Strojniški vestnik - Journal of Mechanical Engineering 51(2005)9, 589-599 UDK - UDC 658.562:53.08 Kratki znanstveni prispevek - Short scientific paper (1.03) Analiza merilnih sistemov za zagotavljanje kakovosti v procesu šest sigm Measuring-System Analysis for Quality Assurance in a Six-Sigma Process Mirko Sokovič - Duško Pavletič - Romeo Matkovič Danes na trgu avtomobilske industrije obstaja velika konkurenca zato morajo podjetja stalno izboljševati kakovost izdelkov/storitev če želijo obdržati svoj položaj. Zagotoviti je treba brezhibno delovanje poslovnega sistema ter nenehno izboljšanje vseh procesov v podjetju. Pri tem si pomagajo z različnimi metodami in orodji, tako že znanimi kakor tudi novejšimi, kakršna je metodologija Šest sigm - 6a. V prispevku je razložena študija merilnih sistemov, ki so zelo pomemben element v metodologiji šest sigm. © 2005 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: sistemi merilni, variacije, metodologija šest sigm, študije ponovljivosti in primerljivosti) To maintain market share, suppliers to the automotive industry must be involved in the continuous improvement of their processes. They have to strive to perfect their processes as well as their overall business. Therefore, the search for appropriate improvement methods is ongoing, whether these methods are well known or completely new, e.g., six-sigma (6 a) methods. This paper explains the analysis of measuring systems as a part of a six-sigma methodology. © 2005 Journal of Mechanical Engineering. All rights reserved. (Keywords: measurement systems, variance, six sigma methodology, gauge repeatability and reproducibility (R&R) study) 0 UVOD Dandanes je znano pravilo, da kupci postavljajo zahteve po 0 ppm slabih izdelkov, kar pomeni raven kakovosti 6s. Takšne zahteve se postavljajo predvsem podjetjem, ki so zmožna zagotoviti raven kakovosti med 3s in 4s, in to tudi obvladovati ([1] do [3]). Pri ravni kakovosti 4s je verjetnost dobave izdelkov ustrezne kakovosti okoli 99,9937 % ali 63 ppm. Teoretično se ta verjetnost lahko sprejme kot trenutno zadostna raven kakovosti, vendar če upoštevamo dopusten premik procesa za ± 1,5 s (kar je v praksi najbolj pogosto), prihajamo do podatka, da je verjetnost pojave neustreznih izdelkov 99,379 % ali 6210 ppm. To dejstvo je, z vidika poslovanja podjetja in obstanka na zahtevnem avtomobilskem trgu, nesprejemljivo. V celotnem sistemu uvajanja filozofije 6s je pomemben element obvladovanje in analiza merilnih sistemov. Analiza merilnih sistemov se v osnovi omeji na statistične analize merilnih sistemov, ki se uporabljajo v izdelovalnem procesu. V metodologiji 0 INTRODUCTION In the modern automotive industry, suppliers are expected to achieve a quality level as high as 0 ppm, which means a 6s quality level. At present, many suppliers are capable of providing a quality level of 3s to 4s ([1] to [3]). At a 4s quality level, the probability of delivering defective products is 0.000063 or 63 ppm. Such a level of quality is theoretically acceptable if we suppose that the process is without shifts. With shifts taken into account (based on experience, the process shifts that can usually be expected equal ± 1.5s) the probability of delivering defective products is as high as 0.006210 or 6210 ppm. Such a level of delivered quality in the modern automotive industry is unacceptable. An important element in 6s methodology is measurement system analysis. Measurement system analysis deals with a statistical analysis of measurement systems used in production processes. In the context of 6s methodology, measurement 589 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)9, 589-599 6ü so znane bolj podrobne analize in statistične metode za obvladovanje merilne in preskusne opreme, to so: analiza ponovljivosti in primerljivosti (znana kot R&R), stabilnost, linearnost, razlikovanje itn. [4]. V prispevku bo prikazan vpliv merilnih sistemov na kakovost izdelkov ter celotno raven kakovosti. Če imamo ustrezen proces in gaželimo obvladovati na ravni procesa 6a, ne bo ta nič boljši, če ga merimo z neustrezno merilno opremo ali merilno opremo, za katero ne vemo, kaj se z njo dogaja, oz. v kakšnem tehničnem stanju je. Merilni odstopek, ki iz tega izhaja, je zelo pomemben dejavnik pri merjenju, ker meritev z neustreznim merilom lahko zavaja in vodi k napačnem sklepu o samem procesu ali izdelku. 