The new concepts of measurement errors regularities and effect characteristics

1 The new conce pts of m easurement error ’ s regularities a nd effec t characteristic s Ye Xiaomi ng[1,2,  ] L iu Haibo [3,4] Xi ao Xuebin [ 5] Li ng Mo[3] [1] School of Geodesy and Geomatics, W uhan University , W u han, Hubei, China, 430079. [2] Key Laboratory of Precision Engineering & Industry Surveying, State Bureau of Survey ing and Mapping, W uhan, Hubei, China, 430079 [3] Institute of Seismology , China Earthquake Administration , W uhan, Hubei China, 430071. [4] W u han Institute of earthquake metrological verification and measurement engineering , W uhan, Hubei China, 43007 1. [5]Wuhan University Library. Wuhan, Hubei, China 430079. Abstract: In several literatures, t he authors give a new thinking of m easurem ent theory syst em bas ed on error non-clas sification phil osophy , which com pletely overthr ows the existing measur ement concept sy stem of precisi on, trueness and accuracy . In this paper , by focusing on the issues of error ’ s regularities and ef fect charact eristics , the authors will do a them atic interpretat ion, and prove th at the error ’ s regularities actually come from different cognitive perspectiv es, are also unable to be used for clas sifyi ng err ors, and t hat the error ’ s ef fect charact eristics actuall y depend on artifici al condition rules of repeated meas urement , and are s till unable to be used for classifyi ng errors. Thus, from the perspe ctives of error ’ s regularities and eff ect characteristics, the existing error classifi cation philosophy is still incorrect ; and an uncer tainty concept system, which must be interpreted by the error non-cl assification philosophy , naturally becomes the only way out of measur ement theory . Key words: measurem ent error; function model ; random model; error’ s regularities; uncertainty . 1. Introduction In se veral literatur es [ 1 ] [ 2 ] [ 3 ], the authors give a new t hinking of measurement theory system bas ed on error non-clas sification philosophy . The main logic of this thinking is briefly introduce d as follows: The concept of error is defined as the dif ference between the measurement result and its tru e value. Because the measurem ent result is unique, and the true value is also unique, so the error of the meas urement result is the only unknown and co nstant devi ation. For a final m easurem ent result, th e co nstant deviation consists of two parts: 1, the de viati on A  between the final measur ement result and mathem atical expectation, which is the so-called random error in existing the ory; 2, the dev iation B  between mathematical expectat ion and tru e value, which is the so-call ed systematic error in existing theory . Because both deviations are unknown and persist constant deviations, and do not have any difference in charact eristics, therefore, having no charact eristi c dif ference m ust not cause any classi fication dif ference! The standard dev iation of dev iation A  is given by the statisti c and analysis of current measur ement data. The deviation B  is also produced by meas urement ; its formation principle is actually the same as the current m easurement ; its standard deviation can be obtained by tracing back to its upstream m easurement. Thus, the standar d deviati on of t otal error of final measurem ent result is equal to t he synthesi s of the two standard dev iations according to t he probability laws. Th is tot al standard deviation is uncertainty , which is the evaluation of the probable interval of the error of final measur ement result (this give a m ore clear m eaning to the uncertai nty concept). This constant deviati on theory is compl etely opposite to th e random variation theory of existing measur ement theory , that is, in the opinion of the autho rs, it is obviously illogical that existing measur ement theory interpret deviation A  as precision but interpret devi ation B  as trueness, and the error classificati on de finiti on and all the concepts of precision, trueness and accu racy should be abolished. For exampl e: in 2005, the Chinese survey ing and Mapping Bureau gave that the elevat ion result of Mount Everest is 8844. 