Transcription of Process Capability Analysis
1 Process Capability AnalysisMarch 20, 2012 Andrea and Quality Management2 Process Capability Analysis3 Process Capability Analysis for Normal Distributions4 Process Capability Analysis for Non-Normal DistributionsProcess Capability Analysis2 / 68 Quality and Quality Management1 Quality and Quality Management2 Process Capability Analysis3 Process Capability Analysis for Normal Distributions4 Process Capability Analysis for Non-Normal DistributionsProcess Capability Analysis3 / 68 Quality and Quality ManagementDefinitions and Implications?ISO 9000 is a family ofstandards related to quality managementsystemsand designed to help organisations ensure that they meetthe needs of customers and other to the end of December 2009, at least 1 064 785 ISO 9001 (2000and 2008) certificates had been issued in 178 countries andeconomies.(ISO Survey 2009)?In Italy, 13 066 certificates had been issued.
2 Italy is the Europeanleader and among the first in the world for number of ISO 9001certificates.(ISO Survey 2009) Process Capability Analysis4 / 68 Quality and Quality ManagementDefinitions and Implications?It can be defined:quality: the degree to which a set of inherentcharacteristicsfulfilsrequiremen t;management: coordinated activities to direct and control;quality management system: todirectandcontrolanorganizationwith regard and Measurement of Product: The organization shallmonitor andmeasure the characteristics of the productto verifythatproduct requirementshave been 22514-4:2007 describesprocess capabilityandperformance measuresthat are commonly used. (Statisticalmethods in Process management - Capability and performance - Part4: Process Capability estimates and performance measures) Process Capability Analysis5 / 68 Quality and Quality ManagementDefinitions and Implications?
3 Process Capability : ability of the Process to realize a characteristicthat willfullfil the requirementsfor that characteristic.(ISO 25517-4)?Specification: an explicit set of requirements to be satisfied by amaterial, product or service. Specifications are mandatory if adoptedby a business contract. Specifications must be respected to Capability Analysis6 / 68 Process Capability Analysis1 Quality and Quality Management2 Process Capability Analysis3 Process Capability Analysis for Normal Distributions4 Process Capability Analysis for Non-Normal DistributionsProcess Capability Analysis7 / 68 Process Capability Analysis ?The Capability Analysis is carried out in the following steps:1select the Process to be analysed and collection of data;2identify specific limits according to which Capability Analysis will beevaluated;3verify the Process is under statistical control;4analyse data distribution;5estimate Capability the Capability Analysis to be performed the Process needs to beunder statistical limits can be: the Upper Specification Limit (USL), the LowerSpecification Limit (LSL) and eventually a target value.
4 Specification limitsare usually provided from outside (production requirements, marketrequirements). Specifications can either betwo-sided(when USL and LSLare both specified) orone-sided(either USL or LSL is specified). Process Capability Analysis8 / 68 Process Capability Analysis ?To sum up, a Process is capable when:?it is under statistical control;?it has a low variability rate compared to the range of specified limits;? Process distribution is possibly centered on specification limits(centering).?If a Process respects specifications and is under statistical control itcan be foreseen that specifications will not change in the future. If aprocess respects specifications but is not under statistical control,specification could change in the variability indicates the spread within which of theprocess distribution is contained. A normal distribution has a6 width range centered on the mean ( 3 ).
5 Process Capability Analysis9 / 68 Process Capability Analysis1516171819202122232425 LSLUSLx 3 ^x+3 ^58111417202326293235 LSLUSLx 3 ^x+3 ^The two distributions have same mean and specification limits. However,dispersion in the distribution on the right is higher. Therefore, the processcapability of the distribution on the right is lower than the Process Capability ofthe distribution on the Capability Analysis10 / 68 Process Capability Analysis58111417202326293235 LSLUSLx 3 ^x+3 ^58111417202326293235 LSLUSLx 3 ^x+3 ^The two distributions have the same characteristics as far as shape, position anddispersion are concerned. The limit spread is the same. The Process on the rightis not centered with respect to its specification limits. Therefore processcapability on the right will be Capability Analysis11 / 68 Process Capability Analysisllllllllllllllllllllllllllllllll llllllllProcess SpreadLSLUSLS pecificationsThe Process is both under statisticalcontrol and Process will produce conformingproducts as long as it remains instatistical Capability Analysis12 / 68 Process Capability Analysisllllllllllllllllllllllllllllllll llllllllProcess SpreadLSLUSLS pecificationsThe Process is under statisticalcontrol but it is not the specifications are realistic, aneffort must be immediately made toimprove the Process ( reducevariation) to the point where it iscapable of producing consistentlywithin Capability Analysis13 / 68 Process Capability Analysisllllllllllllllllllllllllllllllll llllllllProcess SpreadLSLUSLS pecificationsThe Process is out of control but it Process must be monitored.
