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Ch 4 - 28 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Example R-Chart

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Ch 4 - 29 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e x Chart Calculations

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Ch 4 - 30 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e x-Chart Example

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Ch 4 - 31 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Using x- and R-Charts Together Each measures process differently Process average and variability must be in control

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Ch 4 - 32 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Example x-Chart

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Ch 4 - 34 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e UCL LCL UCL Sample observations consistently below the center line Sample observations consistently above the center line Control Chart Patterns

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Ch 4 - 35 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Control Chart Patterns LCL UCL Sample observations consistently increasing Sample observations consistently decreasing

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Ch 4 - 36 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Control Chart Patterns UCL LCL UCL Sample observations consistently below the center line Sample observations consistently above the center line

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Ch 4 - 38 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Control Chart Patterns 1. 8 consecutive points on one side of the center line. 2. 8 consecutive points up or down across zones. 3. 14 points alternating up or down. 4. 2 out of 3 consecutive points in zone A but still inside the control limits. 5. 4 out of 5 consecutive points in zone A or B.

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Ch 4 - 41 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Sample Size Determination Attribute control charts –50 to 100 parts in a sample Variable control charts –2 to 10 parts in a sample

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Ch 4 - 42 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Process Capability Range of natural variability in process – Measured with control charts. Process cannot meet specifications if natural variability exceeds tolerances 3-sigma quality – specifications equal the process control limits. 6-sigma quality –specifications twice as large as control limits

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Ch 4 - 43 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Process Capability Process cannot meet specifications Process can meet specifications Process capability exceeds specifications PROCESS Natural control limits Natural control limits Natural control limits Design specifications Design specifications Design specifications

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Ch 4 - 44 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Acceptance Sampling Accept/reject entire lot based on sample results Not consistent with TQM of Zero Defects Measures quality in percent defective

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Ch 4 - 45 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Sampling Plan Guidelines for accepting lot Single sampling plan –N = lot size –n = sample size (random) –c = acceptance number –d = number of defective items in sample If d <= c, accept lot; else reject

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Ch 4 - 46 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Producer’s & Consumer’s Risk TYPE I ERROR = P(reject good lot) – or producer’s risk –5% is common TYPE II ERROR = P(accept bad lot) – or consumer’s risk –10% is typical value

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Ch 4 - 47 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Quality Definitions Acceptance quality level (AQL) –Acceptable fraction defective in a lot Lot tolerance percent defective (LTPD) –Maximum fraction defective accepted in a lot

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Ch 4 - 48 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Operating Characteristic (OC) Curve Shows probability of lot acceptance Based on –sampling plan –quality level of lot Indicates discriminating power of plan

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Ch 4 - 49 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Operating Characteristic Curve

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Ch 4 - 50 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Average Outgoing Quality (AOQ) Expected number of defective items passed to customer Average outgoing quality limit (AOQL) is –maximum point on AOQ curve

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Ch 4 - 51 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e AOQ Curve 0.015 0.010 0.005 0.010.020.030.040.050.060.070.08 0.09 0.10 AOQL Average Outgoing Quality (Incoming) Percent Defective AQLLTPD

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Ch 4 - 52 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Double Sampling Plans Take small initial sample –If # defective < lower limit, accept –If # defective > upper limit, reject –If # defective between limits, take second sample Accept or reject based on 2 samples Less costly than single-sampling plans

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Ch 4 - 53 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Multiple (Sequential) Sampling Plans Uses smaller sample sizes Take initial sample –If # defective < lower limit, accept –If # defective > upper limit, reject –If # defective between limits, resample Continue sampling until accept or reject lot based on all sample data

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Ch 4 - 54 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Choosing A Sampling Method An economic decision Single sampling plans –high sampling costs Double/Multiple sampling plans –low sampling costs

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