43 meters wit h standard dev iation of ± 0.21 meters. Accordin g to existing err or classifi cation t heory , from the perspe ctive of error’ s definition, th e error of this r esult  xmye@sgg.whu.edu.cn 2 is a single constant deviation and should be classified as system atic error; however , from the perspectiv e of standard deviation ± 0.21m, it should be classifi ed as random error . This is the logical t rap of exist ing error classifi cation theory . And the i nterpretat ion, accor ding to error non- classifi cation theory , is that this result' s error (t he differ ence bet ween the result and the t rue value at impl ementing measurem ent) is an unknown co nstant, and that the standard deviati on of ± 0.21m is only the evaluat ion of the probable interval of the unknow n constant error . That' s it. The dif ference b etween the n ew theory and the exi sting theory is shown in F ig1. Please note that the authors ’ emphasize on the concept of constant dev iation i s to focus on the measur ement result instead of the original observation value s before forming final measurement result. Of course, the author s recognize that there may be indeed a discrete error sample sequence before the m easurement r esult is form ed. However , these discrete error sa mples , w hich have certai n numeri cal value, are the measured values of errors. Th ey belong to the measurem ent result, and naturally cannot be mi xed with the unknown error of final result to discuss the error classification. In addition, the dispersion and deviati on of error sampl e sequences actually depend on the conditions of repeat ed m easurem ents ( Circuit noise i s also a condition) , natural ly cannot be used to prove that the error can be cl assifi ed. The core difference betw een the two theori es is, the existing theory considers that t he er ror can be classifi ed into s ystem atic error and random error , while the new theory holds that the error has no systematic and random classificati on. Alt hough document [1] has mentioned that the regularity and influence charact eristics of errors cannot be used for classi fying errors, the relationship between regularity and randomness, the formation m echanism of error ’s infl uence character istics and related applications have not been interpret ed in detail. Therefor e, this paper will make a detailed interpretat ion on the regul arity and influence charact eristics of error . 2. Error’ s regularity The concept of error is the dif ference between the m easurem ent result and its true value. The error m ust be a constant deviati on, that is to say , any si ngle error is a constant . The task of m easurem ent theory is t o study the methods of reducing and evaluating error . Fr om the unknown and constant characteri stics of single error , th is task naturally faces difficulty . Howev er , before the final measurem ent result is formed, our measurement is usually repeated, and there will be many error samples. When we observe a group of error samples, the errors can show some regularity , including certain regularity and random regulari ty . This prov ides paths for reducing and evaluat ing error : by certain r egularity we can design some methods for compensating and correctin g Existing measurement theory New concept theory After adjustment, the difference between the measurement result and the mathematical expec tation is in random variation , and is discrete. After adjustment, th e diff erence between the measurement result and the mathematical expectation is also a constant, and isn’ t discrete. The systematic error is certain regularity , the rando m error is random regularity , and the two kinds of errors have co mplete diffe rent characteristics. Both so -called sy stematic error and so -called random error are constant deviation , have no diff erence in characteristic , and should not be classified. The total error can only be eva luated with p recision and trueness, and th e precision and trueness cannot be synthesized. Precision, tru eness and accuracy are abandoned, a nd the to tal erro r is evaluated by uncertainty . Fig1. The com parison of two theory ’ s logic 3 error; by random regulari ty we can design the statist ic method for reducing error and obtain the evaluat ion method of err or . That is, the issue of error ’ s regularity is actually a imed at a group of error samples before the final meas urement result is obtained, instead of single error after the final m easurement result is obtained. However , it is important to note that the error’ s certain regularity and random r egularity are actually fro m differ ent perspectives. They are di f ferent error processing methods, and naturally can not be used to achiev e error classi fication. The sam e ki nd of er ror can be processed according to certain regularity , and also ca n be processed a ccording to random regulari ty . There is still not err or ’ s classifi cation issue according to certain regularity and random regulari ty . These are also the ideas from the new theory , which is total ly dif ferent f rom the existing m easurement theory . For example: the measured frequency v alues of a quartz cr y stal at di f ferent temperatures are shown in T able 1. According to T able 1, to observ e the error values alongside the temperature values, w e ca n get the cer tain regular ity as shown in Fig2. However , the error value is observed alone, we can get random regular ity as shown i n Fi g3. That is to say , corresponding to the temper ature values to observe the error values, we see the certain regul arity ; viewing the temper atures as arbitrary and only observing the error’ s distr ibution, we see th e random regul arity . Naturally , there are two ways to deal with it in practice. 