Available online at ScienceDirect. Procedia CIRP 43 (2016 ) th CIRP Conference on Computer Aided Tolerancing (CAT)

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1 Available online at ScienceDirect rocedia IR 43 (06 ) th IR onerence on omuter Aided Tolerancing (AT) Develoment and Standardization o Quality-oriented Statistical Tolerancing in hina Yu Zhang a * Wenlong Lu b a ollege o Mechanical Engineering, Shandong University o Technology, Zibo, 55049,hina b School o Mechanical Science and Engineering, Huazhong University o Science and Technology, Wuhan, ,hina * orresonding author. address:zhangyu_sdut@sdut.edu.cn Abstract The develoment o the quality-oriented statistical tolerancing (ST) technique and its standardization in hina are briely introduced in this aer. Based on the new develoment in the academic area o geometrical roduct seciications (GS) and statistical rocess control (S), it is out that the ST technique must be innovated and imroved to ace the challenges o the modern manuacturing environment. The rincile o quality-oriented ST and the mathematical models are given. A set o standardized rocess quality indices (QIs) or evaluating the nonconorming o rocess, rocess centring and quality loss has been resented. This evaluation system based on QIs and the standardized two-dimensional interace relative to the rocess mean and the standard deviation o rocess has relatively strong comatibility and adatability with the rocess caability analysis and S that are widely alied in the modern manuacturing environment. The standardized QIs may also be used as a art o oulation seciications. The serial ST standards ublished by the standardization committee o hina and their main alications with a case study are introduced, and are exected to lay imortant roles or assuring the designated dimensional seciications and oulation seciications with reset conidence interval. 06 The Authors. ublished by Elsevier B.V. This is an oen access article under the BY-N-ND license 06 The Authors. ublished by Elsevier B.V. (htt://creativecommons.org/licenses/by-nc-nd/4.0/). eer-review under resonsibility o the organizing committee o the 4th IR onerence on omuter Aided Tolerancing. eer-review under resonsibility o the organizing committee o the 4th IR onerence on omuter Aided Tolerancing Keywords: statistical tolerance; oulation seciication; rocess quality; statistical rocess control; standardization; concurrent design Introduction o statistical tolerancing. A brie introduction o statistical tolerancing Statistical tolerancing is based on the ollowing observation: when comonents are made by roerly controlled rocesses, the actual values o most dimensions lie near the centre o their tolerance zone. Statistical tolerance (ST) is a seciication on oulations o comonents. It seciies what oulations o comonents are accetable and what oulations are not accetable. ST is alicable when mass roduction o arts is involved. The outut o mass roduction o arts can be 00% measured or samling insected, and the oulation arameters can be estimated rom the data. Although statistical methods have been introduced into tolerance design [], and S technology has been alied in manuacturing rocesses or many years, there are ew alications in relative tolerance and dimensional chain standards. As early as the 960 s, IBM established a statistical tolerance standard o their comany or romoting the alication o statistical technique in tolerance design. The basic statistic rincile was alied or describing and redicting the relationshi between the standard deviation o closing link and that o comonents o the dimensional chain. Traditional ST design or dimensional chain has an assumtion that there should be no any shit o rocess mean to its target, which is a very restriction and unreasonable in ractice. Evan or the 6σ quality level, rocess mean may have.5σ shit to its target. The irst serious national standard o statistical tolerance was issued in 974 by West Germany. A similar statistical dimensional tolerance standard was roosed in 987 by hina (JB/Z ). The main eature o those two standards is that the tolerance interval is divided into three The Authors. ublished by Elsevier B.V. This is an oen access article under the BY-N-ND license (htt://creativecommons.org/licenses/by-nc-nd/4.0/). eer-review under resonsibility o the organizing committee o the 4th IR onerence on omuter Aided Tolerancing doi:0.06/j.rocir

