Brigid Mullany, Ph.D University of North Carolina, Charlotte


 Imogen Day
 2 years ago
 Views:
Transcription
1 Evaluaton And Comparson Of The Dfferent Standards Used To Defne The Postonal Accuracy And Repeatablty Of Numercally Controlled Machnng Center Axes Brgd Mullany, Ph.D Unversty of North Carolna, Charlotte October 2007
2 Table of Contents Page Introducton 3 Standards relevant to the study 4 ISO 2302: ISO 2302: ISO 2302: VDI / DQG ANSI B JIS Parameters to be reported. 12 Identcal and smlar parameters ISO 2302:2006 & VDI / DQG ISO 2302:2006 & ISO 2302: ISO 2302:1988 & VDI / DQG VDI / DQG 3441 & JIS B ISO 2302:2006 & JIS B Numercal analyss Appendx A UNC Charlotte Mullany 2
3 Introducton Machne tool postonal accuracy and repeatablty are core descrptors of a machne tool and ndcate the machne s expected level of performance. Whle a number of standards and gudelnes exst outlnng how to evaluate machne tool postonal accuracy and repeatablty, they dffer n ther analyss procedures and n key parameter defnton. As a result the values reported for postonal accuracy and repeatablty for any one machne can vary dependng on whch standard was used. As all standards are equally vald t s benefcal to be aware how the standards dffer from each other and how the dfferent calculated values compare to each other. Ths document ams to do ths. The ams of ths report can be explctly broken down nto the followng: o Lst commonly used nternatonal or natonal standards that are related to machne tool postonal accuracy and repeatablty. o Determne whch standards are equvalent to each other and subsequently solate the core standards. o Compare the key parameters from each standard and dentfy dentcal and conceptually smlar parameters. o Perform numercal analyss to evaluate how smlar parameters compare to each other under dfferent condtons and determne f converson factors exst allowng parameters from dfferent standards to be drectly compared. Credt to revewers: The author would lke to thank the followng for ther valuable comments and nsghts: o Alkan Donmez, NIST, MD. o Wolfgang Knapp, Engneerng Offce Dr. W. Knapp, Swtzerland. o Scott Smth and Bob Hocken, UNC Charlotte, NC. UNC Charlotte Mullany 3
4 Standards relevant to the study The core standards ncluded n ths study are lsted n table 1. These standards prmarly deal wth determnng the postonal repeatablty and accuracy of a machne tool. Standards specfcally focused on the geometrc accuracy of the machne tool are not ncluded n the study. Table 1: Core standards under nvestgaton. Name Ttle Comment ISO 2302:2006 Determnaton of accuracy and repeatablty of postonng numercally controlled machne axes ISO 2302:1997 Determnaton of accuracy and repeatablty of postonng numercally controlled machne axes ISO 2302:1988 Determnaton of accuracy and repeatablty of postonng of numercally controlled machne tools England BS ISO (1999) German VDI/DGQ 3441 DIN ISO (2000) USA ASME B5.54(2005) Chna GB/T (2000) Determnaton of accuracy and repeatablty of postonng numercally controlled machne axes Statstcal testng of the operatonal and postonal accuracy of machne tools Determnaton of accuracy and repeatablty of postonng numercally controlled machne axes Methods for performance evaluaton of computer numercally controlled machnng centers Determnaton of accuracy and repeatablty of postonng numercally controlled machne axes Japan JIS B 6192:1999 Determnaton of accuracy and repeatablty of postonng numercally controlled machne axes JIS B Test code for performance and accuracy of numercally controlled machne tools Ths replaced the ISO 2302:1997 verson of the standard. Detals of the changes are gven later. Ths was replaced by ISO 2302:1997. Dfferences between the two standards are gven later. Equvalent to ISO 2302:1997 Equvalent to ISO 2302:1997 Data analyss for machne tool accuracy s equvalent to ISO 2302:1997 Equvalent to ISO 2302:1997 Equvalent to ISO 2302:1997 Ths standard s wthdrawn however detals on the analyss technques wll be gven. UNC Charlotte Mullany 4
5 Key Standards The followng standards wll be looked at n detal; o ISO 2302:2006 o ISO 2302:1997 o ISO 2302:1988 o VDI/DQG 3441 o ANSI B5:54 o JIS B Whle detals of each standard are not gven, specfcs wth respect to the hstory of the standard are provded,.e. whch standard t replaced, whch standards replaced t, whch standards are based on the standard etc. NOTE: Ths document s not a substtute for readng the ndvdual standards. The actual standards should be used when undertakng any of the outlned tests or n determnng the postonal accuracy of a machne tool. UNC Charlotte Mullany 5
6 ISO 2302: 2006 Test Code for Machne tools  Part 2: Determnaton of accuracy and repeatablty of postonng numercally controlled axes. Older Versons : o ISO 2302:1997 o ISO 2302:1988 Other nternatonal standards based on ISO 2302:2006 standard  NONE Scope of the standard: To specfy the methods of testng and evaluatng the accuracy and repeatablty of postonng of NC machne tools and components by drect measurement of ndependent axes on the machne. Used for type testng, acceptance testng, comparson testng, perodc verfcaton, machne compensaton. Dfferences between ISO 2302:2006 and ISO 2302:1997: o A measurement uncertanty statement s added to the 2006 verson and now the measurement uncertanty should be ncluded when reportng the key parameters. An annex s provded wth the standard detalng how to determne the measurement uncertanty. UNC Charlotte Mullany 6
7 ISO 2302: 1997 Test Code for Machne tools  Part 2: Determnaton of accuracy and repeatablty of postonng numercally controlled axes. Older Versons : o ISO 2302:1988 Other nternatonal standards based on the ISO 2302:1997 standard o GB/T (2000) (Chna) Test code for machne toolspart 2: Determnaton of accuracy and repeatablty of postonng numercally controlled axes. Equvalent to ISO 2302:1997 o JIS B 6192 (1999) (Japan) Test code for machne toolspart 2: Determnaton of accuracy and repeatablty of postonng numercally controlled axes. Equvalent to ISO 2302:1997 o BS ISO (1999) (England) Test code for machne toolspart 2: Determnaton of accuracy and repeatablty of postonng numercally controlled axes. Equvalent to ISO 2302:1997 o DIN ISO (2000) (Germany) Test code for machne toolspart 2: Determnaton of accuracy and repeatablty of postonng numercally controlled axes. Equvalent to ISO 2302:1997 Scope of the standard: To specfy the methods of testng and evaluatng the accuracy and repeatablty of postonng of NC machne tools and components by drect measurement of ndependent axes on the machne. Used for type testng, acceptance testng, comparson testng, perodc verfcaton, machne compensaton. Dfferences between ISO 2302:1997 and ISO 2302:1988: 1. The 1997 verson changed some of the termnology. The term standard uncertanty s used nstead of standard devaton to avod makng assumptons wth respect to the dstrbuton of the measured data. 2. The 1997 verson uses an expanded uncertanty coverage factor of two (k=2) nstead of three (k=3). 3. Calculaton of the bdrectonal systematc postonal devaton of an axs, E, s added to correlate to the Accuracy term n the ANSI B5.54 (1992). 4. Calculaton of the range of the bdrectonal postonal devaton range, M s added and t s equvalent to the Postonal Devaton term, P a, as descrbed n the VDI/DGQ UNC Charlotte Mullany 7
8 ISO 2302:1988 Acceptance Code for Machne tools  Part 2: Determnaton of accuracy and repeatablty of postonng numercally controlled machne tools. Older Versons : NONE Other nternatonal standards based on the ISO 2302:1988 standard: NONE Scope of the standard: To specfy the methods of testng and evaluatng the accuracy and repeatablty of postonng of NC machne tools and components by drect measurement of ndependent axes on the machne. UNC Charlotte Mullany 8
