Process Capability Analysis of a Turning Operation

Transcription

1 Proceedngs of the Internatonal MultConference of Engneers and Computer Scentsts 07 Vol II, IMECS 07, March 5-7, 07, Hong Kong Process Capablty Analyss of a Turnng Operaton S. Phanphet, N. Sukprasert, P. Chmboonma, W. Thongyod, S. Bangphan, and P. Bangphan Member, IAENG Abstract Qualty control helps ndustres for mprovements of turnng operaton product qualty and productvty. Process capablty ndces are effectve tools for the contnuous mprovement of qualty, productvty and manageral decsons. Statstcal Process Control (SPC) technques mprove the qualty n mass producton. In ths study, a process-capablty analyss was carred out n the turnng operaton on department of Industral Engneerng, Faculty of Engneerng, ajamangala Unversty of Technology Lanna and Department of Industral Technology Faculty of Scence and Technology Chang Ma ajabhat Unversty that produces machne and rce mll machne parts. For ths purpose, normal probablty plots and bar- charts were prepared and the process capablty ndces C p, C, C, C pm and were calculated. It has shown that the process capablty for the whole process was nadequate and turnng operaton the medum producton was unstable. In order to satsfy the process-capablty measures, t s necessary to mprove the qualty level by shftng the process mean to the target value and reducng the varatons n the process. Index Polshed Cylnder, Statstcal Process Control, Control Charts, Process Capablty. T I. INTODUCTION HE theoretcal framework for accessng the capabltes of a process began wth the development of the C p ndex []. Process capablty ndces contnue to be wdely used tools for process engneers despte a growng recognton that these tools are lmted and, n partcular, S. Phanphet lecturer Department of Industral Technology Faculty of Scence and Technology Chang Ma ajabhat Unversty 0 Chang Puak road, Tambon Chang Puak, Maung Dstrct, Chang Ma, Thaland, , (+66) (E-mal : suwattwong@gmal.com). N. Sukprasert lecturer Department of Industral Technology Faculty of Scence and Technology Chang Ma ajabhat Unversty 0 Chang Puak road, Tambon Chang Puak, Maung Dstrct, Chang Ma, Thaland, 5000 (+66) , (E-mal: narongsuk69@gmal.com). P. Chmboonma lecturer Department of Industral Technology Faculty of Scence and Technology Chang Ma ajabhat Unversty 0 Chang Puak road, Tambon Chang Puak, Maung Dstrct, Chang Ma, Thaland, , (E-mal : prast50@hotmal.com). W. Thongyod lecturer Department of Industral Technology Faculty of Scence and Technology Chang Ma ajabhat Unversty 0 Chang Puak road, Tambon Chang Puak, Maung Dstrct, Chang Ma, Thaland, 5000 (+66) , (E-mal : walapornth@gmal.com). S. Bangphan Asst. Prof. Ph.D. Department of Industral Engneerng, Faculty of Engneerng, ajamangala Unversty of Technology Lanna. 8 Huay kaew oad, Muang Dstrct, Chang Ma, Thaland, 5000; (correspondng author to provde phone:(+66) ; fax:(+66)5-8 ;e-mal : pong_pang49@yahoo.com). P. Bangphan Asst. Prof. Department of Industral Engneerng, Faculty of Engneerng, ajamangala Unversty of Technology Lanna. 8 Huay kaew oad, Muang Dstrct, Chang Ma, Thaland, 5000, (+66) ; fax:(+66)5-8 ;e-mal : foundry8@yahoo.com). ISSN: (Prnt); ISSN: (Onlne) that standard capablty ndces are approprate only wth measurements that are ndependent and reasonably normally dstrbuted []. The popularty of process capablty ndces, along wth the common understandng that n many cases these ndces are flawed tools, has led contnued research n ths area. A recent summary of the state of theory and practce s presented []. The use of capablty ndces such as C p, C, and "Sgma" values are wdespread n ndustry [4]. Therefore, the purpose of ths paper s to generate the length of rce polshed cylnder n dfferent samples after turnng was found to be out of tolerance lmts asked by department of ndustral engneerng, faculty of engneerng and department of ndustral technology faculty of scence and technology, the process capablty found to be less than the standard value. Ths requred the dea of SPC mplementaton and the technques has been practced usng process capablty (C p ). If the process s not n statstcal control, we are unable to use relably on our estmates for spread and locaton. Hence, our formula are