A manufacturing plant produces 10,000 plastic bottles per day. Because the product is inexpensive and the plant operation is normally satisfactory, it is not economically feasible to inspect every bottle. Instead, a sample of n bottles is randomly selected and inspected each day. These n items are

Question

A manufacturing plant produces 10,000 plastic bottles per day. Because the product is inexpensive and the plant operation is normally satisfactory, it is not economically feasible to inspect every bottle. Instead, a sample of n bottles is randomly selected and inspected each day. These n items are called a subgroup, and n is referred to as the subgroup size. The inspection includes measuring the toughness [latex]x[/latex] of each bottle in the subgroup and calculating the sample mean [latex]\bar{x}[/latex].

Accepted Answer

The [latex]\bar{x}[/latex] control chart in Fig. 21.4 displays data for a 30-day period. The control chart has a target (T), an upper control limit (UCL), and a lower control limit (LCL). The target (or centerline) is the desired (or expected) value for [latex]\bar{x}[/latex], while the region between UCL and LCL defines the range of typical variability, as discussed below. If all of the [latex]\bar{x}[/latex] data are within the control limits, the process operation is considered to be normal, or “in a state of control.” Data points outside the control limits are considered to be abnormal, indicating that the process operation is out of control. This situation occurs for the twenty-first sample. A single measurement located slightly beyond a control limit is not necessarily a cause for concern. But frequent or large chart violations should be investigated to determine a special cause.

Question 21.1: A manufacturing plant produces 10,000 plastic bottles per d...

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