# Attribute Control Charts

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## P Chart

The P chart plots the proportion of nonconforming units (also called defectives). For example, you can use a P chart to monitor the following:

• The proportion of flights that depart late
• The proportion of bicycle tires that are flat
• The proportion of printed logos that are smudged

While a unit may have many quality characteristics that can be evaluated, it is always considered as either conforming (not defective) or nonconforming (defective).

The P chart is the most widely used attribute control chart.

### Example:

A satellite monitoring program uses a P chart to monitor the proportion of CubeSats that are out of service each day for 2 months. A CubeSat that is out of service is considered a defective unit.

On average, 8% of the CubeSats are out of service on any particular day. The proportion of defective units for day 19 is out of control. The team should try to identify any special causes that may have contributed to the unusually high rate of defectives.

## NP Chart

The NP chart plots the number of nonconforming units (also called defectives). For example, you can use an NP chart to monitor the following:

• The number of flights that depart late
• The number of bicycle tires that are flat
• The number of printed logos that are smudged

While a unit may have many quality characteristics that can be evaluated, it is always considered as either conforming (not defective) or nonconforming (defective).

### Example:

A satellite monitoring program uses an NP chart to monitor the number of CubeSats that are out of service each day for 2 months. A CubeSat that is out of service is considered a defective unit.

On average, 100 of the CubeSats are out of service on any particular day. The number of defective units for day 19 is out of control. The manager should try to identify any special causes that may have contributed to the unusually high number of defectives.

## C Chart

Usually, C charts are used to chart the total number of defects (or nonconformities) in a sample when the sample size is constant. You can inspect for one type of defect such as dead pixels. You can also inspect for several defects together such as dead pixels, stuck pixels, scratches, and blurry spots. An LCD screen may have 2 or 3 dead pixels, yet still be acceptable.

The U chart also plots defects. However, the U chart plots the number of defects per unit. The U chart is useful when the subgroup size is not constant.

### Example:

An LCD manufacturer wants to monitor defects on 17-inch LCD screens. Technicians record the number of dead pixels for each subgroup of 10 screens per hour. They use a C chart to monitor the number of dead pixels.

On average, technicians find 10 dead pixels in each sample of 10 screens. Sample 17 is out of control. The technicians should try to identify any special causes that may have contributed to the unusually high number of dead pixels.

## U Charts

A U chart plots the number of defects (also called nonconformities) per unit. It is possible for a unit to have one or more defects but still be acceptable in function and performance.

For example, you can use a U chart to monitor the following:

• The number of tears and pulls per 50 running feet of carpet
• The number of dead pixels per foot of LCD screen

You can inspect for one type of defect such as dead pixels. You can also inspect for several defects together such as dead pixels, stuck pixels, scratches, and blurry spots. An LCD screen may have 2 or 3 dead pixels, yet still be acceptable.

The C chart also plots defects. However, the C chart plots the number of defects per sample, not necessarily per unit measurement. The C chart is useful when the subgroup size is constant.

### Example:

An LCD manufacturer wants to monitor defects on 17-inch LCD screens. Technicians record the number of dead pixels for each screen. Each subgroup has a different number of screens. They use a U chart to monitor the average number of dead pixels per screen.

Because of the unequal subgroup sizes, the control limits vary. On average, technicians find about 1 dead pixel on each screen. Subgroup 17 is out of control. The technicians should try to identify any special causes that may have contributed to the unusually high number of dead pixels.