【正文】 measure the same 10 parts Note: Do not allow the appraisers to witness each other performing the measurement. The reason is the same as why the unit markings are concealed, TO PREVENT BIAS. 6. Repeat the measurements for all three appraisers, but this time present the samples to each in a random order different from the original measurements. This is to again help reduce bias in the measurements. Analysis Techniques: Variable Gage Analysis …… 10 Parts 3 Appraisers 3 Trials 1. The Average and Range Method: A range control chart is created to determine if the measurement process is stable and consistent. For each appraiser calculate the range of the repeated measurements for the same part. Analysis Techniques: Variable Gage Analysis Range of Repeated Measures0102030401A 2A 3A 4A 5A 1B 2B 3B 4B 5B 1C 2C 3C 4C 5CM i nXXRR a n g e M a x ??Analysis Techniques: Variable Gage Analysis The average range for each operator is then puted. The average of the measurements taken by an operator is calculated. A control chart of ranges is created. The centerline represents the average range for all operators in the study, while the upper and lower control limit constants are based on the number of times each operator measured each part (trials). P ar t s of N o.R??O p e r a to rRP a r tsT r ia lsXXO p e r a to r *??Analysis Techniques: Variable Gage Analysis RDL C LRDUCLRRRR34O pe r a t o r s N o . o f????The centerline and control limits are graphed onto a control chart and the calculated ranges are then plotted on the control chart. The range control chart is examined to determine measurement process stability. If any of the plotted ranges fall outside the control limits the measurement process is not stable, and further analysis should not take place. However, it is mon to have the particular operator remeasure the particular process output again and use that data if it is incontrol. Analysis Techniques: Variable Gage Analysis Repeatability Equipment Variation (.) The constant d2* is based on the number of measurements used to pute the individual ranges(n) or trials, the number of parts in the study, and the number of different conditions under study. The constant K1 is based on the number of times a part was repeatedly measured (trials). The equipment variation is often pared to the process output tolerance or process output variation to determine a percent equipment variation (%EV). 12** KRdREV ??10 0*)(%10 0*)(%mEVP R O CEVLS LU S LEVTO LEV????Analysis Techniques: Variable Gage Analysis Reproducibility Appraiser Variation(.) Xdiff is the difference between the largest average reading by an operator and the smallest average reading by an operator. The constant K2 is based on the number of different conditions analyzed. The appraiser variation is often pared to the process output tolerance or process output variation to determine a percent appraiser variation (%AV). ? ? ?????????ntEVKXAVD iff222* 100*)(%100*)(%mAVP R O CAVLS LU S LAVT O LAV???Analysis Techniques: Variable Gage Analysis Repeatability and Reproducibility( Gage Ramp。R) is pared to the process output tolerance to estimate the precision to tolerance ratio (P/T ratio). This is important to determine if the measurement system can discriminate between good and bad output. The basic interest of studying the measurement process is to determine if the measurement system is capable of measuring a process output characteristic with its own unique variability. This is know as the Percent Ramp。R), and calculated as follows: 22amp。/ L S LU S L RRTP ?Analysis Techniques: Variable Gage Analysis 1 00* amp。%mRRRR??Process or Total Variation: If the process output variation (?m) is not known, the total variation can be estimated using the data in the study. First the part variation is determined: Rp is the range of the part averages, while K3 is a constant based on the number of parts in the study. The total variation (TV) is just the square root of the sum of the squares of Ramp。 PVRRTVm ????Analysis Techniques: Variable Gage Analysis 1. The ANOVA Method: A weakness with the AverageRange method of using the range to determine gage Ramp。 the operator variation is estimated by ?o2。 while repeatability is estimated by ?r2 22222 rpoopt ????? ????Analysis Techniques: Variable Gage Analysis Source SS dF MS F*Part (P)??2...)..()( YYtnPSS ip11)()(??pPSSPMS)()(*POMSPMSF ?Operator (O)? ??2...)..()( YYnpOSSjt11)()(??tOSSOMS)()(*POMSOMSF ?Interaction (PO)? ????2...).....()( YYYYnPOSSjiij(p1)(t1))1)(1()()(???tpPOSSPOMSMSEPOMSF)(*?Repeatability? ? ??2.)( ijijkYYSSEpt(n1))1( ??nptSSEMSETotal? ? ? ??2...)( YYSSTijknpt1Part: tnSnSPMSSp rop 222 )( ??? Operator: pnSnSOMSSo rop 222 )( ???Interaction: nSOPMSS op r22 )( ?? Repeatability: M SESr ?2Analysis Techniques: Variable Gage Analysis Total: 22222 ropop SSSSSt ????The gage Ramp。 AVEVRR ??Total: 22 PVRRTV ??Analysis Techniques: Variable Gage Analysis 1. Acceptability Criteria: The gage repeatability and reproducibility: %Ramp。 P/T ration:% total of tolerance): Less than 10% Outstanding 10% to 20% Capable 20% to 30% Marginally Capable Greater than 30% NOT CAPABLE For the P/P ratio and the P/T ratio, either or both approaches can be taken depending on the intended use of the measurement system and the desires of the cus