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International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.

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  1. 1. Mr.Ravindra Dhawale, Prof.Dr.D.N.Raut / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.726-730726 | P a g eEvaluating Measurement Capabilities by Gauge R&R UsingANOVA for ReliabilityMr.Ravindra Dhawale *, Prof.Dr.D.N.Raut ***( M.Tech. Production Engineering Department ,VJTI ,Mumbai- 400019)** (Prof. Production Engineering Department ,VJTI ,Mumbai- 400019)ABSTRACTGauge Repeatability andReproducibility i.e. R&R measurement by usingANOVA method is the main step of theproduction control and quality improvement ofthe final outputs. This is because, it is necessaryfor the operators to have particular andaccurate data for analyzing and solvingproblems of the production. This paperunderlines the study of Gauge R&R usingANOVA on the Minitab software for checkingthe tools, equipments, parts, operators if theyare not finished. It can also remove the errors ofthe production that gives the better outputs.Keywords - Analysis of Variance (ANOVA),Gauge Repeatability and Reproducibility, Part-Operator interaction, Quality improvementI. INTRODUCTIONMost of the quality problems in industriesare solved by identifying and correcting inaccuratedata and inaccurate measurement process. Despite thequality being a major concern for any sector,experts in manufacturing industries, express theiranxiety about the measurement reliability which isused in decision making [1]. The quality of thedata measured is vital for appropriateunderstanding, monitoring or improving a process.If the data is contaminated with errors, it could leadto wrong decisions. The ability to make rightdecisions depends on the availability of ameasurement process, selecting the rightmeasurement process and operating themeasurement process in the correct manner. whenthe data quality is low, the benefits of ameasurement system is also low; likewise when thedata quality is high, the benefit is high too [2]. Ameasurement system is the collection of instrumentsor gages, standards, operations, methods, fixtures,software, personnel, environment andassumptions used to quantify a unit of measure orfix assessment. Because of various reasons, eachelement of measurement system may lead to bringvariation and discreteness into the measurementresults, and affect the measurement accuracy. Inorder to ensure the reliability of measurementsystem, it’s necessary to analyze the measurementsystem so as to determine and control the variationsources. So far research work on the statisticaldiscreteness in measurement system is rarelyimplemented. If the discreteness is great, it willincrease the measurement error.II. ERRORS IN A MEASUREMENTSYSTEMThe measurement system errors can becharacterized based on its location and spread(variance) [2]. Location error can be categorized byaccuracy, bias, stability and linearity. The spreaderror can be categorized as precision, repeatability,and reproducibility. Fig.1 illustrates measurementsystem variations.Fig.1. Measurement System VariationsDefinitions of accuracy and precision are given asbelow:A. Accuracy: It is the difference between the averagevalues of the observed measurement and the actualmeasurement.Accuracy can be divided in to three components:1. Bias: It is the difference between the averageobserved value and the reference value of the samecharacteristic on the same part.2. Linearity: It is the difference in bias values overthe expected operating range of the measurementgauge.3. Stability: It is the variation (differences) in theaverage over extended periods of time using thesame gauge and appraiser to repeatedly measurethe same part.B. Precision: Precision or measurement variation isthe variation due to a measurement system and canbe divided into two components:
  2. 2. Mr.Ravindra Dhawale, Prof.Dr.D.N.Raut / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.726-730727 | P a g e1. Repeatability: It is the ability of measurementsystem to obtain small variability by repeatingthe same measurements on the same sampleunder the same conditions. If the operator getsthe same measurement during repeated trials, theGauge is said to have high repeatability. Poorrepeatability could be due to the device beinginaccurate, the instructions being faulty, theoperator not following the instructions, or a numberof other factors. The fig.2 below shows theschematic of repeatability.Fig. 2. Schematic of repeatability2. Reproducibility: It is the ability ofmeasurement system to return consistentmeasurements while varying the measurementconditions (different operators, different humidity,etc.). If several different operators get the sameresult when measuring the same object, themeasurement device is said to have highreproducibility. Note that this does not mean thedevice is accurate, but simply that the same resultis produced over time. The fig.3 shows theschematic of reproducibility.Fig. 3. Schematic of reproducibilityThe purpose of Gauge R&R study as stated byBurdick.R, Borror.C and Montgomery.D [3] is todetermine the amount of variability in the collecteddata that is due to the measurement system, isolatethe sources of variability in the measurement system,assess