9 VDI/ DQG 3441 Statstcal testng of the operatonal and postonal accuracy of machne tools Translated from the German ssue 3/1977 Older Versons: NONE Other nternatonal standards based on the VDI/DGQ 3441 standard NONE Scope of the gudelnes: The gudelne descrbes how statstcal methods can be appled to machnes that are and are not ted to a partcular part to determne operatonal or postonal accuracy of a machne. The standard s n two sectons, one secton focuses on operatonal uncertanty, ths s measured by determnng how accurately a machne can manufacture a defned workpece. The second secton detals how the postonal accuracy of the machne can be determned from drect length measurement,.e. under unloaded condtons. It s ths latter secton of the gudelnes that s referred to n ths document. UNC Charlotte Mullany 9
10 ASME B Methods for performance evaluaton of computer numercally controlled machnng centers Older Versons: ASME B Other nternatonal standards based on ASME B standard  NONE Other standards that reference the ASME B standard  NONE Dfferences between ASME B and ASME B : 1. Changes were made to brng consstency to termnology used between ths standard and ASME B methods for performance evaluaton of computer numercally controlled lathes and turnng machnes. Scope of the standard: Ths standard s very comprehensve and ncludes methodologes to specfy machne tool geometrc parameters, postonal accuracy and repeatablty. It also ncludes nformaton wth respect to envronmental condtons and thermal uncertantes. The secton on postonal accuracy and repeatablty s very smlar n approach to ISO 2302:2006 however t ncludes a secton on perodc error (short wavelength perodc errors). UNC Charlotte Mullany 10
11 JIS B Test code for performance and accuracy of numercally controlled machne tools Ths standard was wthdrawn n 1987 Accordng to the JSA webpage t was replaced by JIS B The JIS B 6201 was frst mplemented n Ths standard has been revsed and reaffrmed several tmes n the past. The last revson was n 1993 and ths has been reaffrmed n 1998 and The JIS B standard does not explctly outlne tests to measure the machne tool postonal accuracy and repeatablty, perhaps earler versons dd. The JIS B whch was establshed n 1999 does however outlne how to measure machne tool postonal accuracy and the analyss secton of the standard s as per 1SO 2302:1997. Scope of the standard: The standard outlnes a method for determnng the postonal accuracy and repeatablty of a machne tool UNC Charlotte Mullany 11
12 Key Parameters recommended for reportng by the dfferent standards. Table 2: Parameters recommended for reportng. ISO 2302: 2006 A 06 & uncertanty (k=2) A 06 and A 06 E 06 & uncertanty (k=2) E 06 and E 06 M 06 & uncertanty (k=2) R 06 & uncertanty (k=2) R 06 and R 06 B 06 & uncertanty (k=2) ISO 2302: 1997 ISO 2302: 1988 VDI/DQG 3441 ANSI B JIS B A 06 A 88 P a Postonng A 06 accuracy test (P s ) A 06 and R 88 P smax A 06 and Repeatablty A 06 A 06 test (R s ) E 06 R 88 and P E s 06 Lost moton R 88 test (U s ) E 06 and B 88 U max E 06 and E 06 Least nput E 06 ncrement test M 06 U M 06 R 06 R 06 R 06 and R 06 R 06 and R 06 B 06 B 06 B 06 B 06 B 06 P 06 Appendx A gves a full lst of the nomenclature for each of the standards. Note 1: Whle the same parameter notaton s used n ISO 2302:1988, 1997 and 2006 the actual mathematcal equatons may vary therefore a two dgt subscrpt (.e. 06 or 88 ) s used to denote the year of the standard beng referred to. The equatons and notaton used n ISO 2302:1997 and ASME B54.5 are dentcal to those used n ISO 2302:2006 and therefore the 06 subscrpt s used when referrng to ISO 2302:1997 and ASME B54.4 parameters. Note 2: As no offcal abbrevatons are gven n the JIS 6330 Standard for the dfferent parameters, names have been assgned n ths report,.e. P s, U s and R s. UNC Charlotte Mullany 12
13 Comparson between the ISO 2302:2006 and the VDI/DQG 3441 Table 3: Identcal and smlar parameters n the ISO 2302:2006 and VDI/DQG ISO 2302:2006 VDI/DQG 3441 Identcal or smlar Mean bdrectonal postonal devaton of an axs, M 06 M 06 = max x [ ] mn[ ] Mean Reversal value of an axs B 06 B 06 Where; B 1 m = B m = 1 = x x x Reversal value of an axs B 06 = max [ ] B Bdrectonal accuracy of postonng of an axs, A 06 A 06 = max mn x [ x + 2s ;x + 2s ] [ 2 2 ] s ;x Undrectonal repeatablty of postonng of an axs, R 06 or R 06 R 06 R 06 = max = max [ 4s ] [ 4s ] s Postonal devaton, P a = x max x mn P a Mean Reversal Error, U 1 m U = U m = 1 Where; U = x x Max reversal error at a poston U max = max[ U ] Postonal Uncertanty, P 1 P = x + ( U + P s ) 2 Max 1 x 2 ( U + ) P s Mn Max Postonal Scatter, P s max P s max = P s max = max[6s ] Repeatablty of an Axs, R 06 No equvalent R max[ R ] 06 = parameter See Appendx A for detals on x, x, s and s Identcal  The dfference between the maxmum and mnmum averaged postonal devaton over the forward and reverse drectons. Smlar  Average reversal error. Due to slght dfferences n the equatons the values may vary. Ths s especally true f the averaged forward and reverse postonal errors lnes ntersect each other as n fgure 4. Identcal  Maxmum reversal error. Smlar  Maxmum range of values based on mean postonal errors, correspondng standard devatons and reversal errors along the axs. As the postonal uncertanty, P uses three tmes the standard devaton n ts calculaton and bdrectonal accuracy, A 06, only uses twce the standard devaton, P s expected to be bgger than A. Smlar  Indcates the maxmum spread of data ponts that occurred at an ndvdual target poston. P smax wll always be larger than ether R 06 or R 06 as P smax uses three tmes the standard devaton n ts calculaton whle R 06, only uses twce the standard devaton, Note that P smax s related to the averaged devaton over the forward and reverse drectons. If B 06 and U are zero then 2/3P smax should be smlar to R 06. Otherwse t s expected that U Ps max should be smlar to R 06. UNC Charlotte Mullany 13
14 Comparson between ISO 2302:2006 and ISO 2302:1988 Table 4: Identcal and smlar parameters n the ISO 2302:2006 and ISO 2302:1988. ISO 2302:2006 ISO 2302:1988 Comparson Mean Reversal value of an axs B 06 1 m B = B m = 1 Bdrectonal accuracy of postonng of an axs, A 06 A = max 06 mn x [ x + 2s ;x + 2s ] [ 2 2 ] s ;x Undrectonal repeatablty of postonng of an axs, R 06 or R 06 R = max 06 R = max 06 [ 4s ] [ 4s ] Repeatablty of postonng of an axs, R 06 [ ] R max R 06 = Where; max [ 2s + 2s + B ; R ; R ] R = s Mean Reversal value of an axs B 88 1 n B = B n = 1 Bdrectonal accuracy of postonng of an axs, A 88 A = max 88 mn [ x + 3s ;x + 3s ] [ x 3s ;x 3s ] Undrectonal repeatablty of postonng of an axs, R 88 or R 88 R = 6s ] 88 R = max[ 6s ] 88 Repeatablty of postonng of an axs, R 88 [ ] R max R 88 = Where; R max [ 3s + 3s + B ; R ; R ] = Identcal  Averaged reversal error Smlar  but ISO 2302:1988 uses three standard devatons n ts calculatons whle the 2006 verson uses two standard devatons. A 88 s expected to be greater than A 06 Smlar drect conversons between the two standards exst, R 06 = 2/3 R 88 R 06 = 2/3 R 88 Lkewse R 88 = 3/2 R 06 R 88 = 3/2 R 06 Smlar Based on same concept, however ISO 2302:1988 uses three standard devatons n ts calculaton as opposed to two standard devatons used n ISO 2302:2006. R 88 wll be bgger than R 06. See Appendx A for detals on x, x, s and s UNC Charlotte Mullany 14
