Module 8C

Module 8C - IE 361 Module 8 Repeatability and...

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Unformatted text preview: IE 361 Module 8 Repeatability and Reproducibility for "0/1" (or Go/No-Go) Contexts Reading: Section 2.7 of Revised SQAME Prof. Steve Vardeman and Prof. Max Morris Iowa State University Vardeman and Morris (Iowa State University) IE 361 Module 8 1 / 16 Go/No-Go Inspection Ideally, observation of a process results in quantitative measurements. But there are some contexts in which all that is determined is whether or not an item or process condition is of one of two types, that we will for the present call "conforming" and "non-conforming." It is, for example, common to check the conformance of machined metal parts to some engineering requirements via the use of a "go/no-go gauge." (A part is conforming if a critical dimension &ts into the larger of two check &xtures and does not &t into the smaller of the two.) And it is common to task human beings with making visual inspections of manufactured items and producing a "OK/Not-OK" call on each. Engineers are sometimes then called upon to apply the qualitative "repeatability" and "reproducibility" concepts of metrology to such Go/No-Go or "0/1" contexts. One wants to separate some measure of overall inconsistency in 0/1 "calls" on items into pieces that can be Vardeman and Morris (Iowa State University) IE 361 Module 8 2 / 16 Go/No-Go Inspection mentally charged to inherent inconsistency in the equipment or method, and the remainder that can be charged to dierences between how operators use it. Exactly how to do this is, in fact, presently not well-established. The best available statistical methodology for this kind of problem is more complicated than can be presented here (involving so-called "generalized linear models"). What we can present is a rational way of making point estimates of what might be termed repeatability and reproducibility components of variation in 0/1 calls. (The estimates presented here are based on reasoning similar to that employed in SQAME to &nd correct range-based estimates in usual measurement RR contexts.) We will then remind you of elementary methods of estimating dierences in population proportions and point to their relevance in the present situation. Vardeman and Morris (Iowa State University) IE 361 Module 8 3 / 16 Some Simple Probability Modeling To begin, think of coding a "non-conforming" call as "1" and a "conforming" call as "0," and having J operators each make m calls on a &xed part . Suppose that J operators have individual probabilities p 1 , p 2 , . . . , p J of calling the part non-conforming on any single viewing,...
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Module 8C - IE 361 Module 8 Repeatability and...

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