1 ANALIZA MERILNIH SISTEMOV Matematično analize merilnih sistemov vključujejo razumevanje variacij v procesu merjenja, kakor je prikazano v enačbi: pri čemer pomenijo: s2 - skupna varianca, s2 -varianca procesa in s2 - varianca merjenja. To je edini pravi način razumevanja variacij v procesu. Pri analizi merilnih sistemov se določajo statistične značilnosti: ponovljivost, primerljivost, linearnost, natančnost. Ponovljivost določamo kot spremenljivost zaporednih meritev enega merilca, ki večkrat meri z istim merilnikom isto lastnost na istem merjencu. Primerljivost je mera za spremenljivost zaporednih meritev različnih merilcev, ki merijo isti merjenec ali iste lastnosti z istim merilnikom. Linearnost je je mera zanesljivosti merilnika na celotnem merilnem območju merilnika. Odmik je razlika med povprečjem izmerkov in imensko vrednostjo. Odmik predstavlja tudi mero točnosti. Študija ponovljivosti in primerljivosti (PP) merilnih sistemov se uporablja tako za začetno oceno merilnih sistemov kakor tudi za določanje velikosti vpliva merilnega sistema na vrednost indeksa sposobnosti procesa. 1.1 Viri merilnih odklonov Analiza merilnih sistemov izmeri in razpozna različne vire odklonov, ki lahko vplivajo na merilni sistem. Merilni odklon je skupna variacija system analysis consists of the following: a detailed statistical analysis of a measurement and experimentation equipment or gauge R&R analysis, an analysis of stability, linearity and discrimination [4]. This paper deals with the effect of a measurement system on the quality of products and the overall quality of manufacturing. For processes that are at the 6s quality level, the measurement equipment should also be at a high quality level; otherwise, the measurement error could be high, causing the wrong decision to be made. 1 MEASUREMENT SYSTEM ANALYSIS Measurement system analysis involves understanding measurement process variations, presented by the following equation: where: sT2 - total variance, s2p - process variance, sm2 - measurement variance. Measurement system analysis deals with several statistical characteristics: repeatability, reproducibility, linearity and bias. Repeatability is a measure of the variability of successive measurements of the same part, or the same characteristic, by the same operator, using the same measuring instrument. And reproducibility is a measurement of the variability of successive measurements of the same part, or the same characteristic, by different operators, using the same measuring instrument. Linearity is a measure of an instrument’s accuracy over the range of the instrument’s capability. Bias is the difference between the average of the measurements and the nominal value.Bias also represents a measure of precision. A gauge R&R analysis can be used for a first evaluation of measurement systems, as well as for finding the magnitude of a measurement system’s effect on the process capability index. 1.1 Sources of measurement variation Measurement system analysis quantifies and identifies different sources of variation that might affect the measurement system. Measurement variation is the s sp2 +sm2 590 Sokovič M. - Pavletič D. - Matkovič R. Strojniški vestnik - Journal of Mechanical Engineering 51(2005)9, 589-599 Sl. 1. Blokovni diagram skupne opazovane variance Fig. 1. Total-observed-variation flow chart pri merjenju, ki je lahko posledica variacije na vzorcu total observed variation in measurements, which can be merjenja ali variacije merilnega sistema. Na sliki 1 je attributed to the variation in the item being measured or nazorno prikazano, kako določimo skupno variacijo: to the measurement system itself. Components of the ta je setavljena iz variacije meritve in variacije total observed variation are shown in Figure 1. The total izdelka. Pomembna pri analizi merilnih sistemov je observed variation includes the actual product/process variacija meritve, ki izhaja iz variacije merilnega variation and a measurement variation, which consists sistema (merilni instrument ali naprava, merilec, of the variation due to the operator, the variation due to okolje itn.) the gauge and the variation within the sample. 