15 Comparson between ISO 2302:1988 and VDI/DQG 3441 Table 5: Identcal and smlar parameters n the ISO 2302:1988 and VDI/DQG ISO 2302:1988 VDI/DQG 3441 Identcal or smlar Mean Reversal value of an axs B 88 B 88 Where; 1 n = B n = 1 B = x x Bdrectonal accuracy of postonng of an axs, A 88 A 88 = max mn [ x + 3s ;x + 3s ] [ x 3s ;x 3s ] Undrectonal repeatablty of postonng of an axs, R 88 or R 88 R 88 R 88 = max = max [ 6s ] [ 6s ] Repeatablty of postonng of an axs, R 88 [ ] R max R 88 = Where; R [ 3s + 3s + B ; R ; R ] = max Mean Reversal Error, U 1 m U = U m = 1 Where; U = x x Postonal Uncertanty, P 1 P = x + ( U + P s ) 2 1 x ( U + P s ) 2 Max Mn Max Postonal Scatter, P s max P s max = P s max = max[6s ] No equvalent parameter Smlar  Average reversal error. Due to slght dfferences n the equatons the values may vary. Ths s especally true f the averaged forward and reverse postonal errors lnes ntersect each other as n fgure 4. Smlar  Maxmum range of values based on mean postonal error and correspondng standard devatons about each target poston. As the postonal uncertanty, P uses the averaged standard devaton over the forward and reverse drectons t s expected to be slghtly smaller than the bdrectonal accuracy, A 88. Smlar  Indcates the maxmum spread of data ponts that occurred at an ndvdual target poston. As P smax s based on the averaged standard devaton t s expected to be slghtly smaller than R 88 or R 88 If B 88 and U are zero then P smax should be smlar to R 88. Otherwse t s expected that U + P s max should be smlar to R 88 See Appendx A for detals on x, x, s and s UNC Charlotte Mullany 15
16 Comparson between VDI/DQG 3441 and JIS B Table 6: Identcal and smlar parameters n the VDI/DQG 3441 and JIS VDI/DQG 3441 JIS B Identcal or smlar Max reversal error at a poston U = max[ U max Max Postonal Scatter, P s max P s max = P s max = max[6s ] ] Lost Moton test U JIS = max [ U ] Repeatablty test, R s 1 R JIS = ± max[ R ] 2 JIS Where; = max[ R JIS x ] mn[ x ] Identcal, however U s s averaged over 7 measurements at each pont and not 5 as per the VDI/DQG Smlar: P smax s 6 tmes the largest averaged standard devaton of data ponts at a target pont, whle R s s ½ the maxmum range of data ponts measured at a target pont. R s wll be much smaller than P smax. Note the number of requred measurement ponts for the JIS B6330 s less than that requred for the VDI/DQG Comparson between ISO 2302:2006 and JIS B Table 7: Identcal and smlar parameters n the ISO 2302:2006 and JIS B ISO 2302:2006 JIS B Reversal value of an axs B 06 = max [ ] B Lost Moton test U JIS = max [ U ] Identcal, however U s s averaged over 7 measurements at each target pont and not 5 as per the ISO Undrectonal repeatablty of postonng of an axs, R 06 or R 06 R 06 R 06 = 4s = 4s Repeatablty test, R s 1 R JIS = ± max[ R ] 2 JIS Where; = max[ R JIS x ] mn[ x ] Smlar: R 06 s 4 tmes the largest standard devaton of data ponts at a target pont, whle R s s ½ the maxmum range of data ponts measured at a target pont. R s wll be much smaller than R 06. Bdrectonal systematc postonal devaton of an axs, E 06 E 06 mn x = max[ x ; x ] [ ; ] x Postonal accuracy PJIS = max x [ ] mn[ ] x Smlar: Both terms are smlar n concept, but as there are sgnfcant dfferences between the standards regardng the number of data ponts requred the two parameters may vary substantally. Note the number of requred measurement ponts for the JIS B6330 s less than that requred for the ISO 2302:2006. UNC Charlotte Mullany 16
17 Numercal Evaluaton Identcal parameters from the dfferent standards need no further explanaton. Lkewse for parameters that have no comparable parameter n other standards. However t s worth examnng the relatonshp between smlar parameters and determnng f gudelnes can be wrtten that wll allow for translaton between the conceptually smlar parameters defned by the dfferent standards. For example, can the ISO 2302:2006 bdrectonal accuracy of an axs, A, be converted drectly n the VDI/DQG 3441 postonal uncertanty, P? Numercal analyss was undertaken to determne the ratos between the conceptually smlar parameters and the expected range of ±percentage errors assocated wth each rato. Methodology A Monte Carlo approach s taken whereby several hundred sets of measurement ponts are generated usng the Gaussan random numbers generator functon n Matlab. Two dfferent approaches were taken when generatng the measurement ponts. In both cases the generated measurement ponts were analyzed as per the varous standards and the core parameters compared. Note on Gaussan assumpton: In general machne tools are not Gaussan n nature. Most errors are systematc. The frst approach taken (detals to follow) assumes a purely Gaussan dstrbuton of the measurement ponts, ths s somewhat lmted n ts valdty. The second approach (agan detals follow) whle stll usng Gaussan dstrbutons has a taken some, but not all, of the expected systematc errors nto consderaton. Nether approach can model machne tools accurately and t should be realzed that defntve (100% accurate) conversons between standards are not possble. That sad an apprecaton of how the dfferent parameters compare to each other s benefcal. It s also worth observng how the startng model assumptons affect the magntude of the expected ratos. 1. Gaussan Random Numbers For a chosen set of eleven target postons (relatve poston of each target pont to each other s not mportant) ten data ponts (fve n the forward drecton and fve n the reverse) were randomly generated n Matlab usng the Gaussan random number generator NORMRND. Ths functon requres a standard devaton and mean value. The fgure 1 below detals a typcal set of data ponts created when the mean and standard devaton were taken to be 0.5μm and 5 μm respectvely. Analyss: Usng the same mean and standard devaton fve thousand sets of measurement ponts were generated.. For each of the fve thousand sets the VDI/DQG 3441, ISO 2302:1988, ISO 2302:2006 and JIS6330 parameters were calculated. Whle a standard devaton value of 5μm maybe consdered somewhat on the large sde, t s worth notng that alterng the standard devaton used n the model does not sgnfcantly affect the resultng ratos or ther respectve standard devatons. The ratos between several comparable parameters are lsted n the frst column of table 10. The values lsted are the ratos averaged over fve thousand runs whle the number n parenthess s the standard devaton over the fve thousand runs. UNC Charlotte Mullany 17
18 x = Averaged postonal devaton at a target poston n the reverse drecton x = Averaged postonal devaton at a target poston n the forward drecton Fgure 1: Typcal data set generated wth a standard devaton of 5μm and a mean value of 0.5μm. 2. Gaussan Random Numbers wth Addtonal Constrants Ths approach also uses the Matlab NORMRND Gaussan random number generator to generate artfcal measurement ponts, however there are more constrants wth respect to the relatve locaton of the data ponts to the adacent target postons and the measurement ponts n the reverse drecton. Fgure 3 llustrates a typcal set of generated measurement ponts. The methodology can be descrbed n four steps, please also refer to fgure 2. The constrants used are based on ISO 2302:2006 parameters, see table 8 for descrptons of the parameters used and fgure 3 for graphcal llustraton. 1. x, the frst target poston s randomly selected wthn a predefned range. 2. The mean value of postonal error, x at each of the subsequent target locatons n the forward drectons s randomly generated by a Gaussan functon wth the mean value taken as the poston of the target pont generated n step 1 and the devaton taken as a typcal undrectonal systematc postonal dvded by four, E / 4 or E / 4. E s the range n whch the averaged target poston error les and thus t devaton can be taken as E /4 (k=2). 3. Gaussan functons were used to generate the locaton of the mean postonal devaton values at each target poston n the reverse drecton. The value s determned by the subtractng a number generated usng the mean reversal value, B, as the mean and the UNC Charlotte Mullany 18
