Formulating Appropriate Measures of Process PerformanceBasic Terminology and Concerns of MetrologyA Simple Measurement Model–Using Probability to Describe Measurement ErrorSome Implications of Simple "One Sample" Inference Formulas When Measurement Error is RecognizedIE 361 Module 2Basic Concerns of Metrology and Some Simple Applications ofElementary Probability and Statistics to MetrologyReading: Section 2.2 Statistical Quality Assurance for Engineers(Sections 2.1-2.2.1 of Revised SQAME )Prof. Steve Vardeman and Prof. Max MorrisIow a State Univer sityVardeman and Morris (I owa State Uni versity) IE 361 Module 2 1 / 26Formulating Appropriate Measures of Process PerformanceIn a quality assurance/process improvement context, measures of processperformance should be customer-oriented.A nice example of this point is an early attempt by one of the "Big 3" USauto makers to track initial customer satisfaction. This company …rsttried using corporate warranty costs (charged to the company by dealersdoing in-warranty service) as its measure of satisfaction. That was clearlynot anything a customer cares about. A more appropriate measure thatwas later adopted was "per vehicle visits to a dealer for warranty service."Huge modern marketing e¤orts are aimed at …nding out what is importantto customers. In successful organizations, these help de…ne what measuresof process performance are employed and monitored by the organizations.Vardeman and Morris (I owa State University) IE 361 Module 2 2 / 26Formulating Appropriate Measures of Process PerformanceIn any data collection context (including a process improvement e¤ort)direct measures of a quantity are always preferable to relatively indirectones. If one wants to know about y, it is better to try to measure y thanto measure w that is presumed to be related to y. If, for example, one isdesigning a controller for a clothes dryer, somehow measuring weight lossas water is removed from a load is preferable to measuring air temperatureof the dryer’s exhaust, even if it is easier to do the latter than to …gure outhow to do the former. In the above auto initial customer satisfactioncontext, some direct inquiries to customers about satisfaction is probablypreferable to reliance on only the per vehicle service calls measure.The matter of measuring process performance brings us naturally to thegeneral topic of measurement, or the science of "metrology."Vardeman and Morris (I owa State University) IE 361 Module 2 3 / 26Basic Terminology and Concerns of MetrologyA quantity for which one hopes to establish a true or correct value is calleda measurand. (A measurand can be anything from the surface roughnessof a machined metal part, to the torque delivered by a pneumatic torquegun, to the color of a printed carton.) "The problem" is that in the realworld, a measurand can rarely (if ever) be known perfectly. That is, thereis almost always some measurement error associated with attempts toevaluate a measurand. A measurement y never perfectly re‡ects ameasurand x. This is illustrated in cartoon form in the next …gure. (Weare here going to use the generic term "device" to describe a particularcombination of equipment, people, procedures, etc. used to produce ameasurement.)Vardeman and Morris (I owa State University) IE 361 Module 2 4 / 26Basic Terminology and Concerns of MetrologyFigure: A Cartoon Illustrating How a Measurand x is Measured With Error toProduce a Measurement yIf one is going to do real world quality assurance, one must then have aworking understanding of the nature of measurement error, how toquantify it, and how to account for its presence in assessing, monitoring,and improving quality. Probability and statistics are essential to ols inunderstanding, quantifying, modeling, and assessing the impact ofmeasurement error.Vardeman and Morris (I owa State University) IE 361 Module 2 5 / 26Basic Terminology and Concerns of MetrologyBasic issues in metrology are:Validity (is a measurement device or system really tracking what onewants it to track?)Precision (consistency of measurement)Accuracy (getting the "right" answer on average)In developing an e¤ective measurement system, these issues are addressedin the order given above. While these terms may appear to have similarcolloquial meanings, they are technically quite di¤erent and it is essentialthat you use the correct terminology in IE 361.Vardeman and Morris (I owa State University) IE 361 Module 2 6 / 26Basic Terminology and Concerns of MetrologyA common analogy that should help you keep straight the di¤erencebetween precision and accuracy is the analogy between measurement andtarget shooting.N ot Accu rate/No t Pr ecise Accur ate/N ot PreciseNo t Accu rate/Pr ecise Accu rate/PreciseFigure: Measurement/Target Shooting AnalogyVardeman and Morris (I owa State University) IE 361 Module 2 7 / 26Basic Terminology and Concerns of MetrologyGood organizations devote signi…cant resources to ensuring that theirmeasurement systems are properly maintained and adequate to supportprocess monitoring and improvement e¤orts. The comparison of theoutput of a measurement device to "known"/"standard" values (andsubsequent adjustment of how that device reads to the standards) is knownas calibration. Calibration has to do with assuring measurement accuracy.Vardeman and Morris (I owa State University) IE 361 Module 2 8 / 26A Simple Measurement Mo del–Using Probability toDescribe Measurement ErrorA basic statistical/probabilistic model for measurement is that what ismeasured, y, is the measurand, x, plus a normal random measurementerror, e, with mean δ and standard deviation σd evi ce.y = x + ePictorially this is as in the following …gure.Vardeman and Morris (I owa State University) IE 361 Module 2 9 / 26A Simple Measurement Mo delFigure: A Basic Probability Model for MeasurementVardeman and Morris (I owa State University) IE 361 Module 2 10 / 26A Simple Measurement Mo delThe di¤erence between the measurand and the mean measurement is thebias in measurement, δ. Ideally, this is 0 (and it is the business ofcalibration to attempt to make it 0). At a minimum, measurementdevices are designed to have a "linearity" property. This means that thatover the range of measurands a d evice will normally be used to evaluate, ifits bias is not 0, it is at least constant (i.e. δ does not depend upon x).This is illustrated in cartoon form in the next …gure (where we assumethat the vertical and horizontal