whether the measurement system is suitablefor broader application, and quantify the variabilityin the measurement process attributed by theoperators, parts and operators-part interaction.Raffaldi and Kappele (2004) mentioned that, if themeasurement variations can be reduced along withimproved repeatability and reproducibility ratios, itis easier to differentiate the parts between in and outof specification with increased level of confidence foracceptance or rejection of the part [4].Hence, the Gauge R&R can be use as amonitoring tool which provides feedback to improvemeasuring systems and methods. In the view pointof mathematical statistics, the repeatability andreproducibility(R&R) is an important quality indexwhich can reflect measurement capability andprecision, namely the discreteness caused bystatistical random effect. The discreteness must becontrolled within a certain range to ensure thatmeasurement results are reliable. Relation betweenR&R can be shown by fig.4 given below;Fig. 4. Correlation between R&R [6]III. R&R ANALYSIS METHODSGenerally in the Gauge R&R studies,repeatability and reproducibility observationsillustrate how much of the production processvariations belong to the measurement systemdispersion. Various methods could calculate aninstrument’s R&R index and persisting some ofthem are evaluated.1) Range Method: It is used to determine a quickapproximation in measurement systemvariation. But this method could not dividethese variations to the two interprets likerepeatability and reproducibility.2) Average and Range Method: This is acomputational way for representing a systemrepeatability and reproducibilityapproximation. Evaluating the range methodthis method divides variation to theseinterprets.3) Average and Standard Deviation: This methodhas the same features as the earlier method.4) Analysis of Variance (ANOVA) Method: Thismethod could separate the repeatability andreproducibility interprets. These separationsare between variations related to operators andtools.
  3. 3. Mr.Ravindra Dhawale, Prof.Dr.D.N.Raut / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.726-730728 | P a g eSince all these methods, the Average Range andANOVA methods are the most common andimportant. Although all of them containinformation on variation reasons but ANOVAmethod has a more extensive usage. This functionleads to its comparison with Average and Rangemethod. This can also be thought of as betweenoperator variation. In addition, it enables the use ofstatistical hypothesis testing on the results toidentify statistically significant effects. In order todetermine the considerable effects in our gagestudy, we make a use of the examination of thedifference (ANOVA) technique.IV. ANALYSIS OF VARIANCE (ANOVA)Analysis of variance (ANOVA) is astatistical technique estimates the amount ofvariability induced in measurements by themeasurement system itself, and compares it to thetotal variability observed in order to determine theviability of the measurement system. The ANOVAmethod tests the hypotheses of mean biases of theexperiment and also provides estimates of thevariance components attributed to gage andoperator. The assumptions of ANOVA methodinvolved in this analysis as stated by Tsai [5] are asfollows:1. The operator, part interaction and gage (error)effects are additive.2. The operator, part and gage effects arenormally distributed with zero mean andvariances.3. The gage errors must be independent of theoperator, part and interaction effects ofeach other .The total variation is partitioned into operator, part,interaction between operator and part as shown inthe table 1 below.Table 1. ANOVA CalculationsRegarding to the ANOVA table, the belowdefinitions could be presented:A. Sum of squares (SS): The sum of squares iscalculated by squaring the deviations of eachcategory and adding them together. Sum of squaresrepresents how much the data varies in the samples.B. Degree of Freedom (DF): This is the factor thatconsiders number of groups and adjusts how largethe groups could be.C. Mean square (MS): which is the product of thesum of squares divided by the degrees of freedom.The mean square value represents how much acategory varies between its sum of squares anddegrees of freedom. One important mean squarevalue is the error mean square, which shows thevariance within the groups.D. F-statistic. The F-statistic displays thedistribution of values regarding the data and thenull hypothesis. A large F-value generally lends torejecting the null hypothesis and a small F-valuegenerally leads to failing to reject the nullhypothesis.E. P-value (not shown in table): Finally the mostimportant part in the ANOVA table is the P-Valueamount which iss shown by P. Its related factorwould be more important and significant when thisvalue is lower.For example, if it is use a 5 percenttest and the P-value is less than 5 percent, it canreject the null hypothesis.ANOVA Methods divides in to two categories:A. One-Way ANOVA: It has been termed as one-way as there is only one category whose effect hasbeen studied and balanced. Thus the basic idea is totest whether the samples are all alike or not.B. Two-Way ANOVA: It allow for experimentswhere populations are classified in two categoricalfactors. This method remove some of the