19 B /24 as the standard devaton. Takng ths approach the mean postonal errors n the forward and reverse drectons wll not ntersect. Ths ssue s addressed n secton Fve data ponts are randomly created for each of the mean postonal devatons n the forward and reverse drectons. For the Gaussan functon the mean value s taken to be the relevant x or x value and the devaton s a typcal R / 4 value. Step 1: x 1 Step 2: generate 10 other x Postonal error, mcrons 0 P1 P2 P3 Target locaton,p,mm Postonal error, mcrons Mean = P1, Stdev= E /4 0 P1 P2 P3 Target locaton,p,mm Locaton P1 s randomly pcked Ponts P2, P3 etc are generated usng a Gaussan dstrbuton random number generator n Matlab wth the mean and standard devaton set as llustrated above Step 3: generate 11 x ponts Postonal error, mcrons Mean = B, Stdev=Fn(B ) 0 P1 P2 P3 Target locaton,p,mm Step 4: generate data ponts at all target postons Mean = x, Stdev= R /4 Postonal error, mcrons 0 P1 P2 P3 Target locaton,p,mm Fgure 2: Steps nvolved n generatng the random numbers. Table 8: Parameters used n generatng the measurement pont sets and ther meanng. Parameter Meanng E It gves nformaton wth respect to the range of the averaged postonal devatons ( x or x ) calculated along the axs n ether the forward or the reverse drecton. It contans no nformaton wth respect to the spread of data ponts at each measurement poston. See table 7 for ts numercal defnton. B B, the reversal value at a target poston, P, s the dfference between the averaged postonal devaton n the forward x and the reverse x drectons. The mean reversal value recorded along the axs s taken as the average of all the reversal values, B, along an axs. See table 3 for ts numercal defnton. R R, the undrectonal repeatablty of postonng at a poston n the forward drecton, s related to the maxmum spread of measured postonal errors at a target poston, P, the spread s taken as 4 s (coverage k=2), where s s the standard devaton of the measurement ponts at a target poston. UNC Charlotte Mullany 19
20 x = Averaged postonal devaton at a target poston n the reverse drecton B E R x = Averaged postonal devaton at a target poston n the forward drecton Fgure 3: A typcal set of data ponts generated by the second method. Analyss: For ths approach there are effectvely three test parameters ( E, B, R ). Three test sets were run whereby upper and lower lmts were gven to each of the three parameters. The three testng bands were: 0.1 μm to 5 μm, 5 μm to 10 μm and lastly 10 μm to 30 μm. Wthn each test set the values were systematcally vared (eght dfferent combnatons) and fve hundred smulatons run for each combnaton, see table 9. Table 9: Combnatons tested for the frst bandwdth, 0.1μm to 5μm. Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 E B R The key ISO 2302:1988, ISO 2302:2006, VDI/DQG 3441 and JIS 6330 parameters were calculated and the rato between conceptually smlar parameters as outlned n tables 3 to 7 were determned. The averaged rato and the averaged standard devaton (n parenthess) wthn each of the three test sets are lsted n the last three columns of table 10. UNC Charlotte Mullany 20
21 Table 10: Summary of the parameter ratos (and standard devatons) calculated from the Monte Carlo smulatons. Rato Gaussan 0.1 μm 5μm 5 μm 10μm 10 μm 30μm A 06 /P 0.8 (0.06) 0.9 (0.03) 0.86 (0.05) 0.87 (0.05) A 88 /A (0.04) 1.19 (0.03) 1.22 (0.04) 1.22 (0.04) A 88 /A (0.04) 1.29 (0.05) 1.33 (0.06) 1.32 (0.06) A 88 /P 1.16 (0.1) 1.06 (0.05) 1.05 (0.06) 1.05 (0.06) R 06 /P smax 0.75 (0.1) 0.76 (0.1) 0.76 (0.1) 0.76 (0.1) R 88 /P smax 1.13 (0.15) 1.14 (0.16) 1.14 (0.16) 1.14 (0.16) R 06 /(U+2/3P smax ) 1.14 (0.11) 1.06 (0.06) 1.03 (0.05) 1.04 (0.05) R 88 /(U+P smax ) 1.16 (0.11) 1.06 (0.06) 1.03 (0.05) 1.03 (0.05) R 88 /R (0.03) 1.26 (0.02) 1.27 (0.06) 1.28 (0.06) Rs/R (0.05) 0.35 (0.05) 0.35 (0.05) 0.35 (0.05) Rs/R (0.03) 0.26 (0.03) 0.26 (0.03) 0.26 (0.03) Rs/P smax 0.23 (0.03) 0.23 (0.03) 0.23 (0.03) 0.23 (0.03) Ps/E 0.66 (0.21) 0.73 (0.13) 0.76 (0.12) 0.75 (0.13) See Notes 1& 2 on page 12 and table 11. Table 11: Rato Key. Rato Detal A 06 /P B drectonal Accuracy (ISO 2302:2006) / Poston Uncertanty (VDI/DQG 3441) A 88 /A 06 B drectonal Accuracy (ISO 2302:1988) / B drectonal Accuracy (ISO 2302:2006) A 88 /A 06 Undrectonal Accuracy (ISO 2302:1988) / Undrectonal Accuracy (ISO 2302:2006) A 88 /P B drectonal Accuracy (ISO 2302:1988) / Poston Uncertanty (VDI/DQG 3441) R 06 /P smax Undrectonal Repeatablty (ISO 2302:2006)/ Postonal Scatter (VDI/DQG 3441) R 88 /P smax Undrectonal Repeatablty (ISO 2302:1988)/ Postonal Scatter (VDI/DQG 3441) R 06 /(U+2/3P smax ) Undrectonal Repeatablty (ISO 2302:2006)/ (Reversal error + ⅔Postonal Scatter (VDI/DQG 3441) ) R 88 /(U+P smax ) Undrectonal Repeatablty (ISO 2302:1988)/ (Reversal error + Postonal Scatter (VDI/DQG 3441) ) R 88 /R 06 Repeatablty (ISO 2302:1988) / Repeatablty (ISO 2302:2006) R s /R 06 Repeatablty (JIS B )/ Undrectonal Repeatablty (ISO 2302:2006) R s /R 88 Repeatablty (JIS B )/ Undrectonal Repeatablty (ISO 2302:1988) R s /P smax Repeatablty (JIS B )/ Postonal Scatter (VDI/DQG 3441) P s /E Postonal Accuarcy (JIS B )/ Bdrectonal Postonal Devaton (ISO 2302:2006) 2.1. Intersectng and A lmtaton of the prevous method used to generated measurement ponts s that the forward and reverse drectons wll not ntersect, a phenomena that may well occur n realty. The program was modfed so that the forward and reverse drectons were forced to ntersect. Ths was acheved by removng steps 2 and 3 outlned n secton 2 and specfyng the locaton of the averaged postonal error n each drecton, see fgure 4 for an example of a typcal output. R and E values were used to determne the spread of the data ponts at a target poston and the range of postonal errors n ether the forward or reverse drectons. The program was run 500 UNC Charlotte Mullany 21
22 tmes and the results are presented n Table 12. Agan the averaged rato and the averaged standard devaton (n parenthess) are gven for the three test bands. x = Averaged postonal devaton at a target poston n the reverse drecton x = Averaged postonal devaton at a target poston n the forward drecton Fgure 4: Randomly generated data ponts where and are forced to ntersect. Table 12: Summary of the parameter ratos (and standard devatons) calculated from ntersectng and. Rato 0.1 μm 5μm 5 μm 10μm 10 μm 30μm A 06 /P 0.85 (0.04) 0.82 (0.05) 0.84 (0.05) A 88 /A (0.03) 1.29 (0.04) 1.29 (0.04) A 88 /A (0.04) 1.29 (0.04) 1.29 (0.04) A 88 /P 1.08 (0.06) 1.07 (0.07) 1.08 (0.07) R 06 /P smax 0.76 (0.1) 0.76 (0.1) 0.76 (0.11) R 88 /P smax 1.14 (0.16) 1.14 (0.15) 1.14 (0.16) R 06 /(U+2/3P smax ) 1.26 (0.09) 1.17 (0.1) 1.19 (0.1) R 88 (U+P smax ) 1.23 (0.09) 1.12 (0.09) 1.08 (0.07) R 88 /R (0.04) 1.30 (0.05) 1.29 (0.05) R s /R (0.05) 0.35 (0.05) 0.35 (0.05) R s /R (0.03) 0.26 (0.03) 0.26 (0.03) R s /P smax 0.23 (0.03) 0.23 (0.03) 0.23 (0.03) See Notes 1& 2 on page 12 and table 11. UNC Charlotte Mullany 22
23 To provde the reader wth a hgher degree of transparency, table 13 detals the possble percentage varatons n the rato value assocated wth ± three standard devatons (k=3). In all cases there are sgnfcant percentage varatons possble. And n certan cases, such as comparng JIS 6330 parameters to ISO or VDI/DQG 3441 parameters, or comparng ISO repeatablty values to VDI/DQG 3441 postonal scatter values, the percentage varatons assocated wth the ratos are very large,.e. > ±34%. In these cases attemptng a drecton converson from one standard to another wth any degree of certanty s not advsed. Table 13: Ratos and ther percentage varatons. Rato Gaussan Rato +/ % error 0.1 μm 5 μm Rato +/ % error Intersectng 0.1 μm 5 μm Rato +/ % error A 06 /P 0.8 ±14.1% 0.9 ±10.0% 0.85 ±14.1% A 88 /A ±8.3% 1.19 ±7.6% 1.27 ±7.1% A 88 /A ±8.3% 1.29 ±11.6% 1.27 ±9.4% A 88 /P 1.16±25.9% 1.06 ±14.2% 1.08 ±16.7% R 06 /P smax 0.75 ±40.0% 0.76 ±39.5% 0.76 ±39.5% R 88 /P smax 1.13 ±39.8% 1.14 ±42.1% 1.14 ±42.9% R 06 /(U+2/3P smax ) 1.14 ±28.9% 1.06 ±17.0% 1.26 ±21.4% R 88 /(U+P smax ) 1.16 ±28.4% 1.06 ±17.0% 1.23 ±22% R 88 /R ±6.1% 1.26 ±4.8% 1.28 ±9.4% R s /R ±42.9% 0.35 ±42.9% 0.34 ±44.1% R s /R ±34.6% 0.26 ±34.6% 0.26 ±34.6% R s /P smax 0.23 ±39.1% 0.26 ±39.1% 0.23 ±39.1% P s /E 0.66 ±95% 0.73 ±53.4% See Note 1 on page 12 and table 11. Verfcaton of the Monte Carlo predcted ratos. To verfy the Monte Carlo analyss ratos two sets of data ponts were consdered. The frst set of ponts taken were from the worked example n the ISO 2302:2006, the second set of measurement data ponts were taken from an actual test carred out on the Monarch mllng machne at UNC Charlotte. Both sets of data ponts underwent VDI/DQG 3441, ISO 2302:2006 and ISO 2302:1988 analyss to calculate the key parameters defned by each standard. The ratos between the conceptually smlar parameters were determned and compared to the range of rato values obtaned from the Monte Carlo analyss. The results are presented n table 14. The Predcted Rato Ranges reported n the fnal column of table 14 are the hghest and lowest possble ratos as gven by method 2 n the 0.1μm to 5μm test band (based on k=3). ISO ratos n column 2 refers to the ratos obtaned based on the data ponts lsted n ISO 2302:2006, smlarly the Monarch ratos were determned from the data ponts taken off the Monarch machne at UNC Charlotte. UNC Charlotte Mullany 23
