14-2 Control Charts for Attributes 713 Key Concept This section presents a method for constructing a control chart to monitor the proportion p for some attribute, such as whether a service or manufactured item is defective or nonconforming. (A good or a service is nonconforming if it doesn’t meet specifications or requirements. Nonconforming goods are sometimes discarded, repaired, or called “seconds” and sold at reduced prices.) The control chart is interpreted using the same three out-of-control criteria from Section 14-1 to determine whether the process is statistically stable: 14-2 Control Charts for Attributes As in Section 14-1, we select samples of size n at regular time intervals and plot points in a sequential graph with a centerline and control limits. (There are ways to deal with samples of different sizes, but we don’t consider them here.) DEFINITION A process is not statistically stable or is out of statistical control if one or more of the following out-of-control criteria are satisfied. 1. There is a pattern, trend, or cycle that is obviously not random. 2. There is at least one point above the upper control limit or at least one point below the lower control limit. 3. Run of 8 Rule: There are at least eight consecutive points all above or all below the centerline. (With a statistically stable process, there is a 0.5 probability that a point will be above or below the centerline, so it is very unlikely that eight consecutive points will all be above the centerline or all below it.) Out-of-Control-Criteria DEFINITION A control chart for p (or p chart) is a graph of proportions of some attribute (such as whether products are defective) plotted sequentially over time, and it includes a centerline, a lower control limit (LCL), and an upper control limit (UCL). The notation and control chart values are as summarized in the following Key Elements box. In this box, the attribute of “defective” can be replaced by any other relevant attribute (so that each sample item belongs to one of two distinct categories). Monitoring a Process Attribute: Control Chart for p Objective Construct a control chart for p (or a “p chart”) that can be used to determine whether the proportion of some attribute (such as whether products are defective) from process data is within statistical control. Requirements 1. The data are process data consisting of a sequence of samples all of the same size n. 2. Each sample item belongs to one of two categories (such as defective or not defective). 3. The individual sample data values are independent. KEY ELEMENTS continued
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