1.2 Vpliv merilnega odstopka na indeks sposobnosti 1.2 Measurement error effect on the process procesa Cp capability index Cp Merilni odstopek je prikazan na sliki 2 kot Measurement error as a result of actual skupni seštevek odstopka izdelka in odstopka product variation and measurement system variation merilnega sistema. V prvem izrazu je definirana is shown in Figure 2. The first equation defines the natančnost skozi srednjo vrednost meritve. V accuracy, taking into account the average of the drugem izrazu izhaja natančnost kot mera variacije measurements. The second equation defines merilnega sistema. precision as a measure of the measurement system. Na podlagi preizkusov in analiz A measurement error’s effect on the process proizvodnega procesa smo dobili rezultate, ki capability index Cp is determined through pokažejo, kako vpliva odstotek odmika merilnega experiments and the process analysis, Figure 3. For sistema na indeks sposobnosti procesa Cp ([5] in example, 10% of the measurement system error has a [6]). S slike 3 je razvidno, da 10 % napake merilnega negligible effect on the actual process capability index sistema skoraj ne vpliva na dejanski Cp izdelka. Izkaže Cp ([5] and [6]). On the other hand, with an observed se tudi, če pri izračunu sposobnosti za določen process capability index of Cp = 1.3 and a proces dobimo vrednost Cp = 1,3 in upoštevamo 10 % measurement system error equal to 10%, the value odmik merilnega sistema, bo tudi dejanski Cp približno of the actual Cp will be approximately 1.3. If the enak. Vendar, ker je večja napaka merilnega sistema, measurement system error is bigger, the actual je dejanski Cp boljši od opazovanega. To pove, da process capability is then better observed. This moramo zelo dobro poznati merilni sistem, preden means that the measurement system error has to be Analiza merilnih sistemov za zagotavljanje kakovosti - Measuring-System Analysis for Quality Assurance 591 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)9, 589-599 Sl. 2. Skupna varianca in srednja vrednost Fig. 2. Accuracy and precision of the measurement system ugotavljamo izhod določene meritve z ustrezno negotovostjo. V primeru, ko smo analizo Cp delali z merilno napravo, ki ima odstotek merilnega odstopka do 30 %, je iz diagrama razvidno, da ta nima tako pomembnega vpliva na dejanski Cp. Vendar, če uporabljamo merilno napravo z več ko 30 odstotki merilnega odstopka, je zelo pomemben vpliv na dejanski Cp; pri 70 odstotkih merilnega odstopka je opazovani Cp = 1,3, dejanski pa Cp = 3,0. Na podlagi tega bi lahko napačno sklepali, kaj se v resnici dogaja s procesom. Da bi se temu izognili, je treba vedeti, kaj se dogaja z merilnim instrumentom ter kako določiti odstotek merilnega odstopka, da bi lahko ustrezno ukrepali. 1.3 Kakovost merilnih sistemov Merilni sistemi imajo določene karakteristike, po katerih jih razlikujemo glede na kakovost. Kakovost merilnih sistemov lahko delimo na: - razlikovanje, - natančnost, točnost, odmik, - ponovljivost ali test-retest, - učinek odmika vključno s primerljivostjo, - stabilnost (skladnost), - linearnost. Vsaka od naštetih komponent merilnega odstopka vpliva na variacijo rezultatov meritev in known in order to be certain of the measurements results. In general, measurement system errors up to 30% will have little or no effect on the capability index, so the values of the observed and actual capability indices will be almost the same. A measurement system error greater than 30% will have a significant effect on the capability index, e.g., with a measurement system error as high as 70% the observed process capability equals Cp = 1.3, while the actual Cp = 3.0. So, to make a sound decision about process capability, a measurement system should be evaluated and the magnitude of its variability should be taken into account. 