24 Table 14: Actual ratos compared to predcted ratos. Rato ISO Ratos Monarch Ratos Predcted Rato Ranges A 06 /P A 88 /A A 88 /P R 06 /P smax R 88 /P smax R 06 /(U+2/3P smax ) R 88 /(U+P smax ) R 88 /R See Notes 1 & 2 on page 12 and table 11. Conclusons Analyss of the dfferent standards solated parameters that were dentcal to each other and those that were smlar n concept but mathematcally dfferent, see tables 3 to 7. A Monte Carlo approach was taken to determne the relatonshp between conceptually smlar parameters. Two dfferent approaches were taken; purely Gaussan and Gaussan combned wth some systematc errors. Twelve relatonshp pars were consdered, however as the percentage varaton assocated wth the ratos was qute large n some cases (over 40%) only three conversons ratos could be consdered (A 88 /P, A 88 /A 06 and R 88 /R 06 ). These rato values stll had assocated ± percentage varatons up 14% and thus great cauton should be taken f consderng an attempt to convertng from one standard to another. Ultmately when seekng to compare values obtaned from the dfferent standards there s no substtute for actually conductng the analyss on actual measured data. UNC Charlotte Mullany 24
25 Appendx A Nomenclature used by the varous standards ISO 2302:2006 & 1997 A & A Undrectonal Accuracy of postonng of an Axs A Bdrectonal Accuracy of postonng of an Axs E & E Undrectonal systematc postonal devaton of and axs E Bdrectonal systematc postonal devaton of an axs M Mean bdrectonal postonal devaton of an axs, M B Reversal value of an axs R & R Undrectonal repeatablty of postonng R Bdrectonal repeatablty of postonng of an axs x & x Mean undrectonal postonal devaton at a target poston x Mean bdrectonal postonal devaton at a poston s & s Estmator for the undrectonal axs repeatablty of postonng at a target pont ISO 2302:1988 A Accuracy of an axs W and W Range of postonal devaton B Mean reversal error B Reversal value of an axs R & R Undrectonal repeatablty of postonng R Bdrectonal repeatablty of postonng of an axs x & x Mean undrectonal postonal devaton at a target poston s & s Estmator for the undrectonal axs repeatablty of postonng at a target pont VDI/DQG 3441 P smax Maxmum postonal scatter U max Maxmum reversal error at a poston U Mean reversal error P a Postonal devaton P Postonal uncertanty x & x Mean value of ndvdual values at a poston System Devaton from the desred value at a target poston x = s & s Standard devaton at a target poston n one drecton Mean standard devaton at a target poston s UNC Charlotte Mullany 25
26 ASME B A & A Undrectonal Accuracy of postonng of an Axs A Bdrectonal Accuracy of postonng of an Axs E & E Undrectonal systematc postonal devaton of and axs E Bdrectonal systematc postonal devaton of an axs M Mean bdrectonal postonal devaton of an axs, M B Reversal value of an axs R & R Undrectonal repeatablty of postonng R Bdrectonal repeatablty of postonng of an axs P Perodc errors x & x Mean undrectonal postonal devaton at a target poston x Mean bdrectonal postonal devaton at a poston s & s Estmator for the undrectonal axs repeatablty of postonng at a target pont JIS Postonng Accuracy test Repeatablty test Lost moton test Least nput ncrementfeed P s R s U s L s UNC Charlotte Mullany 26
An Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMISP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationbenefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationI. SCOPE, APPLICABILITY AND PARAMETERS Scope
D Executve Board Annex 9 Page A/R ethodologcal Tool alculaton of the number of sample plots for measurements wthn A/R D project actvtes (Verson 0) I. SOPE, PIABIITY AD PARAETERS Scope. Ths tool s applcable
More informationInequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001.
Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.
More informationCalculation of Sampling Weights
Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a twostage stratfed cluster desgn. 1 The frst stage conssted of a sample
More informationCHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol
CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL
More informationPassive Filters. References: Barbow (pp 265275), Hayes & Horowitz (pp 3260), Rizzoni (Chap. 6)
Passve Flters eferences: Barbow (pp 6575), Hayes & Horowtz (pp 360), zzon (Chap. 6) Frequencyselectve or flter crcuts pass to the output only those nput sgnals that are n a desred range of frequences (called
More informationIntroduction: Analysis of Electronic Circuits
/30/008 ntroducton / ntroducton: Analyss of Electronc Crcuts Readng Assgnment: KVL and KCL text from EECS Just lke EECS, the majorty of problems (hw and exam) n EECS 3 wll be crcut analyss problems. Thus,
More informationMoment of a force about a point and about an axis
3. STATICS O RIGID BODIES In the precedng chapter t was assumed that each of the bodes consdered could be treated as a sngle partcle. Such a vew, however, s not always possble, and a body, n general, should
More informationStudy on CET4 Marks in China s Graded English Teaching
Study on CET4 Marks n Chna s Graded Englsh Teachng CHE We College of Foregn Studes, Shandong Insttute of Busness and Technology, P.R.Chna, 264005 Abstract: Ths paper deploys Logt model, and decomposes
More informationSolution of Algebraic and Transcendental Equations
CHAPTER Soluton of Algerac and Transcendental Equatons. INTRODUCTION One of the most common prolem encountered n engneerng analyss s that gven a functon f (, fnd the values of for whch f ( = 0. The soluton
More informationChapter 3 Group Theory p. 1  Remark: This is only a brief summary of most important results of groups theory with respect
Chapter 3 Group Theory p.  3. Compact Course: Groups Theory emark: Ths s only a bref summary of most mportant results of groups theory wth respect to the applcatons dscussed n the followng chapters. For
More informationIDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS
IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS Chrs Deeley* Last revsed: September 22, 200 * Chrs Deeley s a Senor Lecturer n the School of Accountng, Charles Sturt Unversty,
More informationMAPP. MERIS level 3 cloud and water vapour products. Issue: 1. Revision: 0. Date: 9.12.1998. Function Name Organisation Signature Date
Ttel: Project: Doc. No.: MERIS level 3 cloud and water vapour products MAPP MAPPATBDClWVL3 Issue: 1 Revson: 0 Date: 9.12.1998 Functon Name Organsaton Sgnature Date Author: Bennartz FUB Preusker FUB Schüller
More informationStaff Paper. Farm Savings Accounts: Examining Income Variability, Eligibility, and Benefits. Brent Gloy, Eddy LaDue, and Charles Cuykendall
SP 200502 August 2005 Staff Paper Department of Appled Economcs and Management Cornell Unversty, Ithaca, New York 148537801 USA Farm Savngs Accounts: Examnng Income Varablty, Elgblty, and Benefts Brent
More informationCan Auto Liability Insurance Purchases Signal Risk Attitude?
