# Sample Pages. Edgar Dietrich, Alfred Schulze. Measurement Process Qualification

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1 Sample Pages Edgar Dietrich, Alfred Schlze Measrement Process Qalification Gage Acceptance and Measrement Uncertainty According to Crrent Standards ISBN: For frther information and order see or contact yor bookseller. Carl Hanser Verlag, München

2 8. Principal Standard Uncertainty Components Standard Uncertainty Cased by the Operator Inflence AV Since every inspector handles a measring device differently, the reslting measrement deviation is significant. In order to assess the operator inflence, several operators (e.g. 3) may take several repeat measrements on several objects (e.g. 10), as described in chapter Example The standard ncertainty cased by the appraiser variation AV for the series of measrements in Table 8-4 amonts to AV 0.1µm according to the ANOVA method (see Figre 8-7) Standard Uncertainty Cased by the Test Object OBJ The variation of the test objects (part variation )is another inflencing factor affecting the measrement process. In repeat measrements, form and shape deviations lead to a measrement deviation at the same test object. This deviation mst be considered as standard ncertainty pa.depending on the material/properties of the test objects, the properties might even change over time (elasticity, viscosity, etc.). In order todetermine the inflence of the test objects, an inspector takes several repeat measrements (at least 0) from one test object. The standard deviation calclated from the series of measrements corresponds to the wanted standard measrement ncertainty component pa. Examples 1. If the figre specifies the form deviation (see Figre 8-8) itwill bemonitored dring the prodction process in order that noparts show aform deviation exceeding the one given inthe figre. OBJ can becalclated from the tolerance of the figre TOL = 3µm: OBJ TOL m

3 0 8 Extended Measrement Uncertainty according to ISO or VDA 5 a=3µm Figre 8-8: Standard ncertainty object inflence from tolerance Note This calclation method leads to the greatest standard ncertainty besides the inflence of the object. Particlar measrements on the object (see example and 3)lead toa smaller standard ncertainty.. If an appropriate measring device measres the form deviation, the distance a = 1µm and the standard deviation s g =0. can betaken from the record incase ofthis example (see Figre 8-9). This leads to the standard ncertainty of the object variation a 1 m OBJ m 3 3 s m OBJ g or

4 8. Principal Standard Uncertainty Components 03 Diameter of the averages Figre 8-9: Standard ncertainty object inflence from measred object variation 3. In an air-conditioned room, an inspector takes 0 repeat measrements from a flange heated to 0 C. The vales listed in Table 8-5 lead to the vale chart displayed in Figre ,0 Drchmesser [µm] 7,5 7,0 6,5 6,0 5,5 5,0 x g+1sg x g x g-1sg Vale No. Table 8-5: Repeat measrements Figre 8-10: Actal vale chart The statistical vales R g and s g from this series of measrements are displayed in Figre Figre 8-11: Reslt

5 04 8 Extended Measrement Uncertainty according to ISO or VDA 5 Different formlas may beapplied inorder tocalclate the estimate for OBJ : as per determination method B (normal distribtion) range method where Rg OBJ a b Rg 3.0 OBJ a b 0.76 d R g = a standard deviation method OBJ =s g =0.87 d determined de to MC simlation 8..9 Standard Uncertainty Cased by the Temperatre Inflence T As is generally known, linear measres are extremely temperatre-sensitive depending on the material. The actal vale of a linear measrement vale at standard temperatre differs from the actal vale at a different temperatre. This deviation is cased by the thermal expansion behavior of the material. An aggravating factor isthat the thermal expansion depends on the type of material. The thermal expansion coefficients of different materials are listed in tables, e.g. in VDA 5([70], Table A.3.). In practice, the following sitation often occrs: The thermal expansion coefficient of the material of the gage s linear standard differs from the one of the material of the part to be inspected. If the temperatre deviates from the standard temperatre of 0 C, the linear expansion of the part is different from the one of the gage. This leads to the following problem: Assming that the expansion coefficient of the part s material exceeds the one of the gage s material, the recorded measrement vale for the length of the part is too high. If yo took this measrement at standard temperatre, the actal vale of the part wold besmaller. This deviation is cased by the bias de to different linear expansions. For this reason, the temperatre inflence affecting the measrement process mst be observed. There are some particlar sitations where the temperatre inflence is negligible. 1 st case: The measrement process operates at standard temperatre and the work pieces are heated to standard temperatre. There is no linear expansion cased by the temperatre. nd case: The work piece and the linear standard ofthe gage consist of the same material and have the same temperatre. There is no linear expansion cased by the temperatre. 3 rd case: The different linear expansions ofthe work piece and the gage are corrected by means of calclations for each measrement vale (temperatre compensation). The 1 st case is often not feasible becase of high setp costs and operating expenses. The nd case may beregarded asexceptional sitation. The 3 rd case can hardly be

