Measurement Process Capability – Trends and …

1 1 IntroductionSeveral years can be observed attempts to stan-dardise evaluation of the processes (whether pro-duction or Measurement ) Capability . Such attemptshave not been successful yet. Many factors mustbe taken into account processes heterogeneous-ness, changing requirements, wide variety of usedtechnological means. Therefore big production en-terprises (General Motors, Volkswagen, Siemens,Bosch, etc.) have established their shop methodol-ogies for the evaluation of the processes capabili-ty. Capability of Measurement processes is searchedsimilarly to that of production processes most Capability means ability of the processto meet technological or other requirements, tofulfill demands put on Process Capability is determinedby total variation caused by random reasons influ-encing the Process . Variation is caused by variabi-lity of the measured quantity values that are notconnected to the Measurement conditions and mustbe excluded.

2 Therefore it is recommended to per-form preventive measurements. In those texts checkstandards are measured by the measuring equip-ment being of the measured data (caused by themeasurement Process ) as well as the systematicdeviation from the required values is observed du-ring evaluation of the Measurement Process capa-bility. Both such efforts are determined by the tech-nological development of the measuring instru-ments. Due to the technical innovations (incorpo-rating electronics enabling predictive diagnostics,autocalibration, automatic correction of the out-put signal according to the status of the measuringinstrument) variability of the Measurement processis decreasing and the effort for its centering impro-ve Capability of the measuring instruments (see ). Economical savings represent the direct impact possibility for better setting of the productionprocess, decreasing of the number of nonconfor-ming products and resulting the increased produc-tion Indexes of the Measurement processcapabilitySeveral types of the Process Capability indexesexist.

3 They differ one another by calculation meth-od, by properties as well as by intended use. Buttheir design principle is approximately the ratio of prescribed (required) accuracy andreally achieved Process accuracy is always to philosophy of the quality controlapproach, Capability indexes of any Process canbe divided to the Capability indexes of the first andsecond of the first generation Capability index-es (Cp, Cpk) is based on classical philosophy of thestatistical Process control. According to that phi-losophy all Measurement results within requiredtolerance interval are intended to be good. Mea- Measurement Process Capability Trends and ApproachesEva Kurekov AbstractA Measurement control system ensures that measuring equipment and Measurement pro-cesses are fit for their intended use and its important in achieving product quality objec-tives. The following paper introduces theoretical foundations for determination of the mea-suring Process Capability .

4 Defines three Capability indexes in short and recommended useof the Cpm Process control, Measurement Process control, Capability index, Taguchi functionDr. Eva Kurekov , Faculty of Mechanical Engineering,STU, n m. Slobody 17, 812 31 Bratislava, Slovak Republic,e-mail: SCIENCE REVIEW, Volume 1, Number 1, 200143surements outside tolerance interval are consideredto be generation Capability index (Cpm) is ris-ing from new approach to the quality improvement(Taguchi approach ). It is not enough to know thatmeasurements are so called good (being within thetolerance interval) but important is knowledge onhow good they are. Such index enables to deter-mine whether the values of the searched qualityindex approach to the tolerance limits even whenall Measurement results fit within the Process Capability index CpProcess Capability index Cp is a simple relativenumber comparing value of the required processvariability (required tolerance interval) to a natu-ral Process variability (natural tolerance interval).

5 For measuring Process given by expanded un-certainty U, Capability index Cp is calculated as 362 UUC==P(1) kLTLUTLC6 =P(2)where k = 3 to index Cp expresses only the po-tential Process Capability . It does not representthe position of the natural tolerance interval con-sidering the position of the required toleranceinterval. Therefore it does not give a clear an-swer whether measured value of the searchedquality indicator fits within the tolerance inter-val. Another disadvantage of the Cp index is thefact that it does not represent the conformity ofthe Measurement Process average mean Xto acheck standard nominal value Process Capability index CpkCapability index Cpk reacts to deviation of themeasurement Process average mean Xfrom checkstandard nominal value X0 (see Fig. 2). Index iscalculated asFig. 1 Influence of the Measurement Process variability and the effort for its centeringFig. 2. Design of the Cpk indexwhere s is a Process requirements puton Measurement Process are giv-en by tolerance interval T, suchinterval must be defined interval T is defined asa difference between the uppertolerance limit UTL and the low-er tolerance limit LTL.

