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Chapter 13 Statistical Quality Control Metho

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  • Chapter 13 Statistical Quality Control Method

  • Statistical Quality Control MethodsStatistical QualityControl MethodsAcceptance SamplingStatistical ProcessControlAttributesVariablesAttributesVariablesType of Data

  • Statistical Quality Control MethodsAttribute Data: data which count items, such as the number of defective items on a sample Variable Data: data which measure a particular product characteristic such as length or weight

  • Statistical Quality Control MethodsSampling Error Sample results are not representative of the actualpopulation or process Prducers riskCustomersrisk

  • Acceptance SamplingDesigning a Sampling Plan for AttributeCosts to justify inspectionFull or 100% inspection or not?

  • Acceptance SamplingPurpose of Sampling PlanFind its quality

    Ensure that the quality is what it is supposed to be

  • Acceptance Samplingn: Number of units in the sample depended on the lot sizec: the acceptance numberDesigning a Sampling Plan for AttributeAQL (acceptable quality level): maximum percentage of defects that a company is willing to accept

    LTPD (lot tolerance percent defective): minimum percentage of defects that a company is willing to reject

    : producers risk

    : consumers risk

  • Acceptance SamplingDesigning a Sampling Plan for Attributec LTPD/AQL nAQL

    0 44.890 0.052 10.946 0.355 6.509 0.818 4.890 1.366 4.057 1.970 3.549 2.613 3.206 3.286 2.957 3.981 2.768 4.695 2.618 5.426=0.05=0.10MIL-STD-105E

  • Operating Characteristic Curve

  • Operating Characteristic CurvepnpP(r c)1%0.990.972%1.980.95

  • Acceptance SamplingDetermine a Sampling Plan for VariablesControl Limit: Points on an acceptance sampling chart that distinguish the accept and reject regions. Also, points on a process control chart that distinguish between a process being in and out of control.

  • Acceptance SamplingDetermine a Sampling Plan for Variables

  • Acceptance Sampling

  • Statistical Process ControlStatistical process control (SPC) Statistical method for determining whether a particularprocess is in or out of control. Central Limit Theorem

  • Statistical Process Control

  • Statistical Process Control

  • Statistical Process ControlSPC Using Attribute MeasurementAttribute data are data that are counted, such as good or badunits produced by a machine.SamplesdefectsSample size=6defects=2

  • Statistical Process ControlSPC Using Attribute MeasurementCenter line = = Long-run average percent defective Standard deviation of sample = Note: X~Bernoulli distribution E(x)=p V(x)=p(1-p)

  • Statistical Process ControlVariable Measurements Using X and R ChartsAn X chart tracks the changes in the means of samples by plottingthe means that were taken from a process.

    An R chart tracks the changes in the variability by plotting the range within each sample.

  • Statistical Process ControlVariable Measurements Using X and R ChartsSetup Control Chart:At least 25 samplesSetup control limitsControl limits forUpper control limit forLower control limit for

  • Statistical Process Controln A2 D3 D4 1.88 0 3.27 1.02 0 2.57 0.73 0 2.28 0.58 0 2.11 0.48 0 2.00 0.42 0.08 1.92 0.37 0.14 1.86 0.34 0.18 1.82 0.31 0.22 1.78 0.29 0.26 1.74 0.27 0.28 1.72 0.25 0.31 1.69 n A2 D3 D4 0.24 0.33 1.67 0.22 0.35 1.65 0.21 0.36 1.64 0.20 0.38 1.62 0.19 0.39 1.61 0.19 0.40 1.60 0.18 0.41 1.59

  • Statistical Process Control

  • Process Capability

  • Process CapabilityProcess Capability RatioThe larger the ratio, the greater the potential for producingparts within tolerance from the specified process.

  • Process CapabilityCapability IndexTo determine whether the process mean is closer to theupper specification limit, or the lower specification limit.

  • Six SigmaQuality improvement program developed by Motorola to reduceprocess variation to 50% of design toleranceCp=1; defect rate = 2700 per million partsCp=2; defect rate = 3.4 per million parts