1, Random model proces sing: Error equation: 0 f f v i i   According to the least square method, the final m easurement result is : MHZ n f f n i i 0 5 0000 . 5 1 0     Its standar d deviati on ： 0 6 1 2 10 8 . 15 1 f n v n i i f           That is, the frequency value of the quartz crystal is 5.000050MHZ, and its standard deviation (in the temperat ure between -40 and 100 degrees) is ± 15.8 × 10 -6 . This ex presses that the actual error of the freque ncy v alue exist s in a probability interval with standard dev iation ± 15.8 × 10 -6 at arbitrary temperat ure between -40 and 100 degrees. 2, Funct ion model proces sing : The functi on model of t emperature- frequency error is 3 2 dT cT bT a R     . Error equation: 3 2 i i i i i dT cT bT a R v      According to t he least square met hod, there is                                                               3 2 6 5 4 3 5 4 3 2 4 3 2 3 2 i i i i i i i i i i i i i i i i i i i i i i T R T R T R R d c b a T T T T T T T T T T T T T T T n Substituti ng the values in T able 1 in to above equ ation, th ere are: T able 1. T he me asured frequency va lues of a quartz crystal at diff erent temperatures T emperature ˚ C Frequency MHz Error value ) 10 ( / -6 0    f f R i i - 40 ° 4.999900 - 30 - 30 ° 4.999975 - 15 - 20 ° 5.000040 -2 - 10 ° 5.000085 7 0 ° 5.0001 15 13 10 ° 5.0001 10 12 20 ° 5.000070 4 30 ° 5.000035 -3 40 ° 5.000010 -8 50 ° 4.999995 - 11 60 ° 4.999995 - 11 70 ° 5.000010 -8 80 ° 5.000045 -1 90 ° 5.000125 15 100 ° 5.000235 37 4                                             42713000 304500 4610 1 000 1983295000 0 2195250000 256870000 292500 0 2195250000 256870000 2925000 41500 256870000 2925000 41500 450 292500 41500 450 15 d c b a Solving t he equations, get: . 0 .0 00 21 4 , 0 .0 1 8 6 01 0 .0 13 51 8, , 1 9 . 9 8 3 25       d c b a Therefore, t he frequency error’ s funct ion model is fitted as: 3 2 0 .0 00 21 4 0 .0 18 60 1 0 .0 13 51 8 9 .9 83 25 1 T T T R     Fig4 is t he compar ison curve between t he model and the actual error . The standard dev iation of residual error is 6 1 2 10 3 . 2 4          n v n i i R  Finally , the frequency of quartz cry stal is giv en as follow s: ) 10 1 ( 6 0     R f f That is, temperatur e-frequency error can be corrected by the measurement value of temperature sensor , and a m ore accurate frequency v alue can be cal culated. Resi dual err or (as shown i n Fi g5) is still processed by statistical rules, and the standard deviati on of the residual error is reduced to ± 2.3 × 10 -6 . This error process ing m ethod has been widely used in the manuf acture of photoel ectric geodimet er [ 4 ][ 5 ] . Note that, although th e effec t of random model is not as good as the fun ction model, it does not mean that the random model processing method is incorrect! In fact, at above function model processing, the final resi dual error (F ig 5) is st ill processed by r andom m odel. However , it can be seen from t he F ig 5, the residual error is act ually st ill a regular error r ather t han w hite noise, and has Fig2.The temperature-frequency error of quartz crystal Fig4.Frequency error curve fitted by function model Fig5.The residual error ’ s curve Fig3.The frequency error ’ s distribution 5 no essential di f ference wit h F ig 2. Another example, the cycle error of the phase type photoelectri c geodim eter [4][5] shows periodic function regularity with distance. Its function model is:  si n A y  , but when the phase  is regarded as ar bitrary , its probability density f unction is :              A y A y y A y f 0 1 ) ( 2 2  Its standar d deviati on is : 2 A y   It can be seen, when relati ng er ror y with phase  to observe, the err or show s sine regularity ; when the phas e  is view ed as arbitrary , t he sine cy cle error is also to fol low a random distribut ion. T able 2 is the testing data of an instrument. B y the data of T able 2, the cycle error ’ s function model is fitted as ) )( 41 . 254 360 20 sin ( 7 . 5 mm S y      (see Fig6). Naturally , as shown in Fig7, its probability density function is:              mm y mm y y y f 7 . 5 0 7 . 5 7 . 