Wishing you all a Total Quality New Year!

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1 Total Qualty Management and Sx Sgma Post Graduate Program Sesson 4 Vnay Kumar Kalakband Assstant Professor Operatons & Systems Area 1 Wshng you all a Total Qualty New Year! Hope you acheve Sx sgma heghts 2 1

2 Recap Statstcal process control Manufacturng and servce sector applcatons Implementaton challenges 3 Agenda Magnfcent seven SPC tools Addtonal tools for servces Techncal aspects of SPC usage Ratonal subgroupng Phases of SPC mplementaton Shewart Control Charts Phase 2 mplementaton CUSUM charts EWMA charts Short producton runs: DNOM charts, Q charts Multple stream processes Economc desgn of control charts Adaptve samplng for better control usng SPC 4 2

3 Magnfcent seven Hstogram or stem-and-leaf plot Check sheet Pareto chart Cause-and-effect dagram Defect concentraton dagram Scatter dagram Control charts 5 SPC n servces Natural measurement systems non-exstent Observablty s low Process mappng Value stream mappng 6 3

4 Ratonal subgroupng Subgroups or samples should be selected such that Chance of dfferences between subgroups should be maxmzed Chance of dfferences due to assgnable causes wthn a subgroup should be mnmzed Tme order s the logcal bass Snapshot approach v/s random sample approach Subgroup based on shfts, machnes, operators etc 7 Phases of Implementaton Phase 1 When SPC s ntroduced Brngng the process n control Detect hgh levels of varaton Phase 2 When major assgnable causes have been detected and corrected Sustanng the process n control Detect low levels of varaton as well Before t s too late!! 8 4

5 Shewart control charts Varable control charts X-bar and R charts/s-charts Attrbute control charts p-charts and c-charts Iteratve correctve procedure Impact of non-normalty Control chart performance 9 Control Chart Performance Average Run Length The average run length (ARL) s a very mportant way of determnng the approprate sample sze and samplng frequency. Let p = probablty that any pont exceeds the control lmts. Then, 1 5

6 Control Chart Performance 11 Indvdual measurements When there s no bass for ratonal subgroupng Data s avalable relatvely slowly Multple measurements taken on the same unt of the product Contnuous flow process Use movng range MR wth the assumpton that the same sze s 2 Pros and cons Hgh ARL Normalty assumpton 12 6

7 The Cumulatve-Sum Control Chart The cusum chart ncorporates all nformaton n the sequence of sample values by plottng the cumulatve sums of the devatons of the sample values from a target value. If s the target for the process mean, s the average of the jth sample, then the cumulatve sum control chart s formed by plottng the quantty x j C (x j ) j1 13 The Tabular or Algorthmc Cusum for montorng the Process Mean Let x be the th observaton on the process If the process s n control then x ~ N(, ) Assume s known or can be estmated. Accumulate dervatons from the target above the target wth one statstc, C + Accumulate dervatons from the target below the target wth another statstc, C C + and C -- are one-sded upper and lower cusums, respectvely. 14 7

8 The Tabular or Algorthmc Cusum for Montorng the Process Mean The statstcs are computed as follows: The Tabular Cusum C C max, x max,( ( k) x k) C C startng values are C C K s the reference value (or allowance or slack value) If ether statstc exceed a decson nterval H, the process s consdered to be out of control. Often taken as a H = The Tabular or Algorthmc Cusum for Montorng the Process Mean Selectng the reference value, K K s often chosen halfway between the target and the outof-control value of the mean 1 that we are nterested n detectng quckly. Shft s expressed n standard devaton unts as 1 = +, then K s 1 K

9 Cumulatve Sum The Tabular or Algorthmc Cusum for Montorng the Process Mean Example 8-1 = 1, n = 1, = 1 Interested n detectng a shft of 1. = 1.(1.) = 1. Out-of-control value of the process mean: 1 = = 11 K = ½ and H = 5 = 5 (recommended, dscussed n the next secton) The equatons for the statstcs are then: C max, x 1.5 C C max,1.5 x C The Tabular or Algorthmc Cusum for Montorng the Process Mean Example 8-1 CUSUM Chart for x 5 Upper CUSUM 5-5 Lower CUSUM Subgroup Number 18 9

10 The Tabular or Algorthmc Cusum for Montorng the Process Mean Example 8-1 The cusum control chart ndcates the process s out of control. The next step s to search for an assgnable cause, take correctve acton requred, and rentalze the cusum at zero. If an adjustment has to be made to the process, may be helpful to estmate the process mean followng the shft. 19 The Standardzed Cusums It may be of nterest to standardze the varable x. The standardzed cusums are then C C y x max, y max,k y k C C