Internatonal Journal of Busness and Economcs, 2011, Vol. 10, No. 2, 159164 Can Auto Lablty Insurance Purchases Sgnal Rsk Atttude? ChuShu L Department of Internatonal Busness, Asa Unversty, Tawan ShengChang
More informationCausal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting
Causal, Explanatory Forecastng Assumes causeandeffect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of
More informationCalculating the high frequency transmission line parameters of power cables
< ' Calculatng the hgh frequency transmsson lne parameters of power cables Authors: Dr. John Dcknson, Laboratory Servces Manager, N 0 RW E B Communcatons Mr. Peter J. Ncholson, Project Assgnment Manager,
More informationCHAPTER 14 MORE ABOUT REGRESSION
CHAPTER 14 MORE ABOUT REGRESSION We learned n Chapter 5 that often a straght lne descrbes the pattern of a relatonshp between two quanttatve varables. For nstance, n Example 5.1 we explored the relatonshp
More informationDescribing Communities. Species Diversity Concepts. Species Richness. Species Richness. SpeciesArea Curve. SpeciesArea Curve
peces versty Concepts peces Rchness pecesarea Curves versty Indces  mpson's Index  hannonwener Index  rlloun Index peces Abundance Models escrbng Communtes There are two mportant descrptors of a communty:
More informationRisk Model of LongTerm Production Scheduling in Open Pit Gold Mining
Rsk Model of LongTerm Producton Schedulng n Open Pt Gold Mnng R Halatchev 1 and P Lever 2 ABSTRACT Open pt gold mnng s an mportant sector of the Australan mnng ndustry. It uses large amounts of nvestments,
More informationTo manage leave, meeting institutional requirements and treating individual staff members fairly and consistently.
Corporate Polces & Procedures Human Resources  Document CPP216 Leave Management Frst Produced: Current Verson: Past Revsons: Revew Cycle: Apples From: 09/09/09 26/10/12 09/09/09 3 years Immedately Authorsaton:
More informationInstitute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic
Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange
More informationMultivariate EWMA Control Chart
Multvarate EWMA Control Chart Summary The Multvarate EWMA Control Chart procedure creates control charts for two or more numerc varables. Examnng the varables n a multvarate sense s extremely mportant
More informationAryabhata s Root Extraction Methods. Abhishek Parakh Louisiana State University Aug 31 st 2006
Aryabhata s Root Extracton Methods Abhshek Parakh Lousana State Unversty Aug 1 st 1 Introducton Ths artcle presents an analyss of the root extracton algorthms of Aryabhata gven n hs book Āryabhatīya [1,
More informationInterIng 2007. INTERDISCIPLINARITY IN ENGINEERING SCIENTIFIC INTERNATIONAL CONFERENCE, TG. MUREŞ ROMÂNIA, 1516 November 2007.
InterIng 2007 INTERDISCIPLINARITY IN ENGINEERING SCIENTIFIC INTERNATIONAL CONFERENCE, TG. MUREŞ ROMÂNIA, 1516 November 2007. UNCERTAINTY REGION SIMULATION FOR A SERIAL ROBOT STRUCTURE MARIUS SEBASTIAN
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More information) of the Cell class is created containing information about events associated with the cell. Events are added to the Cell instance
Calbraton Method Instances of the Cell class (one nstance for each FMS cell) contan ADC raw data and methods assocated wth each partcular FMS cell. The calbraton method ncludes event selecton (Class Cell
More informationNasdaq Iceland Bond Indices 01 April 2015
Nasdaq Iceland Bond Indces 01 Aprl 2015 Fxed duraton Indces Introducton Nasdaq Iceland (the Exchange) began calculatng ts current bond ndces n the begnnng of 2005. They were a response to recent changes
More informationPSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 12
14 The Chsquared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed
More informationGraph Theory and Cayley s Formula
Graph Theory and Cayley s Formula Chad Casarotto August 10, 2006 Contents 1 Introducton 1 2 Bascs and Defntons 1 Cayley s Formula 4 4 Prüfer Encodng A Forest of Trees 7 1 Introducton In ths paper, I wll
More informationEfficient Project Portfolio as a tool for Enterprise Risk Management
Effcent Proect Portfolo as a tool for Enterprse Rsk Management Valentn O. Nkonov Ural State Techncal Unversty Growth Traectory Consultng Company January 5, 27 Effcent Proect Portfolo as a tool for Enterprse
More informationThe Development of Web Log Mining Based on ImproveKMeans Clustering Analysis
The Development of Web Log Mnng Based on ImproveKMeans Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.
More information8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by
6 CHAPTER 8 COMPLEX VECTOR SPACES 5. Fnd the kernel of the lnear transformaton gven n Exercse 5. In Exercses 55 and 56, fnd the mage of v, for the ndcated composton, where and are gven by the followng
More information1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP)
6.3 /  Communcaton Networks II (Görg) SS20  www.comnets.unbremen.de Communcaton Networks II Contents. Fundamentals of probablty theory 2. Emergence of communcaton traffc 3. Stochastc & Markovan Processes
More informationOn the Optimal Control of a Cascade of HydroElectric Power Stations
On the Optmal Control of a Cascade of HydroElectrc Power Statons M.C.M. Guedes a, A.F. Rbero a, G.V. Smrnov b and S. Vlela c a Department of Mathematcs, School of Scences, Unversty of Porto, Portugal;
More informationCommunication Networks II Contents
8 / 1  Communcaton Networs II (Görg)  www.comnets.unbremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP
More informationLuby s Alg. for Maximal Independent Sets using Pairwise Independence
Lecture Notes for Randomzed Algorthms Luby s Alg. for Maxmal Independent Sets usng Parwse Independence Last Updated by Erc Vgoda on February, 006 8. Maxmal Independent Sets For a graph G = (V, E), an ndependent
More informationStudy on Model of Risks Assessment of Standard Operation in Rural Power Network
Study on Model of Rsks Assessment of Standard Operaton n Rural Power Network Qngj L 1, Tao Yang 2 1 Qngj L, College of Informaton and Electrcal Engneerng, Shenyang Agrculture Unversty, Shenyang 110866,
More informationL10: Linear discriminants analysis
L0: Lnear dscrmnants analyss Lnear dscrmnant analyss, two classes Lnear dscrmnant analyss, C classes LDA vs. PCA Lmtatons of LDA Varants of LDA Other dmensonalty reducton methods CSCE 666 Pattern Analyss
More informationSIX WAYS TO SOLVE A SIMPLE PROBLEM: FITTING A STRAIGHT LINE TO MEASUREMENT DATA
SIX WAYS TO SOLVE A SIMPLE PROBLEM: FITTING A STRAIGHT LINE TO MEASUREMENT DATA E. LAGENDIJK Department of Appled Physcs, Delft Unversty of Technology Lorentzweg 1, 68 CJ, The Netherlands Emal: e.lagendjk@tnw.tudelft.nl
More informationChE 4520/5520: Mass Transport. Objective/Introduction. Outline. Gerardine G. Botte
ChE 450/550: Mass Transport Gerardne G. Botte Objectve/Introducton In prevous chapters we neglected transport lmtatons In ths chapter we wll learn how to evaluate the effect of transport lmtatons We wll
More informationIMPACT ANALYSIS OF A CELLULAR PHONE
4 th ASA & μeta Internatonal Conference IMPACT AALYSIS OF A CELLULAR PHOE We Lu, 2 Hongy L Bejng FEAonlne Engneerng Co.,Ltd. Bejng, Chna ABSTRACT Drop test smulaton plays an mportant role n nvestgatng
More informationConversion between the vector and raster data structures using Fuzzy Geographical Entities
Converson between the vector and raster data structures usng Fuzzy Geographcal Enttes Cdála Fonte Department of Mathematcs Faculty of Scences and Technology Unversty of Combra, Apartado 38, 3 454 Combra,