5 1 ) ( 2 2  That is to say , to observe by relating the distance with the error value, we see the c y cle regularity ; viewing the distance as ar bitrary and only observing error dist ribution, we see a random regulari ty . Naturally , in practice, there are also two m ethods t o deal with it. 1 ． Random m odel processing: T able 3 is the simul ation data of using the cycl e error ) )( 4 2 20 sin ( 5 mm S y      under the measur ed distance S BC =8.0000m , and sim ulated the 15 groups distance dif ference data r andomly and arbitrar ily . Error equation: 0 2 1 S S S v i i i    According t o the least square method, the final measur ement result is : T able 2. The testing data of cycle error of a geodimeter Standard distance (m) Measured distance (m) Error value (mm) 1 6.0237 6.0232 0.5 2 7.0239 7.0228 1.1 3 8.0243 8.0204 3.9 4 9.0246 9.0187 5.9 5 10.0250 10.0183 6.7 6 1 1.0253 1 1.0178 7.5 7 12.0256 12.0196 6.0 8 13.0258 13.0213 4.5 9 14.0263 14.0232 3.1 10 15.0266 15.0261 0.5 11 16.0269 16.0270 -0.1 12 17.0269 17.0284 -1.5 13 18.0269 18.0287 -1.8 14 19.0 268 19.0307 -3.9 15 20.0267 20.0325 -5.8 16 21.0268 21.0320 -5.2 17 22.0269 22.0320 -5.1 18 23.0269 23.0305 -3.6 19 24.0270 24.0290 -2.0 20 25.0271 25.0277 -0.6 21 26.0272 26.0272 0 Fig6.The function model fitting of cycle error Fig7.The cycle error ’ s d istribution ) ( 0014 . 8 ) ( 1 2 1 0 m n S S S n i i i      6 V isible, the error i s only 1.4 mm , less than the am plit ude of the cy cle error . 2 ． Funct ion model processing : The function m odel of cy c le error is:      2 20 c o s 2 20 sin ) 2 sin (        S b S a S A y The error equat ion is: 0 2 1 2 1 2 1 0 2 2 1 1 ) 2 20 c os 2 20 (c os ) 2 20 sin 2 20 (sin ) ( S S S b S S a S S S y S y S v i i i i i i i i i i i                     M ake . 2 20 c o s 2 20 c o s , 2 20 sin 2 20 sin , 2 1 2 1 2 1               i i i i i i i i i S S B S S A S S S The error equat ion becom e into: 0 S b B a A S v i i i i     According to t he least square m ethod, there is:                                           i i i i i i i i i i i i i i i S B S A S b a S B B A B B A A A B A n 0 2 2 Replace the data in T able 3 in to above equat ion:                                19.2 4404 29.2 2612 120 .021 4 26.4 4747 3.44 106 - 2 .395 34 3.44 106 - 27.8 3084 3.642 49 2.39 534 3.6424 9 15 0 b a S There are: 00353 . 0 , 00353 . 0 , 0 0000 . 8 0    b a S In this way , the am plitude of the cycle error is ) ( 00499 . 0 2 2 m b a A    , and its phase is 4 a rc t a n     b a . It can be seen, regular err or follows random distribution, can be processed according to function model, and also can be processed according to random m odel. Although t he ef fect of function model is actually better than the random model, the premi se of using function model is that the function model is known. I f the function model is unknown, we naturall y think its regularity is an “ unpredictable manner ” , and use the random m odel to process it. In the practice of measurem ent, it i s a com m on fact that one or m ore re gular errors are processed according to random model , and t he so- called random regul arity is m ore because their certain regul arities ar e ignored or unknow n. For exampl e: besides the c y cle error , the mult iplicativ e constant error of photoelectric geodimet er [4][5] , which is the residual error after temperature corrected, is still the function of temper ature(see F ig5), and call ed as system atic er ror by exist ing theory , but processed accordi ng t o random m odel inst ead of tem perature funct ion model in traverse sur vey [ 6 ] . Another exam ple: in the lev el [ 7 ][ 8 ] , the i angle err or , cross e rror , com pensation error , focusing error , and so on, are the regular errors, and called the s y stematic error b y existing theory , but processed ac cording to ra ndom model in lev eling network m easurem ent [ 9 ] . Another example: steel ruler’ s thermal expansion er ror , watch’ s running error , gauge nom inal value’ s error , a lso are the regular errors, but manufacturers usually only give these equipment’ s maxim um permissible error (MPE) or total standar d devi ation indicator , which is actually also the T able 3. T he sim ulation data of using cycle error S AB (m) S AC (m) S 2 = S AB +y AB (m) S 1 = S AC +y AC (m) 1 10 18 9.9965 18.0008 2 12 20 1 1.9951 20.0035 3 33 41 32.9951 41.0045 4 27 35 27.0008 34.9965 5 22 30 22.0049 29.9965 6 28 36 27.9992 35.9977 7 30 38 29.9965 38.0008 8 36 44 35.9977 44.0045 9 38 46 38.0008 46.0023 10 26 34 26.0023 33.9955 11 34 42 33.9955 42.0049 12 16 24 15.9977 24.0045 13 18 26 18.0008 26.0023 14 19 27 19.0023 27.0008 15 42 50 42.0049 49.9965 AC 0 - AB 0 = 8.0000 7 random m odel process ing. Although these error handl ing methods