6 Itcannot be expected it will respectspecifics in the Capability Analysis14 / 68 Process Capability Analysisllllllllllllllllllllllllllllllll llllllllProcess SpreadLSLUSLS pecificationsThe Process is both out of controland it is not Process must be adjusted to beunder control, then the capabilityanalysis must be performed Capability Analysis15 / 68 Process Capability Analysis for Normal Distributions1 Quality and Quality Management2 Process Capability Analysis3 Process Capability Analysis for Normal Distributions4 Process Capability Analysis for Non-Normal DistributionsProcess Capability Analysis16 / 68 Process Capability Analysis for Normal DistributionsCP Index?TheCP indexis the most widely used capacity can be calculated only whenUSL and LSL are both theoretical value is:CP=USL LSL6 ifdata is normally can be seen as the ratio between the acceptable variabilityspread and the Process variability practical terms, real values are never known and need to beestimatedaccording to one of the following estimation Capability Analysis17 / 68 Process Capability Analysis for Normal DistributionsPPM Index?
7 Another capacity index is Parts per Million (PPM). This indexindicates the ratio between the number of pieces exceeding thespecification limits and a million produced example, the following CP values produce the PPM shown below:?CP = 1 PPM = 2700;?CP = PPM = 64;?CP = PPM = can be estimated based on empirical data ( the number ofexceeding elements over one million) or with the cumulativedistribution function of the theoretical Capability Analysis18 / 68 Process Capability Analysis for Normal DistributionsCP and PPM interpretationProcess SpreadLSLUSLS pecificationsCase 1: CP> fairly capable processThis Process should produce less than 64non-conforming Process will produce conformingproducts as long as it remains in statisticalcontrol. The Process owner can claim thatthe customer should experience leastdifficulty and greater reliability with thisproduct. This should translate into Process is contained within fourstandard deviations of the Capability Analysis19 / 68 Process Capability Analysis for Normal DistributionsCP and PPM interpretationProcess SpreadLSLUSLS pecificationsCase 2: 1<CP< barely capable processThis Process will produce greater than 64 PPM but less than 2700 Process has a spread just about equalto specification width.
8 It should be notedthat if the Process mean moves to the leftor the right, a significant portion of productwill start falling outside one of thespecification limits. This Process must beclosely Process is contained within three tofour standard deviations of the Capability Analysis20 / 68 Process Capability Analysis for Normal DistributionsCP and PPM interpretationProcess SpreadLSLUSLS pecificationsCase 3: CP<1A not capable processThis Process will produce more than 2700non-conforming is impossible for the current Process tomeet specifications even when it is instatistical control. If the specifications arerealistic, an effort must be immediatelymade to improve the Process ( reducevariation) to the point where it is capable ofproducing consistently within Capability Analysis21 / 68 Process Capability Analysis for Normal DistributionsCP and PPM interpretationProcess SpreadLSLUSLTARGETS pecificationsCase 4: CP<1A not capable processThis Process will also produce more than2700 non-conforming variability and specification width isassumed to be the same as in case 3, butthe Process average is off-center.
9 In suchcases, adjustment is required to move theprocess mean back to target. If no action istaken, a substantial portion of the outputwill fall outside the specification limit eventhough the Process might be in Capability Analysis22 / 68 Process Capability Analysis for Normal DistributionsCP and PPM interpretationThe table presents some recommended guidelines for minimum values ofCP and PPM (source: AIAG):One-SidedTwo-SidedSpecificationsSp ecificationsCPPPMCPPPME xisting existing new Capability Analysis23 / 68 Process Capability Analysis for Normal DistributionsCP and PPM interpretationThe Figure below shows control charts for a Chartfor xGroupGroup summary UCLCLN umber of groups = 40 Center = = = 0 UCL = beyond limits = 0 Number violating runs = 0xbar Chartfor xGroupGroup summary UCLCL lllllllllNumber of groups = 40 Center = = = = beyond limits = 4 Number violating runs = 5 Process Capability Analysis24 / 68 Process Capability Analysis for Normal DistributionsCP and PPM interpretationThe Capability Analysis performed on firsts twenty batches returns a CPgreater than ( , , , , , , , , , , , , , , , 74, , , , 74)
10 = 74 USL = 74 LSL = 74 USL = 74 TARGETP rocess Capability using normal distribution for batches 1 20cp= 20mean= 74sd= from distribution ( , 5)Expected Fraction NonconformingptpLpU= 06= 06= 06ppmppmppm= ( , 5)Observedppm = 0ppm = 0ppm = 0 Process Capability Analysis25 / 68 Process Capability Analysis for Normal DistributionsCP and PPM interpretationThe Capability Analysis performed on lasts twenty batches, where theprocess goes out-of-control, returns a CP less than ( , , , , , , , , , , , , , , , , , , , ) = 74 USL = 74 LSL = 74 USL = 74 TARGETP rocess Capability using normal distribution for batches 21 40cp= 20mean= 74sd= from distribution ( , 5)Expected Fraction NonconformingptpLpU= 05= ( , 5)Observedppm = 0ppm = 0ppm = 0 Process Capability Analysis26 / 68 Process Capability Analysis for Normal DistributionsCPK Index?
