vdoc
Share Embed Flag
Download ePaper

vdoc

huu.bui
03.05.2023 Views

Chapter 13: G. Measurement System Analysis 123variation. As mentioned earlier, the total process variation can be divided into twomajor categories, that is, variation due to parts and variation due to gages or themeasurement system. Part-to-part variation may be due to environment, methods,materials, machines, or some combination thereof, and other factors. The variationdue to the measurement system mainly consists of two major components:one due to the instrument being used for taking measurements, and the otherdue to the operators who use the instrument. In the industrial world, these componentsare usually referred to as repeatability and reproducibility, respectively.Thus, repeatability and reproducibility may be considered as the major indicatorsof measurement system performance. A little later we will discuss repeatabilityand reproducibility in more detail.Since repeatability refers to the variation generated by the instrument(that is, measurement equipment or gage) it is referred to as equipment variation(EV). Reproducibility refers to variation generated by operators using measurementinstruments and is referred to as appraiser (or operator) variation (AV). Thestudy of gage repeatability and reproducibility is usually referred to as a gageR&R study.In the Automotive Industry Action Group (AIAG) reference manual on MSAseveral methods for conducting GR&R are given. In this book we will study twomethods: the range-based method and the analysis of variance (ANOVA) method.Since analysis of variance is an advanced statistical technique that is not coveredin this book, we will not go into much detail. We will focus our attention onexplaining and interpreting the results of an example that we will work out usingcomputer software.Part II.GTHE RANGE-BASED METHODThe method discussed in this section has been presented by various authorsincluding IBM (1986) and Barrantine (2003). Before we discuss the details of thismethod, we will define certain terms, namely, measurement capability index, K 1factor, and K 2 factor. In addition, we will define some other terms that are very usefulin understanding the measurement system analysis.A measurement system analysis is a technique for collecting data andanalyzing it to evaluate the effectiveness of the gage. In order to collect data werandomly select some parts and select a certain number of operators (three ormore, but as a general rule, the more the better). Then each operator takes multiplemeasurements (at least two) on each part. All the parts are measured in randomorder. These measurements are also known as trials. Using the terminology ofcontrol charts, the measurements on each part or the number of trials constitutesa rational subgroup and the number of parts times the number of operators constitutesthe number of subgroups or samples. Then R – is defined as the average ofthe ranges of trials within the same operator and R – is defined as the average of theR – ’s among the operators.Measurement capability index (MCI) is a measurement that quantifies our beliefthat the gage is reliable enough to support the decisions that we make under theexisting circumstances. The MCI relates to four characteristics of a measurementsystem that are the key to any measurement system. These characteristics are:

124 Part II: MetrologyPart II.G• Precision• Accuracy• Stability• LinearityThe characteristic precision is further subdivided into two categories, that is, repeatabilityand reproducibility. Repeatability measures the preciseness of observationstaken under the same conditions, which is achieved by computing the varianceof such observations. For example, we say a gage possesses the characteristic ofrepeatability if an operator obtains similar observations when measuring thesame part again and again. Reproducibility measures the preciseness of the observationstaken by different operators when measuring the same part. For example,we say a gage possesses the characteristic of reproducibility if various operatorsobtain similar observations when measuring the same part again and again.Accuracy of a measurement system is the closeness of the average of measurementstaken to the true value. The distinction between precision and accuracy isvery well explained by the diagram shown in Figure 13.2.Stability is defined by the total variation in measurements obtained with ameasurement system on the same master or same parts when measuring a singlecharacteristic over an extended period of time. The smaller the total variation, themore stable the measurement system is.Linearity is the difference between the true value (master measurement) andthe average of the observed measurements of the same part that has the same distributionover the entire measurement range. Linearity is best explained by thediagram in Figure 13.3.In any manufacturing process the total variability consists of two components,one due to the variability between the parts and the other due to the variabilityin the measurement system. Thus, the MCI of a measurement system, which isdirectly related to the variability due to the measurement system (gage), is a verypertinent factor in improving any process. The total variability due to the measurementsystem itself consists of three components: variability due to the operators,the instrument, and the interaction between the operators and the instrument.Statistically, these relationships can be expressed as follows:(a) Target (b) Target (c) Target (d) TargetFigure 13.2(a) Accurate and precise, (b) accurate but not precise, (c) not accurate but precise,(d) neither accurate nor precise.

124 Part II: Metrology

Part II.G

• Precision

• Accuracy

• Stability

• Linearity

The characteristic precision is further subdivided into two categories, that is, repeatability

and reproducibility. Repeatability measures the preciseness of observations

taken under the same conditions, which is achieved by computing the variance

of such observations. For example, we say a gage possesses the characteristic of

repeatability if an operator obtains similar observations when measuring the

same part again and again. Reproducibility measures the preciseness of the observations

taken by different operators when measuring the same part. For example,

we say a gage possesses the characteristic of reproducibility if various operators

obtain similar observations when measuring the same part again and again.

Accuracy of a measurement system is the closeness of the average of measurements

taken to the true value. The distinction between precision and accuracy is

very well explained by the diagram shown in Figure 13.2.

Stability is defined by the total variation in measurements obtained with a

measurement system on the same master or same parts when measuring a single

characteristic over an extended period of time. The smaller the total variation, the

more stable the measurement system is.

Linearity is the difference between the true value (master measurement) and

the average of the observed measurements of the same part that has the same distribution

over the entire measurement range. Linearity is best explained by the

diagram in Figure 13.3.

In any manufacturing process the total variability consists of two components,

one due to the variability between the parts and the other due to the variability

in the measurement system. Thus, the MCI of a measurement system, which is

directly related to the variability due to the measurement system (gage), is a very

pertinent factor in improving any process. The total variability due to the measurement

system itself consists of three components: variability due to the operators,

the instrument, and the interaction between the operators and the instrument.

Statistically, these relationships can be expressed as follows:

(a) Target (b) Target (c) Target (d) Target

Figure 13.2

(a) Accurate and precise, (b) accurate but not precise, (c) not accurate but precise,

(d) neither accurate nor precise.

logo

products

Resources

Company

Terms of service
Privacy policy
Cookie policy
Cookie settings
Imprint
Change language
Made with love in Switzerland
© 2024 Yumpu.com all rights reserved

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!