1.3 Quality of measurement systems Measurement systems have certain characteristics that define their level of quality. These characteristics are: - discrimination, - accuracy, precision, - repeatability, or test-retest, - bias effect with reproducibility, - stability (consistency), - linearity. Each of the various components of measurement error can contribute to a variation in 592 Sokovič M. - Pavletič D. - Matkovič R. Strojniški vestnik - Journal of Mechanical Engineering 51(2005)9, 589-599 6,0 5,0 4,0 3,0 2,0 1,0 0,0 0% 10% 20% 30% 40% 50% 60% 70% 0,5 0,6 0,7 0,8 0,9 1,0 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2,0 Opazovani Cp / Observed Cp Sl. 3. Vpliv odstotka merilnega odstopka na indeks sposobnosti procesa Cp Fig. 3. Measurement error effect on the process capability index Cp provzroča napačno sklepanje o kakovosti merjenca. 2 ŠTUDIJA PP ZA MERILNE SISTEME Z ODČITAVANJEM VREDNOSTI Skozi predhodno razlago smo prišli do analize merilnih sistemov, ki podaja sklepno ugotovitev, kaj se dogaja z merilnim sistemom kot celoto, vključno z merilcem. Merilni sistemi z odčitavanjem vrednosti so merilne naprave, ki imajo možnost merjenja z odčitavanjem določene mere (sl. 4) [7]. the given value causing the wrong decision to be made. 2 GAUGE R&R OF A MEASUREMENT SYSTEM FOR QUANTITATIVE DATA So far we have a measurement system analysis that takes into account all the elements of a measurement system, including operators. Measurement systems for quantitative data enable readings of a measured characteristic numerical value, Figure 4 [7]. Sl. 4. Merilna naprava za merjenje višine Fig. 4. Hight measurement gauge Analiza merilnih sistemov za zagotavljanje kakovosti - Measuring-System Analysis for Quality Assurance 593 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)9, 589-599 Pri šudiji posameznega merilnega sistema izhajamo iz naslednjih postavk [8]: - merita dva ali trije merilci, - običajno se meri 10 vzorcev, - vsak vzorec se izmeri 2 ali 3 krat. Študijo PP (ponovljivosti in primerljivosti) merilnega sistema uporabljamo, ko želimo ugotoviti ([6] in [9]): - ali ima merilni sistem ustrezno razlikovanje; - izvore variacij v merilnem sistemu; - relativno velikost za vsak izvor variacije; - ali je potrebno kakršnokoli ukrepanje, če je, kaj bi priporočili; - kako bo skupina razumela ali bo merilni sistem ustrezen tudi v prihodnosti? Vključno s ponovljivostjo teh rezultatov v prihodnosti in potrebami raziskovanja. Razume se, da smo v našo analizo vključili naslednje izvore variacij: - meritev, - vzorec nasproti vzorcu, - merilec nasproti merilcu. 2.1 Postopek za izvajanje študije PP 1) Umeri merilo ali zagotovi, da je še umerjeno. 2) Zagotovi, da prvi merilec izvaja meritve skozi vse vzorce z naključnim izborom. 3) Zagotovi, da tudi drugi merilec izvaja meritve skozi vse vzorce z naključnim izborom. 4) Nadaljuj, dokler se ne zvrstijo vsi merilci, ki sodelujejo v raziskavi. 5) Ponavljaj korake 2 do 4 za vsa potrebna števila meritev. 6) Uporabi obrazec za ugotavljanje statističnih podatkov študij PP: a) ponovljivost, b) primerljivost, c) standardno odstopanje za obe prej omenjeni karakteristiki, d) odstotek PP, e) odstotek tolerančne analize, 7) Analiziraj rezultate in ukrepaj, če je potrebno. Število merilcev: - Če so v postopku prisotni različni merilci oz. operaterji, izberi od 2 do 4 merilca z metodo naključne izbire. In general, gauge R&R is conducted in the following conditions [8]: - the measurement is conducted by two or three operators, - there are 10 units to measure, - each unit is measured two or three times by each operator. R&R analysis is used when the following are of special interest ([6] and [9]): - Does the measurement system have adequate discrimination? - What are the sources of variation in the measurement system? - What is the relative magnitude of each of the sources of variation? - Is there any action required, and what can be recommended? - How will the team understand whether the measurement system will be adequate in the future, including the repeatability of these results in the future and developing needs? The following sources of variation should be included in the analysis: - measurement, - part-to-part, - operator-to-operator. 2.1 Procedure for performing an R&R study 1) Calibrate the gauge, or ensure that it has already been calibrated. 2) Ensure that the first operator measures all the units once in a random order. 3) Ensure that the second operator measures all the units once in random order. 4) Continue until all the operators have measured all the units once. 5) Repeat steps from 2 to 4 for the required number of trials. 