2 Yu Zhang and Wenlong Lu / rocedia IR 43 ( 06 ) zones and the designer can seciy the requirements to the relative requencies o dimensions alling into each zone at design stage, as shown in igure. However, there was no urther instruction on how to decide the reset values and how to assure the reset value in the two standards. Thereore, they were not widely adated. The U.S. national standard (ASME Y4.5M-994rovides a symbol in drawings to indicate those dimensions to be controlled statistically. It rovides no urther semantics []. manuacturing have been widely alied, many international manuacturers hoe to achieve a new quality level, i.e. to make quality characteristics to their design target values with maximum extent, and the ailure rate at the arts er million [M] level. It is a challenge and chance to develo and imrove existing ST and S aroaches or the needs o excellent quality. lower zone L (max) c (min) Uer zone u (max) (a) a ST zone in k- lane k (b) a ST zone in lane entre LSL USL zone Fig. Tolerance zone division and the required requencies in each zone based on DIN 786 and JB/Z (hina) To estimate whether a rocess meets the seciication limits, rocess caability indices (Is) are widely alied. Many authors have romoted the use o various rocess caability indices and examined with diering degree o comleteness their associated roerties. Kane (986) comletely deinite rocess caability index and k [3]. hang, heng and Sring (988) resented and discussed roerties o m that is an alternative measure consistent with Taguchi s deinition o quality [4]. Boyles (99) comared and analysed the statistical roerties o k and m [5]. ISO/T3 had set u a task grou (WG3) toward international ST standard beore 995, and some valuable eorts or ST and ST zone indications had been done [6]. Srinivasan and O onnor summarized our ways o deining ST zones that are seciied in the k - lane, lane, lane and a normal robability aer resectively [7], as shown in igure. Each way has advantages and limitations. (a) is not desired reresentation orm because k does not only indicate the rocess shit; (b) and (c) are not suitable to be the standardized interace as and have certain hysical measure and meaning; (d) cannot be directly derived into S arameters. As Voelcker H.B. (997) ointed out, today there is growing use o untidy (to the academic mind) mixture o statistical tolerancing notations, statistical rocess control notations, and Taguchi quality-unction notations [8], it is necessary to develo an interace among ST, S and the quality loss unction. Zhang, Low and Fang (998) develoed I-based tolerance that can be used as an interace between design seciications and S to achieve redictable quality assurance [9]. With the Six Sigma quality, lean roduction, S technology and intelligent (c) a ST zone in lane r (x X) 0. Fig. Four tyes o ST zones In the ISO language o Geometrical roduct Seciication (GS), there has been recent work in the develoment o syntax or oulation seciications. This work has culminated in the drat standard DIS 839. It is clearly delineated in DIS 839 that this international standard in not intended to deine a tolerancing method. Its intent is to deine tools allowing the exression o needs coming rom dierent sources (designer, manuacturer and insectors, etc.) [0]. A systematical concurrent design aroach to meet the needs or realizing and assuring the seciied oulation seciication is necessary, esecially ater ublishing o ISO/GS standard on oulation seciication.. Further research and standardization eorts or statistical tolerancing The standardization o ST on GS is involved with rocess quality indices (QIs), the indication o ST zones, the standardization o ST values, the conidence intervals o ST, and it includes the STs in both comonent level and assembly level. Thereore, it s a systematic engineering that needs a comlete lan based on the requirements o enterrises aiming at excellent quality. The researches on X (d) a DF ST zone lotted in a normal robability aer

3 70 Yu Zhang and Wenlong Lu / rocedia IR 43 ( 06 ) the standardization o ST have been done in the ollowing way: to combine statistical method and theory with industrial racticable techniques, and to combine S concets with innovation on ST. There are three research achievements in the world which can be reerred to: the researches on rocess caability analysis and Is; the researches on S and quality engineering; the researches on GS and ST. Further research and international standardization eorts or statistical tolerancing are as the ollowing our asects: () to develo a set o international standardized quantitative reresentations o rocess quality; () to develo an international standardized reresentation o ST zones that can be quantitatively indicated in terms, grahs and tables to realize and assure seciied rocess