Process Optimization

1、process characterization60gage r&r - metrics from excel spreadsheetgage repeatability and reproducibility data sheetmeasurement system analysisnumber of operators =2gage name = enter_gage_name_hereshaded areas identify ranges used for index() functions in column agnumber of parts =10part name =

2、enter_part_name_herenumber of trialsnumber of trials =3total specification width = 67.2leave blank for one-sided spec.enter data and information in open cells . leave cell blank if data is missing.*if range check displays flag, check data for errors or rerun trial(s)partsoperators123456789a116800028

3、16800026.5 16800027.2 16800028.116800023.11680002816800021.5 16800029.2 16800016.5averagetrials 2 16800025.616800026.1 16800026.6 16800027.51680002316800028.4 16800021.6 16800030.2 16800016.616800026316800026.216800026.5 16800028.2 16800027.716800022.516800028.7 16800020.3 16800030.4 16800017.2range

4、range check*b116800023.816800025.51680002516800027.416800021.516800025.4 16800020.5 16800028.116800015averagetrials 21680002416800025.6 16800024.9 16800026.91680002216800026.4 16800021.2 16800029.8 16800014.916800025316800026.416800026.3 16800026.3 16800026.616800022.51680

5、0026.8 16800020.5 16800029.6 16800015.8range0.81.00.9range check*c1averagetrials 23rangerange check*part averages16800026 16800026 16800026 16800027 16800022 16800027 16800021 16800030 16800016process characterization61gage r&r - metrics from excel spreadsheetconsider: p/t rati

6、o and %gr&r enter process distribution width in sigmas (typically 5.15 or 6.00) = 5.15 total process variation = repeatability + reproducibility + part variationnumber of parts repeatability (gage variation)0.637921 (12.5% of total process variation)repeatability = ev = 5.153.285292 (4.9% of spe

7、cification width)reproducibility (operator variation)number of trials0.816797 (16.0% of total process variation)reproducibility = av = 5.154.206506 (6.3% of specification width)repeatability & reproducibility (measurement variation)1.036388 (20.3% of total process variation = %r&r)(goal: 10%

8、)r&r = 5.155.3374 (7.9% of specification width = p/t ratio)(goal: 2000) process stabilitygoal:process characterization75stability of upstream and downstream processesupstream processprocessbeing characterizeddownstream processindependent variablesconsider the stability of upstream processes and

9、factorsprocess stabilityprocess characterization76process / equipment evaluationlots from upstream processrandomize the material across the lots to create new lotsoriginal lotslot1 lot2lot3new randomized lotslot1 lot2lot3always prepare 1 extra lot in case something goes wrongprocess step under test-

10、machine 1machine 2run lots through at the same timecompare results using statistical testsreplicate 2-3 timescontrolling variation of downstream processesprocess characterization77process/machine evaluationcontrolling variation of downstream processesrandomize lots from all the processes under exper

11、iment and run those lots in random orderuse the same pieces of equipment and the same operators for all experimental lots when possibleif more than one machine is used, make sure to randomize lots among both machinesevaluating resultstake dld measurements as soon after the process under study as pos

12、siblethis can be done on a smaller sample basis for manual dld readingstake 100% dld data at final test (always from the first test)always calculate % defective besides means and sigmas due to non-normal nature of dldit may be useful to create rejection limits based on the distribution vs. following

13、 specificationprocess characterization78process/machine evaluationreport guidelinesplease use enough time to plan and document every experimentgood planning increases probability of successdocumentation should include:project purpose and goalplan of actionname of participantsexperimental design desc

14、ribed in detailflowchart of process steps and description how experimental cells will be handledexperiment checklist / traveller that includes all the set-ups, special instructions, records of actual conditions, special circumstances, unusual conditions, names of operators, time, etc.summary of resu

