Defect sampling is used in industrial settings to determine the types and amounts of defects in manufactured items. Items at various stages of production are removed from the process and inspected for defects. Sustained testing allows operations managers to discover whether some part of the manufacturing process is failing to meet performance criteria and product standards. To minimize manufacturing defects, early detection and problem resolution are critical.
ACME Manufacturing produces electronic components used in the assembly of industrial robotic equipment. The components are technologically sophisticated, and quality must be rigorously monitored to ensure that specifications are met. Of course, inspection can be a time consuming and costly activity. ACME production managers must determine how much sampling and testing is needed to minimize costs and maximize yields.
In the current sampling plan, one component from the production line is randomly selected every 15 minutes. Each component is inspected and tested for major and minor defects. Major defects, which affect component performance, must be addressed immediately. Fortunately, major defects are rare and are generally contained and corrected early in the process. Minor defects, such as nicks and scratches, are those that affect the appearance of a component but not its functionality. Monitoring minor defects to ensure the rate doesn’t increase is of particular concern to ACME management.
ACME currently inspects one part every 15 minutes during an eight-hour shift. Production managers have complained this sampling rate is too high, which has driven up costs and decreased output. They suggest implementing sampling plans involving fewer parts.
In this case, we explore the effectiveness of the current defect sampling plan, and several alternative plans, in detecting changes in the occurrence of minor defects.
The data set contains ten days of data on minor defects. Each day, one item is tested every fifteen minutes during an eight-hour shift. The variables in the data set are:
Day Day of the test: 1 – 10
Sample Time of the day that sample was taken in military time (e.g., 13:00 is 1pm)
Defects Number of minor defects detected on the sampled item
A visual examination of the data set is a good place to start. Exhibit 1 organizes the 15-minute data by day. The first thing we note is that the production process is far from error-free. That’s not too surprising, since the errors recorded here are minor ones.
Exhibit 1 Defects Split by Day
(Tables > Split;; Use Defects as the Split Column and Day as Split By. Under Remaining Columns select Keep All)
From Exhibit 2, we see that the average number of defects per item is 10.325 and the standard deviation is 3.17.
Exhibit 2 Distribution of Defects
(Return to the original table. Analyze > Distribution;; Use Defects as Y, Columns.)Over this ten-day period, 320 items were sampled and tested. That’s 32 items per day! A summary report of these tests shows that just over ten defects are detected on average each day (Exhibit 3).
Exhibit 3 Summary of Defects by Day(Analyze > Tabulate;; drag Day in drop zone for rows as a grouping column, and Defects in the drop zone for column as an analysis column. Then, drag N and Mean from the middle panel to the middle of the table.
Note that in JMP versions 10 and earlier Tabulate is under the Tables menu.)
Let’s consider two alternative sampling schemes.
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