quality; (3) to develo a ST design aroach based on given conidence; (4) to develo a concurrent design method via quality-oriented tolerancing and the database or it quality and rocess quality. On the basis o our early research named qualityoriented statistical tolerancing technique (the rogram o NSF, i.e., the national natural science oundation o hina) [-4], a new ST design method or assuring both comonent and assembly quality had been resented. Its main oints are discussed in section. A brie introduction to the general rame o the serial GS standards o ST that are based on the quality-oriented statistical tolerancing technique is resented in section 3. To illustrate the main alications o the serial ST standards, a case study is introduced in section 4. Develoment o quality-oriented statistical tolerancing The main oints o the quality-oriented statistical tolerancing technique are introduced as ollows:. rocess quality indices (QIs) and rocess caability indices I The raction deective o rocess outut has long been the rocess quality level and it is still widely alied in the manuacturing industry. Let d be the symbol o raction deective, it deends on the distribution o rocess outut, and it is relative to manuacturing cost. Let c indicate the raction o rocess outut in the middle one third zone o tolerance, and ql indicate the raction o average quality loss o rocess outut. c and ql are relative to rocess centering erormance. The ormer emhasizes articularly on rocess centering while the latter emhasizes articularly on the well-known concet o quality loss introduced by Taguchi [5]. For mass roduction, we concern the average quality loss o rocess outut. The Taguchi method emhasizes that closeness to target is much more imortant than low nonconorming rates. Thereore, rocess centering exressed by c and ql is more imortant than conormance to seciication or quality imrovement. A set o standardized QIs or evaluating the nonconorming o rocess, rocess centering and quality loss has been resented based on reasoned grading by using the series o reerred numbers and the arithmetical rogression. This evaluation system based on QIs and the standardized two-dimensional interace relative to the rocess mean and the standard deviation has relatively strong comatibility and adatability to S. The objective o rocess quality evaluation is the quality characteristic o a comonent lot that is being manuactured or has been manuactured. The ollowing QIs are all the unctions o the oulation arameters o the rocess outut based on the assumtion that the rocess is in a controlled state that means the rocess outut obeys normal distribution. As the oulation arameters are not standardized arameters, it is necessary to select some suitable standardized arameters as the relative arameters with the oulation arameters. Two rocess caability relative variables, i.e. and k, are such arameters. k is deined as rocess shit actor. Tg k ( USL LSL) / where Tg is target value, USL and LSL are the uer and lower seciication limits resectively. QIs and Is can also be exressed as the unctions o and the standardized rocess shit, T g To estimate whether a rocess meets the requirements, rocess caability analysis is widely alied. k and m are currently widely used Is in ractice. As most rocesses are quite comlex, any single number is unlikely to adequately summarize all ertinent inormation about rocess erormance. Thereore, Is are only indirect and incomlete reresents o rocess quality.. Quality-oriented ST zone in two-dimensional lane QIs and Is are all the unctions o two variables, and k, i.e., (, ) d k, (, ) c k and (, ) ql k. The comutation ormulas o QIs and Is in terms o and k are listed in Table. Table QIs and Is in terms o and k QI omutation ormulas d d = { [ 3 ( k)] + [3 ( k)] } 00 % c T c ( M ) [ ( 3k)] [ ( 3k)] 00% 6 ql ql [ k ] 00% (3 ) k k ( k ) m m 6 3 k Quality-oriented ST zone can be reresented in two orms: () the ixed ST zone indicated as a seciied orm, i.e.,

