1. Copyright 2006 John Wiley & Sons, Inc. Beni Asllani University of Tennessee at Chattanooga Operations Management Chapter 3 Supplement Roberta Russell & Bernard W. Taylor, III Operational Decision-Making Tools: Acceptance Sampling

2. TOOLS FOR DETECTION OF QUALITY PROBLEMS: ACCEPTANCE SAMPLING  Accept or reject batch based on a sample  Reasons to use: supply process is unstable supply process is unstable cost of acceptance sampling is less than cost of 0% sampling or 100% sampling cost of acceptance sampling is less than cost of 0% sampling or 100% sampling  Sampling plans single single double double sequential sequential

3. Acceptance Sampling  Purposes Determine quality level Determine quality level Ensure quality is within predetermined level Ensure quality is within predetermined level  Advantages Economy Economy Less handling damage Less handling damage Fewer inspectors Fewer inspectors Upgrading of the inspection job Upgrading of the inspection job Applicability to destructive testing Applicability to destructive testing Entire lot rejection (motivation for improvement) Entire lot rejection (motivation for improvement)

4. Acceptance Sampling  Disadvantages Risks of accepting “bad” lots and rejecting “good” lots Risks of accepting “bad” lots and rejecting “good” lots Added planning and documentation Added planning and documentation Sample provides less information than 100- percent inspection Sample provides less information than 100- percent inspection

5. Copyright 2006 John Wiley & Sons, Inc.Supplement 3-5 Acceptance Sampling  Accepting or rejecting a production lot based on the number of defects in a sample  Not consistent with TQM or Zero Defects philosophy producer and customer agree on the number of acceptable defects producer and customer agree on the number of acceptable defects a means of identifying not preventing poor quality a means of identifying not preventing poor quality percent of defective parts versus PPM percent of defective parts versus PPM

6. Copyright 2006 John Wiley & Sons, Inc.Supplement 3-6 Producer’s and Consumer’s Risk  AQL or acceptable quality level proportion defect the customer will accept a given lot proportion defect the customer will accept a given lot  LTPD or lot tolerance percent defective limit on the number of defectives the customer will accept limit on the number of defectives the customer will accept   or producer’s risk probability of rejecting a good lot probability of rejecting a good lot  β or consumer’s risk probability of accepting a bad lot probability of accepting a bad lot

7. Copyright 2006 John Wiley & Sons, Inc.Supplement 3-7 Producer’s and Consumer’s Risk (cont.) Sampling Errors Good Lot Bad Lot AcceptReject No Error Type I Error Producer’ Risk Type II Error Consumer’s Risk No Error

8. Copyright 2006 John Wiley & Sons, Inc.Supplement 3-8 Operating Characteristic (OC) Curve  shows probability of accepting lots of different quality levels for a specific sampling plan  assists management to discriminate between good and bad lots  exact shape and location of the curve is defined by the sample size (n) and acceptance level (c) for the sampling plan

9. Copyright 2006 John Wiley & Sons, Inc.Supplement 3-9 An OC Curve Probability of Acceptance Percent defective |||||||||012345678012345678|||||||||012345678012345678 100 100 – 95 95 – 75 75 – 50 50 – 25 25 – 10 10 – 0 0 –  = 0.05 producer’s risk for AQL  = 0.10 Consumer’s risk for LTPD LTPDAQL Bad lots Indifference zone Good lots Figure S3.9

10. Copyright 2006 John Wiley & Sons, Inc.Supplement 3-10 Return whole shipment The “Perfect” OC Curve % Defective in Lot P(Accept Whole Shipment) 100 100 – 75 75 – 50 50 – 25 25 – 0 0 – ||||||||||| 0102030405060708090100 Cut-Off Keep whole shipment

11. Copyright 2006 John Wiley & Sons, Inc.Supplement 3-11 Average Outgoing Quality (AOQ)  Expected number of defective items that will pass on to customer with a sampling plan  Average outgoing quality limit (AOQL) maximum point on the curve maximum point on the curve worst level of outgoing quality worst level of outgoing quality

12. Copyright 2006 John Wiley & Sons, Inc.Supplement 3-12 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

13. Copyright 2006 John Wiley & Sons, Inc.Supplement 3-13 Multiple 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