randomvariability and allow the experimenter to look atthe interactions between factors. It also allowexperiments with a smaller total sample size, astwo things are being studied at once.In a two-way ANOVA with interaction, threehypotheses are tested which are:1. Ho: All parts are similar Vs. H1: All parts are notsimilar2. Ho: All operators are equally good Vs. H1: Alloperators are not equally good3. Ho: Interactions between parts and operatorsare negligible Vs. H1: Interactions between partsand operators are not negligibleThe data collected for ANOVA at random andgraphical analysis could perform on the data,resulting in the output in terms of the Main Effectplot and the Interaction Effect plot. Theexperimentation including the following keys orsteps ;1 Identify factors of interest and a responsevariable.2 Determine appropriate levels for eachexplanatory variable.3 Determine a design structure.4 Randomize the order in which each set ofconditions is run and collect the data.5 Organize the results in order to draw appropriateconclusions.Main Effects Plots are a quick and efficientway to visualize effect size. The grand mean is
  4. 4. Mr.Ravindra Dhawale, Prof.Dr.D.N.Raut / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.726-730729 | P a g eplotted as a horizontal line. The average result isrepresented by dots for each factor level on theMinitab software.V. COMPUTATION OF R&R INDEXTo do the R&R index calculations byANOVA technique several softwares are availablebut the most relevant is Minitab. In order to do theANOVA calculations in Minitab, two ways areoffered: Crossed Gauge R&R and Nested GaugeR&R. Gauge R&R study (Crossed) is to be selectedwhen all operators measure parts from each batchand Gauge R&R study (Nested) is preferredwhenever operators measure unique parts.Minitab provides two methods forassessing repeatability and reproducibility. X-barand R, and ANOVA. The X-bar and R methodbreaks down the overall variation in to threecategories: part-to-part, repeatability andreproducibility. The ANOVA method goes one stepfurther and breaks down reproducibility in to itsoperator, and operator-by-part, components. TheANOVA method is more accurate than the X-barand R method, because it allows the variability ofthe interaction between the operator and the partsto be determined. In the Table No.2 ANOVAcalculations in Minitab are shown as an example.Table 2. ANOVA Computations [7]The above table shows ANOVA outputwith full model and with reduced model made ofthe Gauge R&R Study (Crossed) since eachoperator measures each part. With the ANOVAoutput corresponding to the full model, It is unableto reject the null hypothesis that the operator bypart interaction effect is equal to zero, even at the α= 0.1 level. It is also find that with the reducedmodel, the part component is statisticallysignificant, as one would desire, and it is unable toreject the null hypothesis that the operator effect isequal to zero at 5% level. The variance componentcomputations is shown below in the table no.3which indicates that less than 1% of the totalvariation is due to Gauge R&R.Table 3: Gauge R&RVI. SELECTION CRITERIAThe percentage of the R & R in the totalvariation is an important index that can be used toevaluate whether a measurement system should beaccepted or not. The measurement capability of thesystem is considered enough and acceptable if R &R% is less than 10% and is not enough and shouldbe improved if R & R% is greater than 30% .IffR&R% falls within 10% to 30% , in this case,whether the system is acceptable or not depends onthe practical application.VII. CONCLUSIONThis study is described the measurementsof the Gauge repeatability and reproducibilitydatabase by using the ANOVA analysis in theMINITAB Software. The main purpose of this paperis to study to determine the measurement systemcould produce precise and accurate data for betterresult. Further we are going to study in details usingexperimental and practical section with a particularproduct with interpreting the system with ANOVAon Minitab software.REFERENCES[1] Afrooz Moatari Kazerouni, “Design andAnalysis of Gauge R&R Studies: MakingDecisions Based on ANOVA Method”,World Academy of Science, Engineeringand Technology 52 (2009)[2] AIAG:Automotive Industry ActionGroup(2002), “Measurement SystemsAnalysis, Reference Manual”; third ed.,Detroit,MI[3] Burdick, R. K., Borror, C. M., andMontgomery, D. C. (2005), Design andAnalysis of Gauge R&R Studies: MakingDecisions with Confidence Intervals in
  5. 5. Mr.Ravindra Dhawale, Prof.Dr.D.N.Raut / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.726-730730 | P a g eRandom and Mixed ANOVA Models, SIAM,Philadelphia, PA[4] Smith R.R., McCrary S.W., Callahan R.N.,“Gauge repeatability and reproducibilitystudies and measurement system analysis:A Multi method exploration of the state ofpractice”, Journal of Quality Technology,23, 1, 1-11, (2007)[5] Tsai.P (1988-89). “Variable GaugeRepeatability and Reproducibility StudyUsing the Analysis of variance Method”,Quality Engineering, 1(1), 107-115[6] Lin R., “Strategic Application ofMeasurement System Analysis”, Ford Lio-Ho Motor Company, (2004)[7] Keith M. Bower, Michelle E.Touchton“Evaluating The Usefulness of Data ByGauge Repeatability and Reproducibility”,Minitab Inc. (2009)