Statistical Tolerancing Based on Consumer's Risk Considerations

Setting test limits under prescribed consumer loss

“…The ongoing interest for inspection methods is also evident from the literature, see e.g. Easterling et al (1991).…”

A variety of criteria for setting test limits

“…Suppose that for our example C p /C c 1/100, which corresponds to g 1/101, then we have a VI 1.976, see also Table I in EASTERLING et al (1991). This value of a VI corresponds to a test limit equal to t VI 1.605.…”

“…That means that g ( 1 and quite often g will be smaller than l. So again it becomes clear that the test limits t III a bs À a III s Z , t IV a bs À a IV s Z and t V a bs À a V s Z may be too liberal. In EASTERLING et al (1991) examples are given for C p /C c from 1/1000 up to 1/20, which corresponds to g in between 1/1001 and 1/21. The higher the cost of consumer loss relative to the cost of producer loss, the smaller g and the more strict the test limit becomes.…”

“…In EASTERLING et al (1991), the cost of misclassi®cations is taken into account in the determination of test limits. Suppose the cost of accepting a nonconforming item is C c and the cost of rejecting a conforming item is C p .…”

Applying Bootstrap method to the types I–II errors in the measurement system

“…The magnitude of these risks helps determine the impact of the measurement error and whether or not the measurement system requires capability upgrade. Easterling et al 4 provide an indepth discussion of risks associated with misclassifying items due to measurement variability. Doganaksoy 5 presents a case study to assess the risks associated with misclassifying items due to measurement variability to the case of multiple sources of product variability.…”