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What is an np-CHART

When the interest is in determining the quantity of defective units and the data is collected in subgroups that are of constant size, then the np-chart is appropriate. The p-chart could also be used in this case, but the number of nonconforming items, rather than the fraction, is generally easier to understand. The np-chart measures the output of a process as the actual number of nonconforming or defective items in a subgroup being inspected. Each item is recorded as being either conforming or nonconforming, even if the item has more than one defect. Except for plotting the number defective instead of the fraction and the calculation of control limits, the np-chart is the same as the p-chart. 

The following symbols are used on an np-chart:

n — The number of units in a subgroup (the subgroup, sample, or subset size).
k — The number of subgroups in the current calculation.
np — The number of defective or nonconforming units found in a subgroup. These are the points plotted on the chart. 

np-bar — The average number of defective or nonconforming units for the subgroup in the current calculation. This is drawn as the centerline on the chart. It is found by dividing the total number of defective units 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 defective or nonconforming units for the subgroup in the current calculation. This is drawn as the centerline on the chart. It is found by dividing the total number of defective units found in all subgroups of the study period by the total number of subgroups in the study period

How to Make and Use an np-Chart

Refer to the example in Figure 3.5.1

 The number of coffee cups manufactured with broken handles is shown in the table below. Inspection is lot-by-lot with each lot consisting of 60 cups

1) Gather and record the data. 

2) Calculate np-bar. 

3) Calculate the upper and lower control limits. 

The formulas are:

Calculate the upper and lower control limits

4) Decide on a scale for the control chart.

5) Plot each np, and add np 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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