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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