in all the above cases already exist in measurement practice, it is clear that using random model to deal with the se regular errors is obviously contrary to the concept logic of existing measurement theory . Thes e also show that the conceptual interpretat ion based on the error classification in existing theory does not conform to the actual measur ement. When discussing random reg ularity , we hav e t o di scuss t he el ectronic noise (whit e noi se or 1/f noise), which is a random function of tim e and is an unavoidable error source in the field of electronic measurement , although m ost of measur ements actually have no physical mechanism of electronic noise error . Because of having not mastered its regularity , the electroni c noise error can only be proces sed with rand om model. What is wor thy of noting is , in the actual measurement , because the random ness of var ious process conditions drives one or more regular errors (also m ay include elect ronic noise) to random ly change , er ro r sam ple seque nce also shows random di stributi on (is similar to noise ’ s random distribut ion). However , these discr ete error sam ples aren ’ t the random funct ion of time, because th e finish of m easurem ent data col lection has f ixed all the measur ement data, an d all the dat a are unable to change with time. That is to say , after the data processing is compl eted, the error of final measur ement result is unable to contai n a component which randomly changes with time, and the contributi on of noise to the fi nal res ult ’ s error is al so a constant dev iation. That is, except the function model cannot be used, the electr onic noise has n’t any essential particular ity , and through white noise concept considering the error of final measurement result as random funct ion of tim e is a m isunderstandi ng. In short, the error ’s regularity is an observation ef fect through observing a group of error sampl es instead of a single error; error ’ s variati on is certain ly associated with the variations of measur ement condition, and th ese measurement conditions are temperatur e, measurement range, instrum ent, time, location, l eveling, sighting, electronic noise and so on; error ’ s certai n regularity and random regularity are observat ion results from different perspectives, they have no mutual excl usion, and ta king regul arit ies to achiev e error classificat ion is si mil arly im possible. I t is obviously i nappropriate that VIM [ 10 ][ 11 ] takes “ predict able manner ” and “ unpredictable manner ” to define the er ror classif ication. 3. Error' s effect characteri stics The new theory cons iders error has no sy st ematic and random classification. It refers to that the error has no dif ference whether it follows random distri bution, but does not negative error can produce system atic or random effect s . The err or ’ s effect ch aracteristics and erro r ’ s random distribut ion are two differ ent things: following random distr ibution refers to that the error exists in a finite pr obable interv al, but syst ematic or random ef fects refer to t hat the error sour ces contribute deviati on or dispersi on to subsequent repe ated m easurement. See T able 4. It can be seen, the core of the existing systemati c error concept is that it does not follow random distribut ion, but the new theory stresses that any error follow s a random di stributi on and t hat th e T able 4. The comparison of concept of two theories Current theory The new conce pts theory Error is classi fied as sy stematic err or and random er ror . Error cannot be classifi ed according t o system atic and random way . The sy stematic er ror does not fol low random distribut ion, and the random error follows random di stributi on. Any err or follows a random distr ibution. Random distribut ion is random variati on. Random distribut ion is that the error is in a finite probabl e interv al instead of rand om variation. System atic error cont ributes sy stematic ef fects (contr ibu te deviati on), and random error contri butes random ef fects (cont ribut e dispersion). The error ’ s sy stematic or random ef fects depend on the v ariation r ules of m easuring conditions i n repeated m easurem ents. The sy stematic er ror is certain regularity , and the random error is random regular ity . The error ’ s regularity depen ds on the perspectiv es of observ ation, and the err or can show vari ous regularit ies. 8 error’ s sy stematic ef fect is compl etely dif ferent f rom the concept of e xisti ng system atic error . Just as important , the error ’ s system atic or random effect depends on the variation rule of the measur ing conditions in the repeated measurement