Control Charts for Attributes

1
Control Charts for Attributes

• p chart (fraction of nonconforming items)
• np chart ( number of nonconforming items)
• c chart (number of nonconformities in some unit)
• u chart (number of nonconformities per unit)

2
The p Chart Procedure

• Step1. Gather the data. Select the size,
  frequency and number of samples.
• Step2. Calculate p for each sample.
• Step 3. Set the scale for the control chart.
• Step 4. Plot the p values and connect them.
• Step 5. Calculate p-bar, and the control limits
  after about 20 points have been charted.
• Step 6. Interpret the chart

3
Chart Interpretation

• Shifts. A shift of seven or more points to a
  higher or lower level could mean that something
  has affected the proportion defective or that the
  definition of what is defective has somehow
  changed.
• Trends. A run of seven or more points up or down
  indicates that something is causing the
  proportion that is defective to change in a
  gradual manner, poorly trained operators,
  different inspection criteria, or poorly
  controlled parts in the assembling process.

4
The np Chart

• Standard given
• UCL np0 3?np0 (1-p0)
• LCL np0 - 3?np0 (1-p0)
• No standard given
• UCL ?x 3 ? x (1- x/n)
• LCL ?x - 3 ? x (1- x/n)

5
The c Chart

• Standard given
• UCL c0 3??? c0
• LCL c0 - 3??? c0
• No standard given
• UCL ?c 3???c
• LCL ? c - 3???c

6
The u Chart(variable unit size)

• u c/k k is the number of inspection
• units in each sample
• UCL u0 3??? u0/k
• LCL u0 - 3??? u0/k