6 8. Principal Standard Uncertainty Components 05 realized. The temperatre inflence may also be considered as an ncertainty component in the test process in order to solve this problem. Standard Uncertainty Cased bytemperatre Inflences T according to VDA 5 For the maximm temperatre deviation (0 C at most) occrring dring the operation, the limit vale a is determined for the maximm bias to be expected de to different linear expansions ([70]; formla A.3.9): a= L + Rest The standard ncertainty cased by the temperatre inflence is calclated by mltiplying the limit vale a by the distribtion factor b in case of a rectanglar distribtion ([70]; formla A.3.10): T =a b= a 1 3 L Rest bias cased by different linear expansionsofthe work piece and gage ncertainty ofthe expansion coefficients and temperatres The bias cased by differentlinearexpansions following formla ([70]; formla A.3.8): L L Anz;N ( W T W - N T N ) L is calclated approximately sing the L Anz;N vale displayed bythe measring device at the standard temperatre of 0 C W thermalexpansioncoefficientofthe material of the workpiece N thermalexpansioncoefficientofthe material of thegage T W difference between the temperatre of the work piece and the standard temperatre difference between the temperatre ofthe gage and the standard temperatre T N The residal ncertainty res is assessed bymeans of the following approximate formla ([70]; formla A.3.5): Rest L Anz; N T N αn T W αw α N TN α W TW α W α N T N T W ncertainty ofthe thermal expansion coefficient of the work piece s material (standard vale VDA :0.1 W) ncertainty of the thermal expansion coefficient of the gage s material (standard vale VDA :0.1 N) ncertainty ofthe gage s temperatre (standard vale VDA :1K) ncertainty ofthe work piece s material(standard vale VDA :1K) Normally the tables of thermal expansion factors do not inclde ncertainties. Even the ncertainty of the part s and gage s temperatre is hardly assessable in practice. If

7 06 8 Extended Measrement Uncertainty according to ISO or VDA 5 these vales are reqired, VDA 5 specifies the vales that are shown in brackets above. Chapter gives a nmerical example. Standard Uncertainty Case by the Temperatre Inflence T as per ISO [36] VDA 5 also contains this procedre. T T l temperatre difference expansion coefficient mean temperatre dring the measrement standard ncertainty of the expansion coefficient of the measrement system s material measred measre The ncertainty of the thermal expansion coefficient of the gage s material is neglected when the measring machine makes an atomated temperate compensation bt this has to be proved in each individal case. The standard ncertainty cased by temperatre inflences T is calclated from the standard ncertainty cased by changes in the object TD and the standard ncertainty de to changes in the measrement system TA : This leads to = + T TD TA 1 TD = T L and TA = T- 0C α l 3 Standard Uncertainty Cased by the Temperatre Inflence TD of the Differences between the Reference s Thermal Expansion and the one of the Work Piece l Since the temperatre inflence is often hard to assess, the measrement system can be adjsted with the help of a reference part (calibration master) prior to the actal measrement. The temperatre of the reference part may deviate from 0 C, the temperatre it was calibrated at. This deviation mst be considered when determining T. The measrement system is adjsted incorrectly by this vale. Then the measrement object is measred. This object might have another temperatre than the reference part and ths the deviation cased by the temperatre difference mst also be taken into accont. On the basis of the difference (see Figre 8-1), it is possible to determine how the temperatre depends on the standard ncertainty. TD 1 = l 3

8 8. Principal Standard Uncertainty Components 07 Note As long as the adjsted measrement system does not change its temperatre considerably, it is applicable. If this temperatre changes considerably, it mst be readjsted. 1. Component expansion l l l 1 l Component-SM l 1 =l. 0. component T component l 1 =0.08m K K l 1 =5.5m =5.5 m. Setting masterexpansion l =l. 0. SM T SM l =0.08m K -1. 5K l =1.47m =1.47 m 0 C 5 C 30 C 35 C 3. Difference component/sm expansion l 1, = l 1 - l l 1, =5.5 m 1.47 m l 1, =3.78 m Figre 8-1: Determination of the different temperatre expansions between reference part and component Standard Uncertainty Cased by Non-linearity LIN In case of measring devices withot alinear standard, the inflences cased by nonlinearity mst be considered. The evalation of this inflence is identical to the assessment of the bias bt several points within the measring range (several standards or calibratedreference parts) are inspected. The first standard is to lie near the lower specification limit, the second one shold be in the tolerance center and the third one is to be located near the pper tolerance limit. Yo may apply more than three standards, however this reqires agreater effort. Repeat measrementsare takenfrom each standard in order tocalclate the bias Bi i (Bi 1,Bi and Bi 3 ). Bi x gi x mi where i=1,,3. The maximm vale of Bi (Bi max =max {Bi i }) is sed to calclate the standard ncertainty Bi.According to determination method B, this leads to: BI Example 1 = Bimax 3 One inspector measres 3 reference parts x m1 = m x m = m x m3 = m