redundant. In order to assess whether or not a process s n statstcal control, qualty practtoners use control charts. The most frequently used form of control charts n operaton today are those whch have ther dervaton from the poneerng work of Dr. Walter Shewhart n the early 90.s. In ther basc form, these charts (e.g. bar-, bar-s Chart) are senstve to detectng relatvely large shfts n the process []. SPC tools can be used by operators to montor ther part of producton or servce process for the purpose of makng mprovements [5]. For more nformaton on these charts, the nterested reader s referred to AIAG and Montgomery [6]. Qualty may be defned as that characterstc whch renders a product or servce as havng ftness for purpose or use. There are dfferent reasons why a product may have unsatsfactory qualty. Statstcal methods play a central role n qualty mprovement efforts and recognzed as an effcent and powerful tool n dealng wth the process control aspects [7]. A. Lterature revew The use of statstcal concepts n the feld of qualty emerged n the Unted States n the begnnng of the nneteenth century. But ts democratc use began only n the 90s. W. Edwards Demng, who appled SPC methods n the US durng the Second World War, was the one responsble for ntroducng ths concept n Japan after the war ended. These methods were not used n France untl the 970s. The 980s saw the SPC methods beng used frequently, due to the pressure from large clents lke automoble manufacturers and arcraft manufacturers [7],[8]. Companes who have been operatng n the market IMECS 07

2 Proceedngs of the Internatonal MultConference of Engneers and Computer Scentsts 07 Vol II, IMECS 07, March 5-7, 07, Hong Kong for a whle already have a qualty control process n place. Ths process enables a company to meet four man objectves: hgher qualty, more effectveness, optmum cost savngs and greater rgor, and produces products of optmum qualty [9]. SPC tools can be used by operators to montor ther part of producton or servce process for the purpose of makng mprovements [0]. Statstcs s more applcable to measure and control varaton from common cause (random) than from specal causes []. II. METHOD EPEIMENTAL POCEDUE A. Method Process capablty analyss usng control chart the Normal dstrbuton, one should note that there are an nfnte number of dstrbutons whch may show the famlar bellshaped curve, but are not Normally dstrbuted. Ths s partcularly mportant to remember when performng capablty analyses. Therefore, these need to determne whether the underlyng dstrbuton can ndeed be modeled well by a Normal dstrbuton. If the Normal dstrbuton assumpton s not approprate, yet capablty ndces are recorded, one may serously msrepresent the true capablty of a process. Consder the followng smulaton. Suppose the USL = dameter 5.45 and LSL = dameter 5.5 mllmeters, and our target for ths process s mdway between analyss of the 00 observatons. Frstly, consderng the bar and control chart efer to (), ths see that the dstrbuton s stable over the perod of study. To llustrate the use of a process capablty to estmate process capablty, consder Fg.., whch presents a process capablty of the samples data of 0 sample. The samples data are shown n Table, the 95 % confdence nterval on C p and C. LSL USL TABLE I Polshed Cylnder 0 Sample Data (Dameters, Mllmeters, 0.05) No B. Expermental procedures Process capablty ndex relates the engneerng specfcaton (usually determned by the customer) to the observed behavor of the process. The capablty of a process s defned as the rato of the dstance from the process center to the nearest specfcaton lmt dvded by a measure of the process varablty. Some basc capablty ndces that have been wdely used n the manufacturng ndustry nclude C p, and C, explctly defned as follows. : []. UCL A CL LCL A UCL D 4 CL Process Spread = Performance Spread Acceptable C p USL LCL LSL 6 D () Fg.. process capablty () Capablty ato, C = / Cp () ISSN: (Prnt); ISSN: (Onlne) IMECS 07

