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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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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