1. Variable Control Charts: Charts like the $\bar{X}$-chart (Mean chart) and R-chart (Range chart) are used for measurable characteristics like length, weight, or diameter. They track continuous data.
2. Attribute Control Charts: These are used for characteristics that can be counted rather than measured.
• $p$-Chart: Used to monitor the fraction or proportion of defective items in a sample.
• $C$-Chart: Specifically designed to monitor the actual
number of defects in a single unit or a fixed sample size. It assumes that the opportunity for a defect is large while the actual occurrence is small, following a Poisson distribution.
3. Application of the $C$-Chart: The $C$-chart is ideal for complex products where a single item might have multiple defects, such as the number of surface scratches on a refrigerator or the number of missing rivets on an aircraft wing.
Therefore, for counting the total number of defects in a specific sample or piece, the $C$-chart is the standardized choice in industrial quality engineering.