9 08 8 Extended Measrement Uncertainty according to ISO or VDA 5 Each part is measred 10 times. Table 8-6 shows the reslts. They are displayed in the form of a vale chart (Figre 8-13) and a vale plot (Figre 8-14). The nmerical example istaken from VDA 5([70], Table A.9.3). Table 8-6: Measrement vales linearity 30,008 USL 6 LSL x g USL 30,007 5 Drchmesser [mm] 30,006 30,005 30,004 x g Absolte freqency ,003 LSL Vale No. 0 30,003 30,004 30,005 30,006 30,007 30,008 Drchmesser[mm] Figre 8-13: Actal vale chart Figre 8-14: Actal vale plot The averages of the three measrements on the reference parts are displayed in Table 8-6. They lead to: Bi 1 = µm Bi = µm Bi 3 = µm Bi 1 is the highest bias vale. This vale is sed to calclate LIN according to determination method B. Bi max LIN m Standard Uncertainty Cased by Stability STAB An analysis of the measrement process at an indefinite time does not allow for conclsions abot its behavior in the ftre. For this reason, the measrement stability of a measrement process mst be checked continosly. The intervals of these stability checks depend on the stability of the measrement process and, as described in chapter 3.5.4, mst be inspected first. Then a standard or calibrated reference part is measred once or several times by means of a measring device at the predefined intervals. Three repeat measrements have proved to be most reasonable. Statistical vales sch asr g and s g are calclated from the individal vales orsamples. They help toassess the standard ncertainty Stab.

10 8. Principal Standard Uncertainty Components 09 DeterminationmethodBleads to (assming anormal distribtion): Rg STAB 0.50 If the total standarddeviation is sed as estimate STAB s g Example: Table 8-7 contains the measrement data recorded over a longer period of time. The reference part was always measred three times at each interval and the reslts were displayed inaqality control chart (Figre 8-15). Table 8-7: Measrement vales for stability The series ofmeasrements leads to R g =6µm and s g =1.84 µm according to determination method B (based on the normal distribtion) range method 6 μm STAB μm R 6 m STAB m 3.6 m d Note d from Table , n=3and r=5 and according to determination method A STAB sg.56 m.6 m The estimated vale of the ncertainty according to the range method exceeds the estimate for the ncertainty determined by means of determination method A considerably. The reason for this is that in case of many vales (here: 75 vales) it is more likely that extreme minimm and maximm vales occr and the range is calclated from these vales.

11 10 8 Extended Measrement Uncertainty according to ISO or VDA 5 6,004 6,003 6,00 6,001 x - 99,73%[ n=3; ^1; ^7 ] UCL tar x g x g Drchmesser [mm] 6,000 LCL ,0035 0,0030 0,005 0,000 0,0015 0,0010 0,0005 0,0000 s- 99,73%[ n=3; ^6 ] UCL tar sg sg LCL Figre 8-15: Qality control chart Note This approach incldes the most inflencing factors affecting the measrement process. The recorded series of measrements contains their impacts. Hence, this analysis might be sed in order to evalate the entire measrement process. In addition, only the ncertainty of the standard or the reference part mst be considered. The formla of the combined standard ncertainty of the test process is: = + where MP CAL STAB CAL U = CAL U CAL = extended measrement ncertainty of the reference part specified in the calibration certificate 8.3 Mltiple Consideration of Uncertainty Components Independent of the determination method sed to calclate the standard ncertainty of the single components, these components mst not be assessed more than once. For instance, the eqipment variation U EVR at the reference part may only beconsidered in the evalation ofthe measrement system. In the evalation of the entire measrement process, the standard ncertainty cased by the eqipment variation at the reference part EVR is compared to the one at the object. The maximm vale of these two ncertainties is applied. { } = max, EV EVR EVO The resoltion mst be regarded as aspecial case. On the one hand, the resoltion mst besmaller than 5% of the tolerance (%RE 5% TOL). This reqirement mst be met. On the other hand, it is possible that RE > EVR.Inthis case, RE mst be sed.

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