More informationSection B9: Zener Diodes
Secton B9: Zener Dodes When we frst talked about practcal dodes, t was mentoned that a parameter assocated wth the dode n the reverse bas regon was the breakdown voltage, BR, also known as the peaknverse
More informationAnalysis of Premium Liabilities for Australian Lines of Business
Summary of Analyss of Premum Labltes for Australan Lnes of Busness Emly Tao Honours Research Paper, The Unversty of Melbourne Emly Tao Acknowledgements I am grateful to the Australan Prudental Regulaton
More informationExtending Probabilistic Dynamic Epistemic Logic
Extendng Probablstc Dynamc Epstemc Logc Joshua Sack May 29, 2008 Probablty Space Defnton A probablty space s a tuple (S, A, µ), where 1 S s a set called the sample space. 2 A P(S) s a σalgebra: a set
More informationFixed income risk attribution
5 Fxed ncome rsk attrbuton Chthra Krshnamurth RskMetrcs Group chthra.krshnamurth@rskmetrcs.com We compare the rsk of the actve portfolo wth that of the benchmark and segment the dfference between the two
More informationAn Empirical Study of Search Engine Advertising Effectiveness
An Emprcal Study of Search Engne Advertsng Effectveness Sanjog Msra, Smon School of Busness Unversty of Rochester Edeal Pnker, Smon School of Busness Unversty of Rochester Alan RmmKaufman, RmmKaufman
More informationDamage detection in composite laminates using cointap method
Damage detecton n composte lamnates usng contap method S.J. Km Korea Aerospace Research Insttute, 45 EoeunDong, YouseongGu, 35333 Daejeon, Republc of Korea yaeln@kar.re.kr 45 The contap test has the
More informationEE201 Circuit Theory I 2015 Spring. Dr. Yılmaz KALKAN
EE201 Crcut Theory I 2015 Sprng Dr. Yılmaz KALKAN 1. Basc Concepts (Chapter 1 of Nlsson  3 Hrs.) Introducton, Current and Voltage, Power and Energy 2. Basc Laws (Chapter 2&3 of Nlsson  6 Hrs.) Voltage
More informationActuator forces in CFD: RANS and LES modeling in OpenFOAM
Home Search Collectons Journals About Contact us My IOPscence Actuator forces n CFD: RANS and LES modelng n OpenFOAM Ths content has been downloaded from IOPscence. Please scroll down to see the full text.
More informationNordea G10 Alpha Carry Index
Nordea G10 Alpha Carry Index Index Rules v1.1 Verson as of 10/10/2013 1 (6) Page 1 Index Descrpton The G10 Alpha Carry Index, the Index, follows the development of a rule based strategy whch nvests and
More informationBERNSTEIN POLYNOMIALS
OnLne Geometrc Modelng Notes BERNSTEIN POLYNOMIALS Kenneth I. Joy Vsualzaton and Graphcs Research Group Department of Computer Scence Unversty of Calforna, Davs Overvew Polynomals are ncredbly useful
More informationCHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES
CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES In ths chapter, we wll learn how to descrbe the relatonshp between two quanttatve varables. Remember (from Chapter 2) that the terms quanttatve varable
More informationProject Networks With MixedTime Constraints
Project Networs Wth MxedTme Constrants L Caccetta and B Wattananon Western Australan Centre of Excellence n Industral Optmsaton (WACEIO) Curtn Unversty of Technology GPO Box U1987 Perth Western Australa
More informationThe OC Curve of Attribute Acceptance Plans
The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4
More information"Research Note" APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES *
Iranan Journal of Scence & Technology, Transacton B, Engneerng, ol. 30, No. B6, 789794 rnted n The Islamc Republc of Iran, 006 Shraz Unversty "Research Note" ALICATION OF CHARGE SIMULATION METHOD TO ELECTRIC
More informationQuestions that we may have about the variables
Antono Olmos, 01 Multple Regresson Problem: we want to determne the effect of Desre for control, Famly support, Number of frends, and Score on the BDI test on Perceved Support of Latno women. Dependent
More informationAPPLICATION OF PROBE DATA COLLECTED VIA INFRARED BEACONS TO TRAFFIC MANEGEMENT
APPLICATION OF PROBE DATA COLLECTED VIA INFRARED BEACONS TO TRAFFIC MANEGEMENT Toshhko Oda (1), Kochro Iwaoka (2) (1), (2) Infrastructure Systems Busness Unt, Panasonc System Networks Co., Ltd. Saedocho
More informationSimple Interest Loans (Section 5.1) :
Chapter 5 Fnance The frst part of ths revew wll explan the dfferent nterest and nvestment equatons you learned n secton 5.1 through 5.4 of your textbook and go through several examples. The second part
More informationIntroduction to Regression
Introducton to Regresson Regresson a means of predctng a dependent varable based one or more ndependent varables. Ths s done by fttng a lne or surface to the data ponts that mnmzes the total error. 
More informationCourse outline. Financial Time Series Analysis. Overview. Data analysis. Predictive signal. Trading strategy
Fnancal Tme Seres Analyss Patrck McSharry patrck@mcsharry.net www.mcsharry.net Trnty Term 2014 Mathematcal Insttute Unversty of Oxford Course outlne 1. Data analyss, probablty, correlatons, vsualsaton
More information9.1 The Cumulative Sum Control Chart
Learnng Objectves 9.1 The Cumulatve Sum Control Chart 9.1.1 Basc Prncples: Cusum Control Chart for Montorng the Process Mean If s the target for the process mean, then the cumulatve sum control chart s
More informationA Novel Methodology of Working Capital Management for Large. Public Constructions by Using Fuzzy Scurve Regression
Novel Methodology of Workng Captal Management for Large Publc Constructons by Usng Fuzzy Scurve Regresson ChengWu Chen, Morrs H. L. Wang and TngYa Hseh Department of Cvl Engneerng, Natonal Central Unversty,
More informationPrediction of Wind Energy with Limited Observed Data
Predcton of Wnd Energy wth Lmted Observed Data Shgeto HIRI, khro HOND Nagasak R&D Center, MITSISHI HEVY INDSTRIES, LTD, Nagasak, 8539 JPN Masaak SHIT Nagasak Shpyard & Machnery Works, MITSISHI HEVY INDSTRIES,
More informationStress test for measuring insurance risks in nonlife insurance
PROMEMORIA Datum June 01 Fnansnspektonen Författare Bengt von Bahr, Younes Elonq and Erk Elvers Stress test for measurng nsurance rsks n nonlfe nsurance Summary Ths memo descrbes stress testng of nsurance
More informationFINAL REPORT. City of Toronto. Contract 47016555. Project No: B0002033
Cty of Toronto SAFETY IMPACTS AD REGULATIOS OF ELECTROIC STATIC ROADSIDE ADVERTISIG SIGS TECHICAL MEMORADUM #2C BEFORE/AFTER COLLISIO AALYSIS AT SIGALIZED ITERSECTIO FIAL REPORT 3027 Harvester Road, Sute
More informationForecasting the Direction and Strength of Stock Market Movement
Forecastng the Drecton and Strength of Stock Market Movement Jngwe Chen Mng Chen Nan Ye cjngwe@stanford.edu mchen5@stanford.edu nanye@stanford.edu Abstract  Stock market s one of the most complcated systems
More informationTHE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek
HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo
More informationMetaAnalysis of Hazard Ratios
NCSS Statstcal Softare Chapter 458 MetaAnalyss of Hazard Ratos Introducton Ths module performs a metaanalyss on a set of togroup, tme to event (survval), studes n hch some data may be censored. These
More informationTime Value of Money Module
Tme Value of Money Module O BJECTIVES After readng ths Module, you wll be able to: Understand smple nterest and compound nterest. 2 Compute and use the future value of a sngle sum. 3 Compute and use the
More informationThe Effect of Mean Stress on Damage Predictions for Spectral Loading of Fiberglass Composite Coupons 1