s, which is a ctually another angle of the error’ s regularity issue. In the cas e of quart z cry stal’ s frequency , the frequency error v aries with the temperature, so the temper ature is the related measurement condition. If the repeated measurem ents are in constant temper ature, temper ature - frequency error will remain unchanged, produc e sy stematic ef fects, and not dri ve t he observ ation sequence disper sion ; if the repeated measurements are in dif ferent temper ature, temperature - frequency error will change, produce random ef fects, a nd drive the observati on sequence di spersion. In the case of the photoelectric geodim eter [4][5] , the cycle error is the periodic function of distance, so the distance is the related measur ement condition. If repeated measur ements are in the same dist ance condition, the cycle error wil l remain unchanged, pr oduce sy stematic ef fects, and not drive the observ ation sequence dispersion; if repeated measurem ent is in diff erent distance condition, the cy cle error will change , produce the ra ndom ef fects, and driv e the observati on sequ ence dispersion. (Such as T able 3) . Moreover , besides system atic and random ef fect character istics, error also has the characteri stic of non- ef fect. For example, using the different ial m ethod to m easure dist ance (as show n in T able 3) , the additiv e constant error of photoelectric geodimeter [4][5] has no effect to the observ ations i i i S S S 2 1   . Also, all the errors, which have no intrinsic ph y sical relation with the observation, are unable to affect the observation. For example: the error of instrument A can not af fect the observati on of instrum ent B. Hence , the error ’ s systemat ic and random effects or observati on sequence’ s deviation and dispersion depend on the chang ing rules of repeated measurem ent conditions. T emperat ure , measur ement range, instru ment , time, locations, leveling, even circuit noise, and so on, are measur ement conditions. The sam e error can produce systematic effect s in a repeated measurements, also can produce rand om ef fects i n another repeated measurem ent, and even ca nnot pr oduce ef fect. Naturally , using ef fect char acteristi cs to classi fy error i s still im possible. And it is a mistake that existing t heory equate t he error ’ s ef fect charact eristics with the error’ s classi fications. 4. The ne w interpret ation of uncertaint y concept Because the exist ing uncertai nty [ 12 ] [ 13 ] [ 14 ] concept sy stem accepts the er ror classificat ion philosophy and uncertainty ’ s defini tion clearly expresses the m eaning of "di spersion", m any people naturally understand it as being similar to precision. This kind of uncertainty , i s neither fish nor fowl of course, nat urally causes controv ersy [ 15 ] . Now , any regular error follows a r andom distribution and has its standard dev iation. The theory of error classifi cation is overthrown. Naturally , the concepts of precision, trueness and accuracy must be abolished, and an uncertainty concept sy stem, which must be interpreted by the error non- classifi cation philosophy , has becom e the only way out of m easurem ent theory . The total error of measurement result is a constant deviation and has no classifi cation. Its numeri cal v alue is unknown, and u ncertain. The unknow n and u ncertai n degree of error ’ s num erical value is the uncertainty , which is expressed by the eval uation of the probable interv al of error . Because the total error com es from the synt hesis of many error sources according to al gebraic law , the total standard deviation is equal to the synthesi s of standard deviations of all the sour ce errors according to the co va riance propagation l aw . Further , because the num erical v alue of m easurement r esult is certain and the numer ical val ue of error is uncertain, the unc ertainty also expresses the uncertain degree that the true val ue cannot be determ ined. Uncertainty is the ev aluation value of the probable interval of the error of m easurem ent result, and express es the degr ee th at the tr ue value cannot be de termined or the probabl e degree t hat the measur ements result is close to the true value. This is the new interpretation of the uncertainty concept. In some cases, the variation of the true value in the future and the ambiguity of the true value definiti on also should be considered as the error probl em, thus, a broad under standing of uncertainty is giv en. A sim ple example f or com paring : T he indication error o f photoelectric geodimeter [4][ 5] consists of the additive constant err or C , the multipli cative constant error R , the periodic error P , 9 and the divi ding error δ , w hich are all residual errors after being processed by instr ument. Now , the distance value given by the instrument is S . So, how does the error of the measurem ent result be evaluat ed? 1, According to the traditional error classification thinking, additive constant error C is a constant regular ity , mult iplicativ e cons tant error R is prop ortional regul arity and is also a non-l inear regularity of temperature (Fig5), and periodic error P is sine regularity , so they are a ll systematic errors. Only the regular ity of the dividing error δ is not clear , w hich belongs to the random error and has its standard deviation ) (   . Therefore, the precision of measurement result S is ) (   and express the dispersion of final measurement result, and the systematic errors C , R and P have no standard deviation, express the trueness of measurement result, which belongs to the category of qualitativ e evaluat ion. However , because the uncertainty in the existing theory is also defined as dispersion, then what is the dif fer ence between uncertainty and precision? It is cl ear that thi s cannot be expl ained. 2, According to the concept logic of the new theory , the error of final measurement r esult is from t he superpositi on of four devi ations of C , S R , P and  , and the err or equati on is        P R S C Because error has no classification and any error has its standard deviation, according to the covariance pr opagation law , the uncertai nty of measurement res ult is ) ( ) ( ) ( ) ( ) ( 2 2 2 2 2            P R S C Among them , C, R, P and δ ar e all unknown error s, and thei r standard dev iations are obt ained by consulti ng the product specification of the instrument . The uncertainty ) (   is the evaluation value of t he probable inter val that error  exists. 5. Conc lusion The single error of any fi nal measurem ent result is const ant regularity , and error classifi cation can not be achieved by the same constant regularity . Although a group of error samples can show some certain regularity and random regularity , ce rtain regularity and random regularity are observati on result from dif ferent perspecti ves and also cannot be use d f or classi fying error . Because error ’ s effect characteristics only depend on the variation rule of the m easuring conditions in repeated m easurement s, and the sam e kind of err or can show various kinds of eff ect characteristics , using ef fect char acteristi cs to classify error i s still im possible. From all the perspectives, including single err or ’ s constant characteristic , the variation regularity of a group of error samples , and error ’ s effect char acteristi cs, classifying error can no t be realized. Naturally , the concept logic system of precision, trueness and accuracy of bas ed on error classifi cation theory shall com pletely collapse, and an uncertainty concept system , which must be interpreted by the error non-classi fication philosophy , has becom e the only way out of m easurement theory . T aking the sam e conditi ons in repeated measurem ents will make all the source er rors to remain constant, hence cannot make error to be reduced. By appropriately changing the relev ant measur ement condi tions i n repeat ed m easurement s, any error can be m ade t o contri bute dispersion . Thus, error reducti on can be realized by function model or random model processing, and the evaluat ion of probable int erval of error al so can be obtain ed. Uncer tainty is the evaluati on value of the probable int erval of the error of m easurement result, and express es the probable degree that the final measurem ent result is c lose to the true value. This is the new interpretation of the uncertainty concept. Reference: [ 1 ]. Y e Xiao-ming, Xiao Xue-bin, Shi Jun- bo , Ling Mo , T he new concepts of mea surement error th e ory , Measurement, V olume 83, A pril 2016, Pages 96 – 105 [ 2 ]. Y e Xiao- m ing, Ling M o, Zhou Qiang, W ang W ei-n ong, Xiao Xue-bin, The New Philosophical V iew about Measurement Error Theory . Acta Metrologica Sinica, 2015, 36(6): 666-670. [ 3 ]. Y e Xiao- m ing, Errors Classification Philosophy Critique [C]// Proceedings of National Doctoral Forum on Surveying and Mapping. 201 1 [ 4 ]. JJG703-2003, Electro-optical Distance Meter (EDM instruments) [ 5 ]. ISO 17123-4:20 12, Optics and optical instrume nts -- Field procedures for testing geodetic and surveying instruments -- Part 4: Electro-optical distance meters (EDM measurem ents to reflectors) [ 6 ]. CH/2 007-2001 , Siecifications for the third and fourth order traverse [ 7 ]. G B10156-1997 ， Level. (1997) 10 [ 8 ]. 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