15、ltsstatistical analysisconclusionsrecommendationsnew actionsprocess characterization79stability evaluation two types of data individual readings taken in consecutive order run charts use 3 std dev limits control chart samples x-bar, range or x-bar, sigma charts use control chart limits process stabi

16、lity vs. process capability stability is the ability of the process to produce similar results over time capability is the ability of the process to fit within specification limitsas process capability becomes worse, process stability becomes more critical to producing good parts.process characteriz

17、ation80long term stabilitymake certain to observe the stability of a process over an extended period of time (30-60 days)look for signs of long term instability, often due to equipment wear, buildup of residues or dirt, or gradual breakdown of standard methodologies process stabilitylong term study

18、is most effective in step 4 to evaluatethe effectiveness of process optimization and processcontrols over time.process characterization81identify & eliminate assignable causesif the process is found to be unstable, look for changes in the independent variables that might be associated with chang

19、es in the response variables. look for switches turned on and off, worn parts, dirty parts . . .consider the possibility that an important, uncontrolled independent variable has yet to be identified.consider bad lots, unannounced/unnoticed supply changes, changes in water/air compression, uncalibrat

20、ed gages . . .process stabilityprocess characterization82identify & eliminate assignable causes brainstorming cause and effect analysis paretos fmea passive data collection correlations multi-vary-analysis b vs. cprocess characterization83process capabilitynormal distributionscapability metricsc

21、pcpkone-sided metricsnormal probability plotscapability metrics for non-normal distributionstransformationnon-conforming percentagepearson tableslong term capabilityprocess capabilityprocess characterization84normal distributions-4-3-2-112340-4-3-2-101234-6-556most capability indices assume process

22、data to be normally distributedprocess capabilityprocess characterization85capability metrics - cpcp = usl - lsl6-4-3-2-101234-6-556lslusllslusl-4-3-2-101234-6-556cp = 2.0cp = 1.33the cp metric does not account for off-target processes 6 6 process capabilityprocess characterization86capability metri

23、cs - cp vs sigma3.01.001.334.51.505.01.675.51.836.02.00sigmacppoor capabilitymarginal capabilitygood capabilitysix sigma capabilityassuming the process is on target . . . what if the process is not on target?process capabilityprocess characterization87capability metrics - cpklsluslmeancpk

24、= 2.0lsluslmean3 cpk = 1.5 cpk = min ,usl - meanmean - lsl3 3 3 -4-3-2-101234-6-556 -4-3-2-101234-6-556-7-8 process capability6 distribution on-center6 distribution 1.5 off-center process characterization88capability metrics - cpk - propertiescpk = 1.5lsluslmeanlsluslmeancpk = 1.5cpk = min ,usl - me

25、anmean - lsl3 3 3 3 -4-3-2-101234-6-556-7-8 0-4 -3 -2 -1 1 2 3 4 -6 -5 5 6 process capabilitynarrow distribution off-centerwide distribution on-centerprocess characterization89capability metrics - cpk vs sigma3.00.503.50.674.00.834.51.005.036.01.50sigmacpkpoor capabilitymarginal capability

26、good capabilitysix sigma capabilityassuming the process is shifted 1.5 from target . . . if process is on target, the sigma level will be even higher! process capabilityprocess characterization90capability metrics - one-sided specone-sided cpk = mean - spec. limit30-4-3-2-11234-6-556uslmeana one-sid

27、ed cp does not exist, but . . . 3 process capabilityprocess characterization91normal probability plots0306090120150 0.1 1 5 20 50 80 95 9999.9cumulative percent048121620frequencyx25354555657585y 0.1 1 5 20 50 80 95 9999.9cumulative percent024681012frequencyuse a normal probability plot to determine

28、if the data are normally-distributeduse statistical software to obtain normal probability plotsprocess capabilityprocess characterization92capability metrics for non-normal distributionstransformationtry transforming the data using log, ln, or powerscheck normality using normal probability plotsuse

