SPC_Training

1、1SPC training1/1/20222Beginnings of SPCDr. Walter Shewhart pioneered Industrial Control (SPC) in the 1920s & 30s.The U.S. used industrial control very successfully during WWII.After the war, U.S. industries dropped industrial control in favor of a return to mass production.Japan, devastated by t

2、he war, adopted the teachings of Dr. W. Edwards Deming and Dr. Joseph M. Juran.Japanese companies continued to develop tools for process control such as company wide quality control and quality circles, the 7 Quality Tools and the 7 Management and Planning Tools1/1/20223Definition of Quality“Fitness

3、 for purpose or use” (Juran).“The totality of features and characteristics of a product or service that bear on its ability to satisfy stated or implied needs” (ISO 8402: 1986).Manufacturing based - Quality is defined as the desirable outcome of engineering and manufacturing practice, or conformance

4、 to specifications1/1/20224What is a Process?The transformation of a set of inputs (materials, methods, operations) into a set of outputs (products, information, services - more generally - results)ProcessMaterialsMethods/ProceduresInformation(includingspecifications)People(skills, training,knowledg

5、e)EnvironmentRecordsEquipment(tools, plant)FeedbackThe voice of theprocess (SPC)INPUTSOUTPUTSProductsServicesInformationPaperworkSUPPLIERSCUSTOMERSFeedbackThe voice of thecustomer1/1/20225What is Control?Control refers to the measurements of the performance of a process and feedback required for cor

6、rective action.A process is said to be operating in a state of statistical control when common causes are the only source of variation.Statistical control is not a natural state for most processesIt is an achievement, one by one, special cause eliminationThe initial function of a process control sys

7、tem is to provide a statistical signal when special causes of variation are present, and to avoid giving false signals when they are not present1/1/20226Quality Tool KitStatistical Process Control (SPC) is a methodology which uses the basic graphical and statistical tools to analyze, control and red

8、uce variability within a processSPC uses a number of basic quality tools Run ChartHistogramControl ChartDistributions and confidence intervals (Capability)1/1/20227The SPC SystemA systematic approach to answering the following questionsCan we do the job correctly? (capability)Are we doing the job co

9、rrectly? (control)Have we done the job correctly? (quality assurance)Could we do the job better? (improvement)Enhances process controlRequires empowered employees1/1/20228Sources of VariationVariation is a fact of nature and a fact of life Common cause variation - within the processthey are inherent

10、 in any process all the time (part of system design: equipment design, material characteristics, inspection methods, maintenance)their impact varies from day to dayindividually common causes have a slight effect on variationcollectively, common causes can add up to significant variationaccount for a

11、bout 80 to 90 percent of the observed variation Special cause variation - outside the processspecial causes appear sporadically in a processthey originate outside the process (bad batch of material, poorly trained operator, excessive tool wear, not following procedure, over adjustment)can contribute

12、 a small amount or large amount of variation but typically have a much bigger impact than any one common cause1/1/20229Special Cause Common Cause34115 Filled Hologram AreaU Chart; variable: Hologram DefectsU: .03917 (.03917); Sigma: .02799 (.02799); n: 50.102030405060708090-0.020.000.020.040.060.080

13、.100.120.140.160.0000.03917.12313Statistics(Samples):Mean = .03917Special CauseCommon Cause1/1/202210Precision and AccuracyPrecision - the degree of the spread of the values in a processAccuracy - the ability of a process to hit the target value1/1/202211Precision and AccuracyTrue Value1234512345Tru

14、e ValueTrue ValueNot precise and not accuratePrecise but not accurateTrue Value12345Accurate but not preciseAccurate and precise1/1/202212Precision and AccuracyProcess characterizationThe distinction between precision and accuracy can only be assessed by looking at a number of results or values, not

15、 looking at individual oneTamperingMaking decisions about adjustments to be made to a process on the basis of one individual result may give an undesirable outcome due to lack of information about accuracy and precisionSpecial cause before common causeThe adjustment to correct lack of process accura

16、cy (special cause) is likely to be simpler than the larger investigation usually required to understand or correct problems of spread or large variation (common cause)1/1/202213Measures of Accuracy or CenteringMean / Median / ModeMeasure of centering - meanniinnxnxxxxX1321.z Difference between mean,

