A np chart using the locational information of nonconforming units

The np control chart is used widely in statistical process control (SPC) for attributes. However, there are two troublesome problems with the np chart. Firstly, it is often difficult to design an np chart with the desired in-control average run length ARL₀. Secondly, it is almost always impossible to make an np chart capable of detecting a downward (decreasing) shift in the fraction nonconforming p. This article proposes a new type of np control chart (called the locational np chart) which uses a two-level inspection scheme to decide the process status (in control or out of control). The first level inspection decides the process status based on the number of nonconforming units in a sample or the number of consecutive perfect samples (samples containing no nonconforming unit). And the second level inspection makes a decision based on the location of a nonconforming unit in a sample. The locational np chart is able to make the in-control ARL₀ very close to any specified value so that the sum of the costs incurred by false alarms and by nonconforming units is hopefully close to the minimum. Moreover, the locational np chart is always effective for detecting downward p shifts regardless of the sample size, so that improvement in product quality can be identified. Finally, the design and operation of the locational np chart are simpler than that of many other methods.