3 Proceedngs of the Internatonal MultConference of Engneers and Computer Scentsts 07 Vol II, IMECS 07, March 5-7, 07, Hong Kong Let, CPU and CPL are Upper and Lower Process Often the process data s collected n subgroups. Let j, =,, m and j =,, n represent the process data collected from the j th unt n the th subgroup. Here, m equals the total number of subgroups, and n equals the subgroup sample sze. The two most wdely used capablty ndces are defned as: USL LSL C mn, (4) USL LSL C pm 6t (5) Where t ( T ) C C z 9n n (6) Were, the average, s used to estmate the process mean,and s and / d are dfferent estmates of the process devaton. The estmate (7) Where The estmate wthn S s S r f fr d n ( ) f d n d n s the sample standard devaton ( j ( ) n ) j / d / d s an estmate derved usng the subgroup ranges, =,,m. The parameter d s an adjustment factor needed to estmate the process standard devaton from the average sample range. Snce d s also used n the dervaton of control lmts for bar and control chart t s tabulated n standard references on statstcal process control, such as the QS-9000 [5],[6],[]. Large values of C and C pm should correspond to a capable process that produces the vast majorty of unts wthn the specfcaton lmts. However, Equaton (4),(5) s used when the mean of process data s departure from the medan of specfcaton lmts and Equaton (6) s actually, an upper lmt can also be had by replacng the mnus sgn wth a plus above use z=.645 to be approxmately 95% sure that the real C s above the lmt. Where USL and LSL are the upper and the lower (8) specfcaton lmts, respectvely, bar s the process mean, and σ s the process standard devaton( process varaton). The ndex C p measures the magntude of the process varaton relatve to the specfcaton tolerance and, therefore, t only reflects process potental. The ndex C takes nto account process varaton as well as the locaton of the process mean, whch s desgned to montor the performance of near-normal processes wth symmetrc tolerances. The ndex C p s defned as the followng, where M or T s the md-pont of the specfcaton nterval USL LSL ธT M. The calculaton formulae presented n the Table I are rght when the analyzed parameter s subject to a normal dstrbuton or ts dstrbuton s close to the normal one. In such stuatons, there s oblgatory the rule of three standard devatons accordng to whch wthn the range bar and control chart see table (.e. wthn the range determned by a natural tolerance ()). All possble realzatons of the process should be contaned (Fg.). In ths paper, we consder testng the most popular capablty analyss C p, C, C pm and C usng process capablty. We obtan the posteror probablty (p) for whch the process under nvestgaton s capable, and propose accordngly a Bayesan procedure for capablty testng. To make ths Bayesan procedure practcal for n-plant applcatons, we tabulate the mnmum values of for whch the posteror probablty (p) reaches varous desrable confdence levels. An applcaton example to the workshops process s presented to llustrate the applcablty of the proposed approach. III. IMPLEMENTATION AND ESULTS A. Sample sze Because process capablty ndces are determned from estmates of standard devaton, they are affected by sample sze (degrees of freedom). As expected, the stablty of estmates of the standard devaton ncreases wth sample sze (n) of 5 provde a very stable estmate of process capablty. Even when n s 0 there s stll substantal uncertanty n the estmator of C. See Tables I provde estmates of 95% Confdence Bounds for C (lower bound) and P (two sded nterval), assumng normalty. The data were classfed nto 0 subgroup of fve observaton each by measurng the lengths of n each batch unts. See Table II gves the 00 recorded data observatons. Ths type of capablty study usually measures product functonal performance, not the process tself. When the engneer can drectly observe the process and can control the data collecton methods ths study s a true process capablty study [4]. When hstorcal data s used and drect observaton of the process s not possble, Montgomery refers to ths as a product characterzaton study. In a product characterzaton study turnng operaton we can only estmate the dstrbuton of the product qualty characterstcs; we can say nothng about the statstcal stablty of the process. Hstograms (or stem-and-leaf plots) requre at 0 observatons. If the data sequence s preserved, ĉ ISSN: (Prnt); ISSN: (Onlne) IMECS 07