6) Use the form provided to determine the statistics of the R&R study: a) repeatability, b) reproducibility, c) standard deviation for each of the above, d) % R&R, e) % tolerance analysis. 7) Analyze the results and determine follow-up action, if any. Number of operators: - If the process uses multiple operators, chose 2–4 at random. 594 Sokovič M. - Pavletič D. - Matkovič R. Strojniški vestnik - Journal of Mechanical Engineering 51(2005)9, 589-599 - Če je v postopku samo en operater oz. merilec ali pa nobeden, opravi študijo brez učinka merilca (zanemari primerljivost). Število vzorcev: - Izberi zadostno število vzorcev, in to tako, da je: (število vzorcev) x (število merilcev) > 15. 2.2 Primer študije PP za merilni trn Marposs 4>35,31 mm z metodo ANOVA Poznani sta dve metodi analize PP, in sicer analiza PP po metodi ANOVA (analiza variance) ter po metodi X - R. Razlika med njimi je ta, da se metoda X- R več uporablja, ker kalkulacija izhaja iz kontrolnih kart in je bolj preprosta. Vendar je metoda ANOVA bolj natančna, ker: - metoda ANOVA računa mogoče povezave med merilci in vzorci, metoda X - R pa ne; - komponente variacije, uporabljene pri metodi ANOVA, so bolje ocenjene od razpona uporabljenega pri metodi X- R. V nadaljevanju prispevka bomo podali primer študije PP, ki je bila narejena za proces izdelave okrova turbo kompresorja. Analizo smo naredili s programom MINITABTM, ki je prirejen za metodo ANOVA. V proizvodnem procesu se za merjenje premerov okrova turbo kompresorja uporablja merilni trn Marposs, ki je sestavni del naprave Marposs E9066 in je prikazan na sliki 5. V danem primeru bo podana analiza PP za merjenje premera^5,31 ± 0,08 mm (sl. 6) ([6] in [9]). - If the process uses only one operator, or no operators, perform study without operator effects (ignore reproducibility effect). Number of samples: - Select enough samples so that: (number of samples) x (number of operators) > 15. 2.2 Example of gauge R&R with ANOVA method for a Marposs ^35.31 mm measurement gauge Two gauge R&R methods are known, the ANOVA and the X - R method. TheX - R method is simpler and is used when the gauge R&R analysis is based on control charts. The ANOVA method is more precise because: - The ANOVA calculates possible interactions between operators and samples, while the X - R method does not. - Components of variation used by the ANOVA are better evaluated in comparison with the range used by the X- R method. Later in the paper there will be an example of a gauge R&R analysis in the production of a turbo-charger housing. An analysis will be made with the ANOVA method using the MINITABTM statistical analysis package. The Marposs measurement gauge, which is part of the Marposs E9066 measurement system, is used to measure the diameter of the turbo-charger housing, Figure 5. In the presented example, a gauge R&R analysis for a ^35.31 ± 0.08 mm measurement will be shown (Fig. 6) ([6] and [9]). Sl. 5. Merilna naprava Marposs in merjenje premera 35,31+0,08 mm Fig. 5. Marposs measurement gauge and measurement of diamater 35.31 ± 0.08 mm 4,35,31+0,08 Sl. 6. Pomembna kota na okrovu turbo kompresorja (tip 716108-2-20) Fig. 6. Important dimension on the housing of turbocharger 716108-2-20 Analiza merilnih sistemov za zagotavljanje kakovosti - Measuring-System Analysis for Quality Assurance 595 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)9, 589-599 E I E 5 <ü "S E E i*. ¦— o. a 35,365 - 35,355 35,345 ^V*! ys !-%- Vzorec / Number of parts -,v ^ /- E i E 5 <ü "S L E o N « 11° (o m ,003 ,002 ,001 0,000 PP] Pon'ov/ Reprod / Vz-proti-vz / Gage R&R Repeat Reprod Part-to-Part R karta po merilcu / R Chart by Operator Merilec I/Operetor 1 Merilec 2/Operator 2 Merilec 3/Operator 3 7^M / — ! UCL=0.003467 % Tolerance / %Tolerance 35,345 Vzorec / Number of parts mm 35,365 — 2 3 4 5 6 7 8 Po merilcu / By Operator tf R=0.001347 SKM/ LCL=0 X karta po merilcu / Xbar Chart by Operator mm 35,365 ¦K ™ I | 35,345 35,345 Merilec/Operator ^ 2 3 Merilec*Vzorec medsebojno / Operator' Number of Parts Interaction Merilec / Operator ^ mm ZKM/ -5; 35,365 UCL=35,36 O 35,345 —_ Vzorec / Number of parts Sl. 9. Analiza PP Fig. 9. Gauge R&R analysis Analiza merilnih sistemov za zagotavljanje kakovosti - Measuring-System Analysis for Quality Assurance 597 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)9, 