29、transformed data to calculate capability metricsnon-conforming percentagerequires very large sample sizes (n1000)cp = usl - lslp0.9987- p0.0013cpk = min ,usl - p0.5p0.5- lslp0.9987- p0.5p0.5- p0.0013the 99.87th percentilethe medianprocess capabilityprocess characterization93capability metricsgive bo

30、th cp and cpkcp - the best it can be.cpk - what it actually is.process capabilityprocess characterization94stability vs capability67891011121314usllslusllsl5101520253067891011121314usllsl51015202530usllslcapablenot capablestablenot stableprocess stability and capability are two distinct propertiespr

31、ocess capabilityprocess characterization95if the process is not capable . . .check to see if the process is significantly off target? if so, the process must be optimized in such a way as to move the process mean to the target.if the process is essentially on target, it will be necessary to reduce p

32、rocess variation by identifying the independent variables that are potential sources of that variation.the optimization will identify levels of these independent variables that result in improved process performance.use the cross reference matrix to identify independent variables which may be major

33、sources of variabilityprocess optimizationprocess characterization96capability improvementscpk = 1.0lsluslmeanlsluslmeancpk = 1.03 3 -4-3-2-101234-6-556-7-8 0-4 -3 -2 -1 1 2 3 4 -6 -5 5 6 process capabilitydistribution off-centerdistribution on-centercp = 2.0cp = 1.0process characterization97step 2:

34、 process capabilityobjectivesunderstand measurement system capability.understand process stability and process/machine capability.deliverablesacceptable %gr&r and p/t ratios for the measurement of critical variables (%gr&r 30% min., 10% goal, p/t ratio 30% min., 5% goal)process stabilized (s

35、tability index 5% min., .27% goal)known process capability for critical variableschecksdo %gr%r and p/t ratios meet minimum requirements?does process stability meet minimum requirements?cpk measured for all critical variables?does material or test quality effect process capability?actions (if needed

36、)measurement system improvements or purchase of new measurement systemfinding new measurement methodsimplementing data collection and analysisfinding and removing assignable causes of variationinvolving supplier quality, equipment calibration, etc. to remove variationprocess characterization98proces

37、s optimizationidentify/prioritize independent variables which may have an effect on the response variable characteristiclist controlled independent variables (experimental factors)list uncontrolled independent variables (noise factors)determine levels of controlled independent variablesidentify sign

38、ificant independent variablesscreening experimentsoptimize the processresponse surface experimentsconfirm the optimization modelconfirmation runsprocess optimizationoptimization involves an iterative approach. dont try to optimize a process in one experiment.it is unlikely to locate the true optimum

39、 levels. process characterization99the goal of optimization optimize a process both in terms of the mean output and the variation around the mean doe is used to systematically investigate the relationship between the inputs and the outputs well designed experiments provide the most efficient means f

40、or understanding a process with the highest probability of success poorly designed experiments can waste time and resources; little or no useful informationprocess characterization100identify/prioritize independent variablesmost of the influential independent variables have been identified while des

41、cribing the total process.some new independent variables may have been added as a result of the passive data collection analysis.select those that have the highest probability of influencing the response variable.list both the controlled independent variables and uncontrolled independent variables (

42、noise factors).process optimizationprocess characterization101identify significant independent variablesuse a screening experiment to determine which of the independent variables have a significant impact on the response variable.the screening experiment design should allow estimation of each indepe

43、ndent variables main effects and estimation of the two-way interactions between each pair of independent variables.main effectsabcdtwo-way interactionsabacadbcbdcdprocess optimizationprocess characterization102determine levels of controlled variablesuse best judgment to select low and high levels se

44、nsitivity studies, center pointslevels too close may hide a significant effectprocess variation may mask effect of the experimentlevels too extreme may result in bad outputsome cells may be impossible to performprocess optimizationprocess characterization103screening experiment designsfull factorial

