. In contrast, a C-chart counts defects with a fixed sample size, a P-chart tracks proportion defective and accounts for varying n but focuses on proportions rather than defects per unit, and an X-bar chart tracks the average of a measured attribute rather than defect rate.