589-599 3 SKLEPI 3 CONCLUSIONS Merilni sistemi so v postopku zagotavljanja kakovosti zelo pomemben dejavnik. Če želimo izboljšati sistem kakovosti in dosegati zelo visoko raven zaupanja kupca v naše izdelke/storitve, moramo zelo resno jemati merilne sisteme kot komponente procesa, ki vplivajo neposredno na kakovost izdelka/storitve. Če ne vemo zagotovo, kaj se dogaja z merilno opremo in v kakšni meri ji lahko zaupamo, tudi ne vemo zanesljivo, kaj se dogaja s kakovostjo procesa. Probleme v proizvodnem procesu moramo reševati sistematično in zagotavljati najboljši mogoči način reševanja z ustrezno analizo merilnih sistemov. Obstajajo različne metode v različnih primerih: od analize ponovljivosti, primerljivosti do zelo zapletene analize PP, ki skozi celotno analizo variacij sistema pokaže, kaj se s sistemom dogaja in kako moramo ukrepati, če je z njim kaj narobe. Merilni sistem je kompleksen sistem, ki vključuje množico elementov, od merilnih naprav, človeka do vplivov okolja in podobno. Zato je zelo pomembno imeti pod nadzorom vse elemente, ki jih je mogoče obvladovati. Measurement systems are a very important element in the quality-assurance process. To improve process quality and achieve a high level of customer confidence in products and services, measurement systems, which directly influence the products’ quality, should become important components in the production processes. If the measurement system error is unknown, the exact process quality level cannot be determined for sure. Problems in the production process should be solved systematically using the best available process-improvement methods and an adequate measurement system analysis. For a measurement system evaluation several methods are used, from simple repeatability and reproducibility analyses to complex gauge R&R analysis, which, through an in-depth analysis of measurement system variation, shows what is wrong with the measurement system and what action should be taken to correct existing problems. A measurement system is a complex system that includes measurement gauges, but also the operators, the environment, etc. To ensure sound measurements and confidence in the measurement results, all the elements of the measurement system should be under control. 4 LITERATURA 4 REFERENCES [1] Breyfogle III, F. W., et al. (2001) Managing Six Sigma, John Wiley & Sons, Inc., New York. [2] Pavletič, D., S. Fakin, M. Sokovič (2004) Six Sigma in process design, J. of Mech. Eng., Vol. 50, No 3. [3] Sokovič, M., D. Pavletič, S. Fakin (2005) Application of Six Sigma methodology for process design, J. of Mater. Process. Techn., Vol. 162-163, pp. 777-783. [4] Breyfogle III, F W. (1999) Implementing 6s, John Wiley & Sons, Inc., New York. [5] N.N. (2000) Black belt training material, Honeywel Company, Manchester. [6] Matkovič, R., M. Sokovič (2001) Measuring system analysis for quality assurance in 6s process, Diploma thesis No. S-555, Faculty of Mechanical Engineering, University of Ljubljana (in Slovene) [7] N.N. (1999-2001) Sistemska navodila podjetja Cimos, PS Cimos. [8] N.N. (1999-2001) Delovna navodila PS CIMOS - PC BUZET, PS Cimos. [9] N.N. (1995) Measuring systems analysis - MSA - reference manual, Ford/General Motors/Chrysler 598 Sokovič M. - Pavletič D. - Matkovič R. Strojniški vestnik - Journal of Mechanical Engineering 51(2005)9, 589-599 Naslovi avtorjev: prof.dr. Mirko Sokovič Univerza v Ljubljani Fakulteta za strojništvo Aškerčeva 6 1000 Ljubljana mirko.sokovic@fs.uni-lj.si doc.dr. Duško Pavletič Univerza na Reki Tehnična fakulteta Vukovarska 58 HR-51000 Rijeka, Hrvaška dusko.pavletic@riteh.hr Authors’ Addresses: Prof.Dr. Mirko Sokovič University of Ljubljana Faculty of Mechanical Eng. Aškerčeva 6 SI-1000 Ljubljana, Slovenia mirko.sokovic@fs.uni-lj.si DocDr. Duško Pavletič University of Rijeka Faculty of Engineering Vukovarska 58 HR-51000 Rijeka, Croatia dusko.pavletic@riteh.hr Romeo Matkovič PC Cimos Buzet Most 24 HR-52420 Buzet, Hrvaška Romeo Matkovič PC Cimos Buzet Most 24 HR-52420 Buzet, Croatia Prejeto: Received: 13.4.2005 Sprejeto: Accepted: 25.5.2005 Odprto za diskusijo: 1 leto Open for discussion: 1 year Analiza merilnih sistemov za zagotavljanje kakovosti - Measuring-System Analysis for Quality Assurance 599