11 Improvng Cusum Responsveness for Large Shfts Cusum control chart s not as effectve n detectng large shfts n the process mean as the Shewhart chart. An alternatve s to use a combned cusum- Shewhart procedure for on-lne control. The combned cusum-shewhart procedure can mprove cusum responsveness to large shfts. 21 The Fast Intal Response or Headstart Feature These procedures were ntroduced to ncrease senstvty of the cusum control chart upon startup. The fast ntal response (FIR) or headstart sets the startng values C, C equal to some nonzero value, typcally H/2. Settng the startng values to H/2 s called a 5 percent headstart

12 One-Sded Cusums There are practcal stuatons where a sngle one-sded cusum s useful. If a shft n only one drecton s of nterest then a one-sded cusum would be applcable. 23 The Exponentally Weghted Movng Average Control Chart The Exponentally Weghted Movng Average Control Chart Montorng the Process Mean The exponentally weghted movng average (EWMA) s defned as z x (1 ) z 1 where < 1 s a constant. z = (sometmes z = x) 24 12

13 8-2.1 The Exponentally Weghted Movng Average Control Chart Montorng the Process Mean The control lmts for the EWMA control chart are UCL CL LCL L L (2 (2 1 (1 ) ) 1 (1 ) ) 2 2 where L s the wdth of the control lmts. 25 The Exponentally Weghted Movng Average Control Chart Montorng the Process Mean As gets larger, the term [1- (1 - ) 2 ] approaches nfnty. Ths ndcates that after the EWMA control chart has been runnng for several tme perods, the control lmts wll approach steady-state values gven by UCL CL LCL L L (2 (2 ) ) 26 13

14 Desgn of an EWMA Control Chart The desgn parameters of the chart are L and. The parameters can be chosen to gve desred ARL performance. In general,.5.25 works well n practce. L = 3 works reasonably well (especally wth the larger value of. L between 2.6 and 2.8 s useful when.1 Smlar to the cusum, the EWMA performs well aganst small shfts but does not react to large shfts as quckly as the Shewhart chart. EWMA s often superor to the cusum for larger shfts partcularly f >.1 27 Robustness of the EWMA to Non-normalty As dscussed n prevously, the ndvduals control chart s senstve to non-normalty. A properly desgned EWMA s less senstve to the normalty assumpton

15 DNOM Charts: Devaton from Nomnal Prncples Dfferent parts wll have dfferent target values Calculate the devaton from nomnal value Plot devaton as the qualty characterstc 29 Infnty Wndows Sample Data Three part types: Header Rght jamb Left jamb Nomnal length vares from part to part Part Date Tme Nomnal Length Actual Length Rght Jamb 14-Feb 6:51 AM Header 14-Feb 6:54 AM Header 14-Feb 6:56 AM Rght Jamb 14-Feb 7: AM Left Jamb 14-Feb 7:8 AM Header 14-Feb 7:12 AM Header 14-Feb 7:14 AM Rght Jamb 14-Feb 7:15 AM Left Jamb 14-Feb 7:18 AM Header 14-Feb 1:6 AM Contnuous runs; no batches 3 15

16 Devaton from Nomnal DNOM Chart Infnty Wndows Data.2.1 UCL = CL = LCL = Sample Number 31 DNOM Charts Strengths Groups multple parts and ther data sets on a sngle chart Provdes a contnuous vew of the process Farly smple to construct and understand Shortcomngs Assumes varaton s equal for all parts Requres some hstorcal data to calculate control lmts Does not address qualty costs Only tracks wthn-run varaton 32 16

17 Standardzed Control Charts Prncples Multple part-types flow through a sngle machne Dfferent parts may have dfferent target values Control lmts and plot ponts are standardzed to allow chartng of multple part-types 33 Standardzed Control Charts Strengths Groups multple parts and ther data sets on a sngle chart Provdes a contnuous vew of the process Farly smple to construct and understand Does not assume all parts have equal varaton Shortcomngs Requres some hstorcal data to calculate control lmts Does not address qualty costs Only tracks wthn-run varaton 34 17

18 Standardzed Values Sample Standardzed Chart Sample Standardzed Chart.8 Part A Part B Part C UCL =.577 CL = LCL = Sample Number 35 Modfed and Acceptance control charts When the process s hghly capable It mght be a good dea to relax the control lmts a bt The relaxed control lmts could be based on the specfcaton lmts. OR 36 18

19 Multple stream processes Parallel and dentcal processes Prohbtvely large number of control charts Assgnable causes mght mpact one or few streams at a tme or all streams put together Use samples from the processes to formulate the control lmts Plot max and mn values across all the streams If the same stream s showng up as max or mn value consecutvely, then process out of control 37 Adaptve samplng procedures 38 19

20 Economc desgn of control charts Control chart desgn has statstcal consderatons only Cost categores to consder Costs of samplng and testng Costs assocated wth nvestgatng an out of control sgnal and repar of the assgnable cause Costs assocated wth the producton of nonconfrmng tems 39 THANK YOU 4 2