The Importance of Trending Attribute Data

Dr. Wayne A. Taylor

The use of SPC is preferable to relying on acceptance sampling.  It is better to make defect-free product than to sort out the defects later.  However, with attribute data, care must be taken in implementing SPC to avoid only an illusion of change.

Suppose a packing operation inspects for missing parts using the single sampling plan with sample size 13 and accept number 0.  Whenever a lot is rejected, an attempt is made to fix the process.  Historically, the process has averaged around 0.2% defective.

An edict is received to implement SPC.  So a p-chart of the inspection data is implemented.  This control chart is shown in Figure 1.  The upper control limit is 3.92%.  Samples with 1 or more defects exceed this control limit.  Reaction includes attempting to fix the process and rejection of recent product.  It can now be stated that SPC is used and that corrective actions are taken for out-of-control points.  However, in reality, nothing has changed.  The same data is collected and the same actions taken.  There is only an illusion of change.

p-Chart of Inspection Results
Figure 1: p-Chart of Inspection Results

A better approach is to continue to acceptance sample as before.  Since this does not protect against a gradual increase in the process average, the data should also be analyzed for trends.  Figure 2 shows a p-chart of the same data, but with the data from each day combined.  Figure 2 shows that a change occurred between days 5 and 6.  The process average has increased to around 1%, a fivefold increase in the number of defects going to the customer.  This change is not as apparent in Figure 1.

Daily p-Chart
Figure 2: Daily p-Chart

Figure 3 shows a CUSUM plot of the same data.  On a CUSUM chart, a change in the defect rate results in a change in slope.  Again the change is apparent.

Figure 3: CUSUM Chart

This example illustrates the importance of trending attribute data either by accumulating the data or by using a CUSUM chart.

Appeared in FDC Control, Food Drug & Cosmetic Division ASQC, No. 104, September 1994, p. 6

Copyright © 1994 Taylor Enterprises, Inc.

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