4 Yu Zhang and Wenlong Lu / rocedia IR 43 ( 06 ) ( *, k * ) or ( *, * ); The symbol * indicated a designated value, that means: * * * * * * (, ) or (, ) k * * k k The grahic orm o the ixed ST zone is shown in igure 3 as unclosed rectangle area. () ST zone based on QI or I curve: d (, k ), or d d (, ) d where the subscrit indicates the selected QI. The grahic orm o this ST zone is shown in igure 3 as unclosed area within the symmetrical curve (or d = 0.058%) or line (or k =.0). k (, k) 0.06% k k...3 A new S model to assure redetermined quality via develoed QIs and quality-oriented ST model The rocess quality target, statistical tolerance, conidence interval and relative samling lan, the restrict condition to center lines o the Stewart control chart, arameters o the umulative-sum control (USUM) and the exonentially weighted moving-average (EWMA) control chart can be concurrently designed under the To level: Quality lan or a quality characteristic related rocess ---selecting one or two QI and/or I with their limit value Middle level: Quality-oriented statistical tolerancing ---determining ST based on the seciied curves in - k or - lane The interace o QIs and S --transorm quality-oriented ST into the seciied orm Lower level: Quality-oriented S design ---select a control chart and related arameters d.3 d * : the designated maximum raction deective o a rocess outut c * : the designated minimum raction o rocess outut in center zone ql * : the designated maximum raction o average quality loss o rocess k * : the designated minimum k value m * :the designated minimum m value d (, k) c (, k) ql (, k) k (, k) * k * = Fig3. QI, I curves and ST zones in -k lane d c ql k ( *, k * ) ( *, * ) Shewhart control chart design Determining the ST zone to center line (L) o control chart Establish UL and LL based on L± 3 d (, ) c (, ) ql (, ) m (, ) d c ql m usum and EWMA control chart design Determining the key arameters L,and ARL based on Fig. 4 Flow chart o Quality-oriented concurrent design or QI, ST and S.4.5 guideline o this new aroach which is briely exressed by igure Introduction o the series hinese ST standards The NSF rogram Quality-oriented statistical tolerancing technique had been araised by the Science and Technology Deartment o Shandong rovince on March o 005, and it had been recommended to the hinese national standardization committee o geometrical roduct seciication (T40) or converting the research achievement into ST standard. To meet the needs o concurrent design or ST and S, T40 set u the new serial GS statistical tolerance standards in its long term lan (006-00) in 006. The new serial GS statistical tolerance standards had been comleted by the eorts o several hinese universities, a research institute and a comany, and it had been aroved by the hinese national standardization committee in succession. The series o hinese GS/ ST standards consist o ive arts, as shown in ig.5. Introductions to these arts are as ollows. GB/Z4636. Geometrical roduct seciications (GS)-Statistical tolerance-art : Terms, deinitions and basic concet GB/Z Geometrical roduct seciications (GS)-Statistical tolerance- art 4: Statistical tolerance design based on given conidence levels GB/Z4636.Geometrical roduct seciications (GS)- Statistical Tolerance-art : Statistical tolerance values and their indication on drawing GB/Z4636.3Geometrical roduct seciications (GS)-Statistical tolerance-art 3: Statistical quality indices o a comonent lot ( ) GB/Z4636.5Geometrical roduct seciications (GS)-Statistical tolerance- art 5: Statistical quality indices o an assembly lot (hole-shat it) Fig.5 Relation diagram o the ive arts o hinese ST standards 3. hinese ST standard--art : Terms, deinitions and basic concets The irst art o the serial ST standards deines the terms, deinitions, and basic concets o STs. These 9 terms, deinitions and symbols are the basis or the establishment and alication o ST criteria. Some basic concets o the quality-oriented ST are also roosedin articular, the three levels o statistical tolerancing. Quality-oriented STs can be divided into three levels: uer level, middle level and lower level. In order to ensure the quality requirements indicated as the uer level STs, the selected value o QI or I rom the quality-oriented ST charts can be derived into the middle level ST via the standardized two-dimensional latorm, i.e. -k or - lane. The middle level ST indicated as *, k * or *, * can be determined based on the designated QI or I and known value via the ST zone on the

5 7 Yu Zhang and Wenlong Lu / rocedia IR 43 ( 06 ) standardized two-dimensional latorm. As the ST standard will only rovide the standardized ST tables related to the uer and middle level STs, the lower level STs that may be reresented by the seciied oulation seciication or by the restricted arameters in the control chart design can be transmitted rom ( *, k * or ( *, *. 