4 Proceedngs of the Internatonal MultConference of Engneers and Computer Scentsts 07 Vol II, IMECS 07, March 5-7, 07, Hong Kong Mean Square of Successve Dfferences (MSSD) can be used to estmate the Short Term Standard Devaton (STSD). Or, an estmate of process standard devaton can be obtaned from bar and control chart. B. The results The results of the prelmnary analyss (the values of sze parameters.e. length see Table II, the emprcal dstrbuton Fg. and especally the graphcal test of normalty Fg. ndcate that the analyzed parameter s not subject to a normal dstrbuton. In connecton wth t C capablty analyss have been determned. Fg.. shows the correspondng bar and control chart and all ponts under control lmts. Analyss: Here n the above observaton record, we have a number of varable measurement outcomes for the number of rce polshed cylnder on a Turnng Machne. To analyze the process capablty, the statstcal qualty control chart technques can be mplemented n the followng way: The arthmetc average (mean) of range m Where, A = 0.577, D =.6, D =0.00 and D 4 =.5 (from Table of SPC constants, for N = 5) The control lmts are, UCL D4 CL LCL D.5(0.06) (0.06) 0 Example subgroup No., and No.0 ange = [Hghest value Lowest value] = = 0.00 = = 0.00 Average bar (Process mean), could truly estmate all of the possble realzatons of specal causes n the long term [4]. As we can observe from the bar and control chart, the dameters of all the components are out of the control lmts, ths means that process s capable of producng the dameters wthn specfcaton lmts. It s concluded that the process s now under control and capable of meetng the specfc demand dameters of tolerances (.0.05 mllmeters). TABLE II POLISHED CYLINDE 0 SAMPLE DATA (DIAMETES, MILLIMETES, α 0.05) No TABLE II (contnuous) POLISHED CYLINDE 0 SAMPLE DATA (DIAMETES, MILLIMETES, α 0.05) No bar- Chart of,..., 5 UC L= m 0 The control lmts are, mm. Sample Mean Sample _ =5.405 LC L= UC L= UCL A (0.577)(0.06) 5.40 mm. Sample ange _ =0.06 CL LCL A (0.577)(0.6) 5.90 mm. As the bar and control chart ndcate stablty, even usng all of the Western Electrc rules [5]. We have some justfcaton to use estmates of the process mean () and the wthn subgroup (short-term) standard devaton ( wthn ) from ths course of study. Many practtoners mstrust the estmate of the standard devaton ( ) as they queston whether ths wndow of nspecton ISSN: (Prnt); ISSN: (Onlne) Sample Fg.. bar and control chart for polshed cylnder data The capablty analyss n Fg. shows that wth the USL = 5.45 and LSL = 5.5 mllmeters,. long-term performances are also ndcated, namely that approxmately 0.00 parts per mllon (ppm) for wthn performance would be nonconformng f only common causes of varablty were present n the system, and approxmately 0.00 ppm n the long-term. Based on the data n see Table I, we calculate the LC L=0 IMECS 07

5 Proceedngs of the Internatonal MultConference of Engneers and Computer Scentsts 07 Vol II, IMECS 07, March 5-7, 07, Hong Kong followng quanttes: , wthn and Snce, n ths example, the subgroup sze equals fve, d =.6. Usng the defntons (-8) yelds C p = 5.9,C pl = 5.95,C pu =4.8, C =mn{5.95,4.8}=4.8,c pm =.80, P p =5.8,Ppl=6.4,Ppu=5.0,P =5.0. In ths case, all the values are qute dfferent, and, n fact, le on dfferent sdes of the key cut off values. and.67 gven n QS Whch capablty ndex s better n ths example. As efer to (-8), the measures C p, C, C, C pm and dffer only n the estmate of the process standard devaton used n the denomnator. As a result, to compare the seven capablty measures turnng operaton process we need to compare the two standard devaton estmates wthn and. There s one mportant dfferences between wthn and. / d Snce the range-based estmate s calculated based on subgroup ranges, t uses only the varablty wthn each subgroup to estmate the process standard devaton. The sample standard devaton- based estmate wthn and, on the other hand, combnes all the data together, and thus used both the wthn and subgroup varablty. The total varaton n the turnng process s the sum of the wthn and subgroup varablty. As a result, wthn and estmate the total varaton present n the / d process wthn estmates only the wthn and subgroup varaton. Process Data LSL 5.5 Target 5.4 USL 5.45 Sample Mean Sample N 00 StDev (Wthn) StDev (O v erall) O bserved