EWEA, Specal Topc Conference 24: The Scence of Makng Torque from the Wnd, Delft, Aprl 92, 24, pp. 546555. The Effect of Mean Stress on Damage Predctons for Spectral Loadng of Fberglass Composte Coupons
More informationChapter 4 ECONOMIC DISPATCH AND UNIT COMMITMENT
Chapter 4 ECOOMIC DISATCH AD UIT COMMITMET ITRODUCTIO A power system has several power plants. Each power plant has several generatng unts. At any pont of tme, the total load n the system s met by the
More informationRiskbased Fatigue Estimate of Deep Water Risers  Course Project for EM388F: Fracture Mechanics, Spring 2008
Rskbased Fatgue Estmate of Deep Water Rsers  Course Project for EM388F: Fracture Mechancs, Sprng 2008 Chen Sh Department of Cvl, Archtectural, and Envronmental Engneerng The Unversty of Texas at Austn
More informationNumerical Study of Wave Runup around Offshore Structure in Waves
Journal of Advanced Research n Ocean Engneerng Journal of Advanced Research n Ocean Engneerng 2(2) (2016) 061066 http://dx.do.org/10.5574/jaroe.2016.2.2.061 Numercal Study of Wave Runup around Offshore
More informationNumber of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000
Problem Set 5 Solutons 1 MIT s consderng buldng a new car park near Kendall Square. o unversty funds are avalable (overhead rates are under pressure and the new faclty would have to pay for tself from
More informationDemographic and Health Surveys Methodology
samplng and household lstng manual Demographc and Health Surveys Methodology Ths document s part of the Demographc and Health Survey s DHS Toolkt of methodology for the MEASURE DHS Phase III project, mplemented
More informationA Simplified Framework for Return Accountability
Reprnted wth permsson from Fnancal Analysts Journal, May/June 1991. Copyrght 1991. Assocaton for Investment Management and Research, Charlottesvlle, VA. All rghts reserved. by Gary P. Brnson, Bran D. Snger
More informationInstructions for Analyzing Data from CAHPS Surveys:
Instructons for Analyzng Data from CAHPS Surveys: Usng the CAHPS Analyss Program Verson 4.1 Purpose of ths Document...1 The CAHPS Analyss Program...1 Computng Requrements...1 PreAnalyss Decsons...2 What
More information1 Approximation Algorithms
CME 305: Dscrete Mathematcs and Algorthms 1 Approxmaton Algorthms In lght of the apparent ntractablty of the problems we beleve not to le n P, t makes sense to pursue deas other than complete solutons
More informationForecasting the Demand of Emergency Supplies: Based on the CBR Theory and BP Neural Network
700 Proceedngs of the 8th Internatonal Conference on Innovaton & Management Forecastng the Demand of Emergency Supples: Based on the CBR Theory and BP Neural Network Fu Deqang, Lu Yun, L Changbng School
More informationHOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA*
HOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA* Luísa Farnha** 1. INTRODUCTION The rapd growth n Portuguese households ndebtedness n the past few years ncreased the concerns that debt
More informationQuality Adjustment of Secondhand Motor Vehicle Application of Hedonic Approach in Hong Kong s Consumer Price Index
Qualty Adustment of Secondhand Motor Vehcle Applcaton of Hedonc Approach n Hong Kong s Consumer Prce Index Prepared for the 14 th Meetng of the Ottawa Group on Prce Indces 20 22 May 2015, Tokyo, Japan
More informationQuantization Effects in Digital Filters
Quantzaton Effects n Dgtal Flters Dstrbuton of Truncaton Errors In two's complement representaton an exact number would have nfntely many bts (n general). When we lmt the number of bts to some fnte value
More informationOn Mean Squared Error of Hierarchical Estimator
S C H E D A E I N F O R M A T I C A E VOLUME 0 0 On Mean Squared Error of Herarchcal Estmator Stans law Brodowsk Faculty of Physcs, Astronomy, and Appled Computer Scence, Jagellonan Unversty, Reymonta
More informationEvaluating credit risk models: A critique and a new proposal
Evaluatng credt rsk models: A crtque and a new proposal Hergen Frerchs* Gunter Löffler Unversty of Frankfurt (Man) February 14, 2001 Abstract Evaluatng the qualty of credt portfolo rsk models s an mportant
More informationthe Manual on the global data processing and forecasting system (GDPFS) (WMONo.485; available at http://www.wmo.int/pages/prog/www/manuals.
Gudelne on the exchange and use of EPS verfcaton results Update date: 30 November 202. Introducton World Meteorologcal Organzaton (WMO) CBSXIII (2005) recommended that the general responsbltes for a Lead
More informationQUANTUM MECHANICS, BRAS AND KETS
PH575 SPRING QUANTUM MECHANICS, BRAS AND KETS The followng summares the man relatons and defntons from quantum mechancs that we wll be usng. State of a phscal sstem: The state of a phscal sstem s represented
More informationStatistical algorithms in Review Manager 5
Statstcal algorthms n Reve Manager 5 Jonathan J Deeks and Julan PT Hggns on behalf of the Statstcal Methods Group of The Cochrane Collaboraton August 00 Data structure Consder a metaanalyss of k studes
More informationTopic 10. ANOVA models for random and mixed effects
10.1 Topc 10. ANOVA models for random and mxed effects eferences: ST&DT: Topc 7.5 p.15153, Topc 9.9 p. 57, Topc 15.5 379384. There s a good dscusson n SAS System for Lnear Models, 3 rd ed. pages 191198.
More informationg. Kaptay *, # E/7, 606 Egyetemvaros, Miskolc, Hungary 3515 (Received 24 October 2011; accepted 01 December 2011)
J o u r n a l o f J Mn Metall Sect B Metall 48 (1) B (2012) 153 159 M n n g a n d M e t a l l u r g y On the atomic masses (weights?) Of the elements g Kaptay *, # * Bay Zoltan Nonproft Ltd and Unversty
More informationThe Application of Fractional Brownian Motion in Option Pricing
Vol. 0, No. (05), pp. 738 http://dx.do.org/0.457/jmue.05.0..6 The Applcaton of Fractonal Brownan Moton n Opton Prcng Qngxn Zhou School of Basc Scence,arbn Unversty of Commerce,arbn zhouqngxn98@6.com
More information+ + +   This circuit than can be reduced to a planar circuit
MeshCurrent Method The meshcurrent s analog of the nodeoltage method. We sole for a new set of arables, mesh currents, that automatcally satsfy KCLs. As such, meshcurrent method reduces crcut soluton to
More informationComparing Class Level Chain Drift for Different Elementary Aggregate Formulae Using Locally Collected CPI Data
Comparng Class Level Chan Drft for Dfferent Elementary Aggregate Formulae Usng Gareth Clews 1, Anselma DobsonMcKttrck 2 and Joseph Wnton Summary The Consumer Prces Index (CPI) s a measure of consumer
More informationDesign and Development of a Security Evaluation Platform Based on International Standards
Internatonal Journal of Informatcs Socety, VOL.5, NO.2 (203) 780 7 Desgn and Development of a Securty Evaluaton Platform Based on Internatonal Standards Yuj Takahash and Yoshm Teshgawara Graduate School
More informationTHE TITANIC SHIPWRECK: WHO WAS
THE TITANIC SHIPWRECK: WHO WAS MOST LIKELY TO SURVIVE? A STATISTICAL ANALYSIS Ths paper examnes the probablty of survvng the Ttanc shpwreck usng lmted dependent varable regresson analyss. Ths appled analyss
More informationA system for realtime calculation and monitoring of energy performance and carbon emissions of RET systems and buildings
A system for realtme calculaton and montorng of energy performance and carbon emssons of RET systems and buldngs Dr PAAIOTIS PHILIMIS Dr ALESSADRO GIUSTI Dr STEPHE GARVI CE Technology Center Democratas
More information