17、 median and modeMode -Most frequent valueMedian - middle valueMean - average value1/1/202214Arithmetic MeanThe sample mean is the measure of central tendency that most accurately reflects the population meanVery sensitive to extreme scoresDefined as the point at which the sum of the deviations from

18、the mean equals to zero.0) 1, 0 , 1()4(5 , 4 , 3 isdeviationstheofsumTheofmeanScoreExample:1/1/202215MedianThe point at which one half, or 50% of the scores fall above and one half, or 50%, fall below (50th percentile).List the values in order, either from highest to lowest or lowest to highest.Find

19、 the middle most scoreWhen there is an even amount of scores, the median is simply the average between the two middle valuesExample:084,36500,34668,37500,25456,32500,34668,37365,54456,135 andofaveragemedian1/1/202216ModeThe mode is the value which occurs most frequentlyList all of the values in a di

20、stribution, but list only onceTally the number of times that each value occursThe value that occurs the most often is the mode1/1/202217Measures of Spread and DeviationMeasure of spread - rangekiikkRkRRRRR1321.z Measure of deviation from mean - estimated process standard deviation1)(12nXxsnii1/1/202

21、218Central Limit TheoremWhat is the Central Limit Theorem?If we draw samples of size from a population with mean m m and standard deviation , then as the number of samples increases in size, the distribution of sample means approaches a normal distribution with a mean m m and a standard error of the

22、 means of What does it mean?We can deduce statistical information about a population by taking samples of the populationHow many samples is enough? 30 applies for all distributions, normal or notSmaller sample sizes apply if we believe the population is normally distributed (2 - 10 samples)n1/1/2022

23、19The Normal Distributionm1s2s3s- 3s- 2s- 1s68.3% of valueslie between95.4% of valueslie between99.7% of valueslie betweenThe Normal DistributionzArea under the curve is knownzIf we know product specification and have goodestimates of the population average and standarddeviation, we can estimate the

24、 percentage of manufactured products that fall within (or outside) the requirementsm1s2s3s- 3s- 2s- 1s34. 13%34. 13%13. 59%13. 59%2. 15%2. 15%. 13%. 13%1/1/202220SymbolsSampleSampling Distribution of MeanPopulationMeanXm mxm mStandard DeviationS X nXmm and x1/1/202221Example 36 samples have been tak

25、en from a population with a mean age of 40 and a standard deviation of 6 years. What would the mean of the sampling distribution be? Answer:m1s3s- 3s- 1s34. 1%34. 1%40 mmX What would be the standard deviation of the sampling distribution?Answer:1366 nX1/1/202222Example (cont.)According to the illust

26、ration, what percent of the time would you expect the mean of one sample to be between 40 and 41?Answer: m1s3s- 3s- 1s34. 1%34. 1%1 .34What percent of the time would you expect the mean of one sample to be between 39 and 41?Answer: %2 .681/1/202223Z Score A Z score is simply the number of standard d

27、eviations away from the mean a particular measurement is located. Provides a method for how likely a certain score will occurIt is a standard to compare distributions XXZmIf m m 15 15 and X = 2, what z corresponds to a raw score of 205 . 221520Zm1s2s3s- 3s- 2s- 1s34. 13%34. 13%13. 59%13. 59%2. 15%2.

28、 15%. 13%. 13%1/1/202224Areas under the normal curve Table.48612.2.48212.1.47722.0.47131.9.46411.8.00ZZ Score ExampleA population has a mean of 20 and a standard deviation of 4. You plan to chose a random sample of 64. What is the probability of a sample mean between 20 and 21.0 . 25 . 015 . 0215 .

29、064420mmZnXXUsing a table that provides the probabilities for a normal distribution:%72.474772.0 . 2Z1/1/202225The Normal DistributionCapability Histogram: Blanking Top PositionWithin SD: .0061; Cp: 1.717; Cpk: 1.348Overall SD: .0160; Pp: .6503; Ppk: .5105LSL: -.0313; Nom.: 0.000; USL: .0313Top-0.06

30、-0.05-0.04-0.03-0.02-0.010.000.010.020.030.040.050.060.07-3.*SLSLNominalUSL+3.*S02004006008001/1/202226Error Calculations Type I er r or : Type I I er r or : Type I error - saying the process is out of control when it is really in control. (calculation in tails of distribution curveType II error say

31、ing the process is in control when it is really out of control. (calculation under curve between limits.1/1/202227Control Charts1/1/202228Reasons for Control Chart PopularityProven technique for improving productivityEffective tool for defect preventionPrevents unnecessary process adjustmentProvides