45、 designsfractional factorial designsprocess optimizationscreening designs are two-level designs used to determine which factors have a significant effect on the response variableused to “screen” out unimportant factorsalso used to “hunt” for an optimumprocess characterization104full factorial experi

46、mental designrun every possible combination of high and low levelsrun12345678alowlowlowlowhighhighhighhighblowlowhighhighlowlowhighhighclowhighlowhighlowhighlowhightemppresspowerindependent variablesresponse8.03.2process optimizationprocess characterization105full factorial design

47、- main effectsto evaluate the main effect of a (temperature), compare the averages of the two levelsrun12345678alowlowlowlowhighhighhighhighblowlowhighhighlowlowhighhighclowhighlowhighlowhighlowhightemppresspowerindependent variablesresponse34.20significant difference?the

48、analysis requires a measure of experimental variability process optimizationprocess characterization106replication in a factorial designeach run of the experiments design must be replicated in order to estimate experimental variation and use statistical tests of significance.run12345678alowlowlowlow

49、highhighhighhighblowlowhighhighlowlowhighhighclowhighlowhighlowhighlowhightemppresspowerindependent variables1.73.2response1.73.01.53.3randomize!process optimizationprocess characterization107full factorial design - two-way interactionsrun1234567

50、8alowlowlowlowhighhighhighhighblowlowhighhighlowlowhighhighclowhighlowhighlowhighlowhightemppresspowerindependent variablesresponse05.955.954.90consider the ab interaction.obtain the averages for each combinationprocess optimizationprocess characterization108interaction pl

51、ota = lowa = high3.03.54.04.55.05.56.06.5b = lowb = highresponsethe difference in slopes indicates there is an ab interaction process optimizationprocess characterization109larger screening designssuppose we are considering 8 independent variablesfull factorial 256 runsoverall mean1main effects8a,b,

52、c,d,e,f,g,htwo-way interactions 28ab,ac,bc,bd,ef,eg, . . .higher order interactions 219fractional factorial 64 runsoverall mean1main effects8a,b,c,d,e,f,g,htwo-way interactions 28ab,ac,bc,bd,ef,eg, . . .higher order interactions 27moreefficientfractional factorial designs are more efficient resoluti

53、on v designprocess optimizationprocess characterization110resolution v fractional factorial screening designsresolution v designs are a class of fractional factorial designs that provide estimates of the main effects and the two-way interactions, and minimize the number of runs required.designs with

54、 lower resolution (iii and iv) cannot provide clean estimates of the main effects and two-way interactions. such designs are sometimes used to screen through a very large number of independent variables, and are usually followed by a resolution v interaction experiment.contact your local statistical

55、 resource before using resolution iii or iv fractional factorial designs process optimizationprocess characterization111resolution v fractional factorial screening designsnumber of runsindependent variablesfull factorialres. v fractional factorial24438841616532166643271286482566495121281010241281120

56、48128larger fractional factorial designs are even more efficient process optimizationprocess characterization112analysis of factorial screening experimentscheck data for outliers and/or collection errors. remove improper data values.if there are no significant effects: consider increasing difference

57、s between factor levels. take steps to decrease response measurement variation. consider additional factors.experiment should have been replicated. consult a specialist.use normal probability plot of effects to determine importance of effectsuse interaction plot to determine effect of interacting fa

58、ctors. factors involved in significant interactions cannot be analyzed using main effects plots. use confidence intervals if possible.use anova table to determine importance of effectscalculate the natural log of the standard deviation for each treatment combination. repeat the analysis using this r

59、esponse variable to understand and control variation.use main effects plots to determine the effects of levels for significant factors. use confidence intervals if possible.design is not balanced. contact a specialist for analysis are there extremely large or small data values?are there more than tw

60、o factors?is every treatment combination represented by more than one independent data value?is every treatment combination represented by at least one data value?consider the interaction effects first. are interactions significant?are interaction free main effects significant?yesnononoyesyesnoyesyesnoyesnostartwrite reportprocess optimi