Attribute control chart

Attribute control chart

1. Control charts for attributes

   • p chart
     • the chart for fraction rejected as nonconforming to specification
   • nP chart
     • The control chart for number of nonconforming items
   • c chart
     • The control chart for number of nonconformities
   • u chart
     • The control chart for number of nonconformities per unit.

2. P chart

   • The most versatile and widely used attribute control chart
   • It may be applied to quality characteristics that are considered as attributes.
   • The p chart can be applied to one quality characteristic or a dozen
   • Fraction rejected “p” may be defined as the ratio of the number of non-conforming articles in any inspection or series of inspection to the total number of articles actually inspected.
   • Fraction rejection is always expressed as a decimal fraction.
   • P = fraction rejected
     • P = No of defective in the sample No of items in the sample
   • Formula for p chart
   • Calculation
   • Problems with p chart
     • It should be developed with a constant sub group size.
     • However, if maximum and minimum are not more than 25% away from the average, existing method can be used.
     • A remedial method for different sub group size is “compute new control limit for every sub group” and show these fluctuating limits on the control chart.
   • P chart for variables

3. nP or Pn Control chart

   • When the sub group size is constant, the chart for actual numbers of rejected may be used. Such a chart is called a chart for nP or Pn.
   • Control limits
     • Pn bar± 3 x √Pn bar (1-p bar
     • UCL = Pn bar + 3 x √Pn bar (1-p bar)
     • LCL = Pn bar - 3 x √Pn bar (1-p bar)
     • CL = Pn bar
   • Example
   • Take a graph paper and mark UCL value and CL value. However, here no LCL value, because it is a 0 value
   • Draw the nP chart, where X axis is representing the lot number and Y axis is representing the nP values.

4. C chart

   • This chart used for number of non-conformities and generally it is called as C chart.
   • C chart has more restricted field of usefulness
   • Nevertheless, there are certain manufacturing and inspection situations, C chart is definitely needed.
   • C stands for the number of non-conformities in sub group of constant size.
   • The sub group for a C chart is usually in single article.
   • Control limits = C bar ± 3 x √C bar
   • UCL = C bar + 3 x √C bar LCL = C bar - 3 x √C bar CL = C bar
   • Example

5. U chart

   • The symbol “U” is used to represent non-conformities per unit area, where C is the count of non-conformities.
   • Usually this chart is important for Garment industry.
   • Control limits:
     • Central line = U bar
     • Control limits = U bar± 3 x √U bar/n
   • Example
   • Drawing U chart
     • In drawing the U chart, take sample number for the X axis and U values for the Y axis.
     • In this example, U bar = 0.022 and UCLevels would vary according to the sample size
     • in this example, LCL getting 0 value.