6 Thatmeans T = UTL LTL. Capabil-ity index Cp is calculated in thiscase asTheoretical Problems of Measurement . E. Kurekov 44 CUUpk= KE3 (3)where UKE is the check standard uncertainty, = Process Capability index CpmPractical experiences showed that demand fora low percentage of check standard measurements(or measurements performed directly on productsor processes) falling outside the tolerance limit Tis not satisfactory. Few information are obtainedon spare measurements. Most interesting informa-tion is about the quality of individual how far are measurements performed on checkstandard from the nominal value X0 of the checkstandard or from tolerance limits Taguchi and T. C. Hsiang designed a lossfunction as a new approach to production processquality improvement in 1985 [5]. This dissipationfunction can be adapted fully to the measurementprocess. Its use is intended for decreasing the vari-ability around the target value of searched qualityindicator, around the check standard nominalvalue (see Fig.)

7 3). Process Capability index Cpm defined by Taguchiis based on equation (1) and is defined as 36pmUkLTLUTLC= =(4)where t is standard deviation around the checkstandard nominal value X0. Taguchi advises to cal-culate this deviation as 202)(XX += .Observing equation (4) one can see that increasingprocess variability s2 causes increasing of the de-nominator and therefore decreasing the Cpm retreating of the Measurement Process ave-rage mean Xfrom check standard nominal valueX0 increasing the denominator value and resultingdecreases the Cpm index General remarks on Capability indexesIf the Process is centered, Measurement processis always capable when Capability index value (Cp,Cpk, respectively Cpm) exceeds 1. Practical recom-mendation considers minimal admissible value1,33. The reason is that certain variability is alwayspresented and Process is never fully in statisticallycontrolled status. Therefore indexes value 1,33is recommended for established processes.

8 Newlyadopted Process should produce Capability inde-xes with values 1,50, extremely precise measu-rements should have value 1,66 [4], [6]. Process standard deviation s is usually unk-nown in practical situations and must be estima-ted. Usually is estimated as = =nii)XX( substitution to expressions (1), (2) and (3)gives just estimation of individual indexes. It is arandom variable with probability distribution. The-refore calculation of the index interval estimationis recommended. This interval contains the truevalue of the index with probability of 1 - a. Obje-ctive proof of Process Capability (index gets valueexceeding 1,33) brings statistical ExampleLets calculate Capability indexes Cp, Cpk, Cpmand compare them. Basic parameters of the mea-surement Process : check standard nominal value isX0 = 20 mm, Measurement Process average meanX = 20 mm; Measurement Process uncertainty U= 0,02 mm, check standard uncertainty UKE can beneglected, standard deviation s = 0,004 mm.

9 Thencapability indexesCp = 0,02/(3 0,004) = 1,666 Cpk = (0,02-0)/(3 0,004) = 1,666 Fig. 3 Taguchi loss functionMEASUREMENT SCIENCE REVIEW, Volume 1, Number 1, 2001 45 Cpm = (0,02)/(3 (0,0042+02)) = 1,666;While X0 = X , Process is centered and all ca-pability indexes are equal. However such status isvery rare in technical parameters change to X0 = 20 mm, X =19,995 mm (other parameters remain the same), Capability indexes get following values:Cp = 0,02 / (3 0,004) = 1,666 (without change)Cpk = (0,02-(20-19,995)/(3 0,004)=1,25 Cpm = (0,02) / (3 (0,0042+(20-19,995)2) = 1,04 Process is not centered in this case while X0 index Cp did not record falling-off the pro-cess Capability by remained variability. Indexes Cpk,Cpm are able to record infrigement of the requiredvalue by untouched Process another parameters change to X0 = 20 mm,X = 19,99125 mm, s = 0,004 mm calculated ca-pability indexes obtain following values:Cp = 0,02/(3 0,004)=1,666 (without change)Cpk = (0,02-(20-19,99125)/(3 0,003)=1,25(without change)Cpm = (0,02)/(3 (0,0032+(20-19,99125)2)=0,72 Capability index Cpk is not able to record chan-ges of the Measurement Process average mean Xtowards tolerance limit in the case of changed stan-dard deviation.))))

10 Only Cpm Capability index registe-red such ConclusionsPresented paper defines in short three most ap-plicable methods for calculation of the measure-ment Process Capability . Shows some deficienciesof the Cp and Cpk Capability indexes that are usedalmost exclusively in nowadays practice. Capabil-ity index Cpm represents best the real measurementprocess [1] Bothe, D., R.: Measuring Process Capability :Techniques and Calculations for Quality andManufacturing Engineers. McGraw Hill,1997[2] Janiga, I., Palen r, R.: O jednom probl me sindexom sp sobilosti procesu. Proceedings ofthe international conference MechaniaclEngineering 98, Bratislava, 1998[3] Kane, V., E.: Proces Capability of Quality Technology, vol. 18, ,1986[4] Palen r, R., Kurekov , E., Halaj, M.: Mea-surement Proces Control. Proceedins of theinternational conference New Trends in Auto-mation of Energetic Processes 98, Zl n, 1998,pp. 360 - 365[5] Taguchi, G.