3. hinese ST standard--art : Statistical tolerance values and their indication on drawing The second art o the serial ST standards seciied the value orms o ST and the indicating method in the drawings. The ST orms are determined by the alication level o the seciic ST. The uer and middle layers are the standardized dimensionless numerical value, and the lower is the numerical value with a dimension, such as mm or mating sizes. The quality levels indicated by x and relative STs or general deault requirements and their exression are also stiulated in this art. 3.3 hinese ST standard--art 3: Statistical quality indices o a comonent lot (rocess) Three rocess quality indices (QIs) and their related terms are deined. These direct rocess quality indices are the unctions o and k (or and the relationshis o QIs with and k (or and are exressed by the unctions. The values o QIs to be recommended to designers or statistical tolerancing are normalized and graded in art 3 o the standard. A guideline or the selection o QIs in statistical tolerancing to the geometrical characteristics is given in Aendix A. The ST value tables and ST zone charts that are exressed in two-dimensional ( or - ) lane are given in Aendix B and. art 3 is a core standard o the serial ST standards or the quality design at comonent level. It is alicable to the linear dimensions, esecially to the mating dimensions with higher tolerance degree, which are usually to be in a controlled state via S. The standard is also suitable to the imortant quality characteristics to be in a controlled state with bilateral seciication limits. It also rovides the way to transmit the designer s quality requirements to manuacturers, quality engineers and insectors via the ST zone in a two-dimensional lane and how to imlement the ST via S aroach. 3.4 hinese ST standard--art 4: Statistical tolerance design based on given conidence levels This art o ST standard is necessary or assuring the exected QIs with a reset conidence level to some very imortant key quality characteristics in a batch o comonents. The related terms and their symbols are deined. The ormulas or estimating oulation arameters and QIs are indicated, which exresses the relationshi among the required STs, conidence level, and related samling size. The alication examle o statistical tolerancing with estimated values based on a given conidence level is given in Aendix A. The ST value tables or the estimated value o and k under the given situation are listed in Aendix B. Three reresentations o estimated values or the mean and standard deviation o rocess in S are given in Aendix. 3.5 hinese ST standard--art 5: Statistical quality indices o an assembly lot (hole-shat it) The ith art o the serial ST standards rovides the evaluation indices and relative analysis method or the quality o assembly (hole/shat it) based on the ST and actual oulation arameters o the hole and shat comonent lots. It deines the terms and deinitions o the it quality and the relationshi o it quality indices with the STs o related two mating arts that are exressed by the unctional ormulas. It gives the design method or assuring it quality via correctly designing and imlementing the STs o relative mating arts. Aendix A gives a guideline and alication examle o ST design or assuring a designated it quality index. Aendix B rovides the useul numerical tables or suorting the it quality and ST design. Selecting and imlementing suitable STs or the mating sizes o comonents are an eective way to realize and assure exected it quality. This art o ST standard also shows the way how to transmit the designer s it quality and ST requirements into the STs o two mating sizes based on the relationshi between the it quality indices and the Is o the rocesses relative to hole and shat sizes. On the other side, manuacturers and quality engineers can redict and imrove it quality rom the actual statistical arameters o two mating comonent lots. 4. Alications o the serial hinese ST standards The serial ST standards are to be imlemented as hinese national standardized guiding technical documents or meeting the needs o ursuit o excellence quality. Their alications are mainly in the ollowing asects: () oncurrent design dimensional seciications and STs or assuring both exected rocess quality and it quality; () Quality-oriented S via Quality-oriented ST design; (3) Quality-oriented concurrent design or dimensional chain; (4) Assuring and imroving matchable degree in selective assembly via Quality-oriented ST design. A case study is introduced to show designing STs or mating sizes o holes and shats based on the actual S data, rocess and it quality requirements. The it o the cylinder o the rear wheel and iston is 0.05 H e8( 0.073). The inal manuacturing rocess o the cylinder hole is honing. The inal rocess o the iston diameter is centreless grinding. Each batch to be manuactured o the cylinder and iston is 500 airs. The stes or rocess and it quality design are as ollows. () The inal rocesses o cylinder hole and iston are in the controlled state by the control chart or x R. () The estimated value o the I and the shit arameter

