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What is a c-CHART

In cases where a single unit of process output is likely to have many defects, it may be appropriate to use a c-chart. The c-chart is applied where the defects are scattered continuously throughout the unit output, such as flaws in a roll of paper or bubbles in glass. The interest here is not only that the unit is defective, but how many defects it has. Subgroups will be in square yards of cloth, number of glass containers, an area of sheet metal, etc. The areas or number of items for a subgroup must be the same from subgroup to subgroup.

A c-chart usually has one item per subgroup, but may have two or more. A c-chart also applies where the defects on a single unit, such as individual automobiles, may come from many sources, and where no one such source would produce most of the nonconformities. The c-chart is useful in the final inspection of complicated assemblies. Also, it can be used in non-industrial areas, such as bookkeeping errors and accidents.

The symbols used on a c-chart are:

n — The number of units in a subgroup (the subgroup, sample, or subset size).
k — The number of subgroups in the current calculation.
c — The number of defects or nonconformities in a subgroup. These are the points that are plotted on the chart. 

c-bar — The average number of defects or nonconformities for the study period. This is drawn as the centerline on the chart. It is found by dividing the total number of defects found in all subgroups of the study period by the total number of subgroups in the study period.

The formula is:

The average number of defects or nonconformities for the study period. This is drawn as the centerline on the chart. It is found by dividing the total number of defects found in all subgroups of the study period by the total number of subgroups in the study period.

How to Make and Use a c-Chart

Refer to the example in Figure 3.6.1.

 The number of assembly errors found in complex circuit board assemblies are shown in the table below. Ten boards were inspected per hour

Table for Fig. 3.6.1

1) Gather and record the data. Remember that the size of the inspection sample must be the same (number of units, area of glass, length of wire, etc.). 

2) Calculate c-bar.

3) Calculate upper and lower control limits using the formulas:

Calculate upper and lower control limits

4) Decide on a scale for the control chart. 

5) Plot each c, and add c-bar and the control limit lines.

6) Analyze the data points for evidence of noncontrol. 

7) Find and correct special causes. 

8) Recalculate control limits.

 

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