32、 diagnostic informationProvides information about process capability1/1/2022291/1/202230Control Chart AnatomyUpper Control Limit (UCL) and Lower Control Limit (LCL) are calculated so that if the process is in control, the points will fall within these limits.Center Line (CL) usually the average. Sho

33、ws where the acquired data is centeredControl Charts are always TIME ORDERED plots. Time (or sample number) Sam pl e average UCL LCL CL 1/1/202231The control chart model3-sigma control limits are used to minimize type I and type II errors.Upper Control Limit (UCL), Center line (CL), and Lower Contro

34、l Limit (LCL).Generic formulas that apply to all control charts where L is the distance from the centerline (in most cases 3 for 3 sigma).XmCLnXmLLCLnXmLUCL1/1/202232Control Limits X bar Range Chart1/1/202233Control Limits X bar Range Chart1/1/202234Warning LimitsAction Limits Usually 3, action is t

35、aken to find an assignable cause when a point lies outside these limits.Warning Limits Control limits found inside 3 warn of possible upcoming problems.1/1/202235Control Charts Out of Control ConditionsZONE AZONE AZONE BZONE BZONE CZONE CLCLUCL.34.34.14.14.02.02One of more points fall outside the co

36、ntrol limits.Two points out of 3 consecutive points, are on the same side of the average in ZONE A or beyond.Four points out of 5 consecutive points are on the same side of the average in ZONE B or beyond.Nine consecutive points are on one side of the average.There are six consecutive points, increa

37、sing or decreasing.There are 14 consecutive points that alternate up and down.There are 15 consecutive points within ZONE C (above and below the average).1/1/202236Control ChartsAnalyzing for ActionOut of Control SymptomsConditionOne of more points fall outside the control limits.Special cause is af

38、fecting the processTwo points out of 3 consecutive points, are on the sameside of the average in ZONE A or beyond.Special cause is affecting the processFour points out of 5 consecutive points are on the sameside of the average in ZONE B or beyond.Special cause may be affecting the processNine consec

39、utive points are on one side of the average.The process average is shifting - theprocess is not stableThere are six consecutive points, increasing ordecreasing.Suggests a process drift - the process is notstableThere are 14 consecutive points that alternate up anddown.Suggests two streams are affect

40、ing theprocess - not random variation.There are 15 consecutive points within ZONE C (aboveand below the average).Measuring instrument may have lostprecision or data may be suspect.1/1/202237Control Chart SelectionNeed toConstruct aControl ChartVariables(measurements)orattributes? (go-nogo)Defects or

41、Defective?ConstantSampleSize?np-Chartp-ChartConstantSample Size?c-Chartu-ChartIs n fixedand n10Xbar S ChartIMR ChartXbar R ChartDefectivesYesNoNon=12=n1 then natural variation is less than Engineering ToleranceTarget Cp value should be a minimum of 1.5Rule of Thumb: Cp x 3 = Sigma CapabilityDoes not

42、 consider whether the process average is centeredConsidered to be more of a process potentialCp = Upper Specification Limit Lower Specification Limit61/1/202240Capability Ratio CpkIf Cpk = 1, then the process is just barely capable of producing products within engineered tolerances.If Cpk 1, then th

43、e process is more than capable of producing products within engineered tolerances.If Cpk 1, then the process is not capable of producing 100% acceptable products.If Cpk has a negative value, then the overall process average is outside of one of the specification limits.Cp and Cpk are the same value

44、whenever the process is centered.Whenever the process is not centered Cpk Cp3,3LSLyyUSLMinimumCpk1/1/202241One Sided Indexes Cpu =U pper S pecification Lim it m3Cpl = m - Lower Specification Limit3Cpk = Min (Cpl, Cpu)Cpu = 0.1251 0.08793(0.00673)= 1.842Cpl = 0.0879 0.06253(0.00673)= 1.257Cpk = 1.257

45、AMEX Border Example1/1/202242Process CapabilityLSLUSLLSLUSL4101641016=4=2LSLUSL41016=271/1/202243Process CapabilitySigma levels vs. dpmCapability level with allowed shift of 1.5 capabilitydpm3.4555532552335513502,6125522,75066,80755158,655308,5381/1/202244Control ChartsThree step process from control to capabilityCollectionProcess is