6 Yu Zhang and Wenlong Lu / rocedia IR 43 ( 06 ) are calculated based on the statistical data. The estimated and k value o cylinder hole ˆ.549, kˆ ( H ) H The estimated and k value o iston: ˆ.803, kˆ ( S ) S (3) redict it caability index F and the shit arameter o it k based on the known estimated and k value resectively (to simliy question, estimate the it indices without considering the conidence level). F 3.0 r ( ) ( ) r ( ) ( S ) H ( S ) ( H ) where r is the ratio o hole tolerance to shat tolerance. rkh ks k r (4) redict it quality The ercentage o clearances in middle zone o it c ( ) { [ F ( 3k )] [ F ( 3k )]}*00% = % The raction o average quality loss o it ql( ) [ k ] 00% =.58 % (3F ) (5) Select STs or the mating sizes ST o cylinder hole: (H),k H =.000.0) ST o iston diameter,k (S) S = Table shows the ensured rocess quality o the mating sizes and their it quality via the STs. Table the ensured rocess and it quality via the STs Batch name d rocess quality o the mating sizes ql Hole % 95.9%.88% shat % 90.9% 3.885% it 5. Summary Ensured it quality F.68 k % ( ).66% ( ) Quality-oriented statistical tolerancing technique and its standardization rovide the rocess and it quality evaluation system based on QIs, Is and it quality indices, three levels o STs and the indications o ST zone, a concurrent design aroach or seciication, rocess quality and S, which is the bridge and link among the related designers, manuacturers, quality engineers and insectors. The standardized ST zone in the twodimensional lane has relatively strong comatibility and adatability with the rocess caability analysis and S, ql which can ensure the designated rocess and it quality via quality-oriented S. Quality-oriented ST has absorbed and integrated some advanced concets and technology in the ST and S related area, but it is only suitable or the quality characteristics with bilateral seciication limits to be in a controlled state. It still needs to be imroved and develoed. Future works are in the ollows: () to develo the English edition o these hinese ST standards or international exchanging and sharing GS research achievements and standards, and to strive or consensus at ISO/T3; () to imrove quality-oriented S based on quality-oriented ST, and to strive or consensus with the related standardization technical committee; (3) to aly the ST standards in the enterrises where S have been utilized or excellence rocess and roduct quality; (4) to develo new ST method or the geometrical characteristics with unilateral seciication limit. Reerences [] Sotts M. F. A Faster Way to Set Statistical Tolerancing. roduct Engineering 3(), ~57. [] reveling.m. Tolerance Design: a Handbook or Develoing Otimal Seciications. Addison-Wesley; 997. [3] Kane, V. E. rocess caability indices, J. o Quality Technology, 8, [4] hang, L. K., heng, S.W. and Sring, F. A new measure o rocess caability: m. J. o Quality Technology,0, [5] Boyles, R. A. The Taguchi caability index. J. o Quality Technology, 3, [6] Srinivasan V., O onnor M. A. Towards an ISO Standard or statistical tolerancing. In: Kimura, F. Editor. omuter-aided Tolerancing. London: haman & Hall; [7] Srinivasan V., O onnor A. and Scholz F. W. Techniques or omosing a lass o Statistical Tolerance Zones. in: Zhang, H.. Editor. Advanced Tolerancing Techniques. New York: John Wiley & Sons; [8] Voelcker H.B. Dimensional Tolerancing Today, Tomorrow, and Beyond. in: Zhang, H.. Editor. Advanced Tolerancing Techniques. New York: John Wiley & Sons; [9] Zhang, Y., Low, Y. S. and Fang, X. D. I-based Tolerance as an Interace between Design Seciications and Statistical Quality control, omuter & Industrial Engineering. 35(-) [0] ISO/DIS 839 Geometrical roduct seciication (GS) oulation seciication. 04. [] Zhang Y., Yang M.S. and Zhang H.. The research on Quality-oriented Statistical Tolerancing Technique, roceedings o the 5 th International onerence on Frontiers o Design and Manuacturing, Dalian; [] Zhang Y., Yang M.S. and Zhang Y.X. oncurrent design or rocess quality, statistical tolerance and S ommunications in Statistics - Theory and Methods,35(0), [3] Zhang Y. Reresentation and alication analysis o qualityoriented statistical tolerancing, hina Mechanical Engineering 7(4): [4] Zhang Y., Yang M.S. and Li X Quality-oriented design aroach o dimensional chain and statistical tolerance. hinese J. o Mechanical Engineering 43 (4), [5] Taguchi G.I Introduction to Quality Engineering. Asian roductivity Organization, UNIUB White lain. 986.