Performance PPM < LSL 0.00 PPM > USL 0.00 PPM Total 0.00 Process Capablty of dameters LSL Target USL Exp. Wthn Performance PPM < LSL 0.00 PPM > USL 0.00 PPM Total Exp. O v erall Performance PPM < LSL 0.00 PPM > USL 0.00 PPM Total 0.00 Wthn Overall Potental (Wthn) C apablty C p 5.9 CPL 5.95 CPU 4.8 C 4.8 O verall C apablty Pp 5.8 PPL 6.4 PPU 5.0 P 5.0 Cpm.80 Fg.. graphcal llustraton of the polshed cylnder data In connecton wth t C p, C, C pm, C and capablty analyss have been determned accordng to adequate expresson presented efer to (), (), To determne the values,, wthn and, there are used eght the computable method basng on knowledge of densty functon. The results are shown n see Table III. TABLE III esults- Capablty Analyss C wthn p C C C pm ISSN: (Prnt); ISSN: (Onlne) Estmaton of : USL LSL C mn, S S mn, mn4.8, 5.95 ( ) ( ) C z Percent C 9n n 9(0) (4.8).7.95 (0) Probablty Plot of -bar Normal - 95% CI bar Fg.4. Normal probablty plot of the polshed cylnder data Mean 5.4 StDev N 00 A D.406 P-Value <0.005 From the Normal probablty plot graph n Fg.4, the Normalty test shows that we are unable to reject the null hypothess, H 0 : data follow a Normal dstrbuton vs. H : data do not follow a Normal dstrbuton, at the 0.05 sgnfcance level. Ths s due to the fact that the p-value test s 0.005, whch s p-value less than 0.05 a frequently used level of sgnfcance for such a hypothess test, as opposed to the more tradtonal 0.05 sgnfcance level. The value of C ndex acheved n analyss s not unfortunately an evdence of meetng the samples expectatons (the requred mnmal value of C ndex determned by the polshed cylnder was 4.8 (A Hghly Capable Process)). Snce, the value of process capablty analyss, as requred by the department, department of Industral Engneerng, Faculty of Engneerng, MUTL was greater than, and the process capablty analyss we obtaned after the mplementaton of SPC technques s 5.9 whch s greater enough than. Therefore, then can say that the process s under control now and capable of producng all the components under the gven specfcaton lmts wth the very low normal dstrbuton and closely central lmts. Process capablty ndces C p and C were calculated. It has shown that the process capablty for the whole process was nadequate and turnng operaton process the mass producton was unstable [6]. In order to satsfy the process-capablty measures, t s necessary to mprove the qualty level by shftng the process mean to target value and reducng the varatons n the process [6]. The most mportant problems n busness, there are no traned employees to apply t and there s unsuffcent nvestment. Consequently, SPC must be appled wdely and IMECS 07

6 Proceedngs of the Internatonal MultConference of Engneers and Computer Scentsts 07 Vol II, IMECS 07, March 5-7, 07, Hong Kong contnuously to acheve qualty mprovements [7]. [8] Identfed a gap between how process capablty analyss should be performed n theory compared to how t s actually preformed n practce, and stated that process capablty analyss s often msused n practce. Furthermore, from [9] It s clear that there s a lack of well functonng capablty tools n the cases when the output s non-normally dstrbuted. Several references n these areas are gven, but more research s needed to obtan tools that can be appled by practtoners. IV. CONCLUSION The results of process capablty study of the gven workshop process reveals turnng operaton process, graphcal values of parameters approaches very nearer to the magntude of the analytcal values and hence graphcal approach could be treated as equvalent to analytcal method. Graphcal approach can be used to study the varablty of workshop process. It s one of the tools to convey the results through whch t s easy to make nference on the data. The approach helps a worker (Students) n the workshop can make the assessment about the process parameters. Thus, t also helps to process management and dentfes opportuntes for mprovng qualty and operatonal performance. The estmaton of process capablty s one of the basc tasks of the statstcal process control (SPC). The values of C p, C, C and ndces are very precse nformaton on a process potental relatng to the clent s expectatons. Correct determnaton of C p, C, C and ndces values by