Simultaneous inspection of several product characteristics

In this paper we consider 100% inspection of a product of which several characteristics have to satisfy given specification limits. A 100% inspection procedure may be necessary to bring the percentage of nonconforming items down to a level acceptable for the consumer. If one can observe the actual values of the characteristics, it would be possible to bring this percentage down to zero. However, quite often this is not possible, as a measurement error occurs in measuring the characteristics. Therefore, it is common practice to inspect each characteristic by comparing its measurement to a test limit which is slightly more strict than the corresponding specification limit. An item then is accepted if for each characteristic the measurement conforms to the corresponding test limit. However, instead of inspecting an individual characteristic merely using its own measurement, it is (much) more efficient to use the measurements of the other characteristics as well, especially if some of the characteristics are highly correlated. In this paper it is shown how the measurements of all the characteristics can be used to test whether an item is conforming