countng requres dentfcaton of a dstrbuton sze, at least as a general settlement whether t s a normal dstrbuton or not. If t s a normal dstrbuton, for the estmaton of C p, C, C and ths can use a smple countng classc approach that s based on the rule of three standard devatons. If t s not a normal dstrbuton, the applcaton of a classc approach leads to wrong results. The process-capablty analyss, whch s a SPC technque, helps to determne the ablty for manufacturng between tolerance lmts and engneerng specfcatons. The capablty analyss gves nformaton about the changes and tendences of the systems durng producton. In ths study, Control charts for varables are mplemented to acheve a good control over the process. SPC technque was used to evaluate machnes capablty ( C p ) and process centerng (C ) of manufacturng process to fnd whether the process s capable or not. The number of nonconformng part was determned n observed values, n short and long perods of tme. After montorng the process a sgnfcant mprovement has been experenced n terms of ncrease n process capablty ndces and reducton n defectve parts per mllon (ppm). The most mportant problems n busness s that there are no traned employees to apply t and there s nsuffcent nvestment. Consequently, SPC must be appled wdely and contnuously to acheve qualty mprovements. ACKNOWLEDGMENT Fnancal support from Department of Industral Technology Faculty of Scence and Technology Chang ISSN: (Prnt); ISSN: (Onlne) Ma ajabhat Unversty and Department of Industral Engneerng Faculty of Engneerng, MUTL: ajamangala Unversty of Technology Lanna Chang Ma s gratefully acknowledged. eferences [] Juran, J. M. Qualty Control, Handbook, rd Edton, McGraw-Hll, New York,974. [] odrguez,. N. ecent developments n process capablty analyss, Journal of Qualty Technology 4 (4);99, [] Wu, C. W., Pearn, W. L., Kotz, S. An overvew of theory and practce on process capablty ndces for qualty assurance, Internatonal Journal of Producton Economcs 7;009, [4] Keth M. Bower, M.S, Process Capablty Analyss Usng MINITAB (I) n Qualty Management and Productvty, from the Unversty of Iowa, and s a Techncal Tranng Specalst wth Mntab, Inc,00. [5] oberta ussell & Bernard W. Taylor. Statstcal Process Control, Operatons Management, 5th Edton, III John Wley & Sons. Inc.Ben Asllan, Unversty of Tennessee at Chattanooga, 006. [6] Montgomery, D.C. Introducton to Statstcal Qualty Control, rd Edton, John Wley & Sons, 99. [7] Douglas C. Montgomery. Introducton to Statstcal Qualty Control, Fourth edton, John Wley Publcatons, New York,00. [8] Pyush Kumar Son, Imtyaz Khan, Abhshek ohlla. Process Capablty Improvement by Puttng Statstcal Process Control Into Practce, Int. J. of Power System Operaton and Energy Management ISSN (PINT):- 4407,V,Issue,. [9] Term papers, Statstcal Process Control spc management -, busness and market, 4 pages, 0. [0] oberta ussell & Bernard W. Taylor, III John Wley & Sons. Statstcal Process Control, Operatons Management - 5th Edton, Inc.Ben Asllan, Unversty of Tennessee at Chattanooga, 006. [] SPC9b, fle format: mcrosoft word. statstcal process control (spc) & statstcal qualty control (sqc), chemrat.com/chemhog/spc_fles/spc9b.doc. [] Automotve Industry Acton Group AIAG, Statstcal Process Control, Second edton. Southfeld, MI:AIAG,995. [] Kane, V. E., 986. Process capablty ndces, Journal of Qualty Technology, vol.8 (),986,pp [4] Montgomery, D.C, Introducton to Statstcal Qualty Control, rd Edton, John Wley & Sons,996. [5] Western Electrc, Statstcal Qualty Control, Handbook. Western Electrc Corporaton,965. [6] Parvesh Kumar ajvansh, Dr..M.Belokar. Improvng the Process Capablty of a Borng Operaton by the Applcaton of Statstcal Technques, Internatonal Journal of Scentfc & Engneerng esearch, ISSN 9-558, Volume, Issue 5, May-0. [7] Aysun Sagbas. Improvng the Process Capablty of a Turnng operaton by the Applcaton of Statstcal Technques, UDK 6.94:.; ISSN , Professonal artcle/strokovn- lanek, MTAE; 009,C9,4() 55. [8] Deleryd, M, On the Gap Between Theory and Practce of Process Capablty Studes, Journal of Qualty & elablty Management.,998, 5, pp [9] Kotz, S. & Johnson, N. L, Process Capablty Indces A evew, wth Dscusson. Journal of Qualty Technology.,00,pp.. 4, -5. IMECS 07