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Chapter 9

Chapter 9. Lot-by-Lot Acceptance Sampling for Attributes. Acceptance-Sampling Problem . Acceptance sampling is concerned with inspection and decision making regarding products. Three aspects of sampling are important : Involves random sampling of an entire “lot”

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Chapter 9

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  1. Chapter 9 Lot-by-Lot Acceptance Sampling for Attributes

  2. Acceptance-Sampling Problem • Acceptance samplingis concerned with inspection and decision making regarding products. • Three aspects of sampling are important: • Involves random sampling of an entire “lot” • Accept and Reject Lots (does not achieve quality improvement) “Lot sentencing” • Audit tool

  3. Acceptance-Sampling Problem • Three approaches to lot sentencing: • Accept with no inspection • 100% inspection • Acceptance sampling

  4. Acceptance-Sampling Problem Why Acceptance Sampling and Not 100% Inspection? • Testing is destructive • Cost of 100% inspection is high • 100% inspection is not feasible (require too much time) • If vendor has excellent quality history

  5. Acceptance-Sampling Problem Advantages and Disadvantages of Sampling Advantages • Less expensive • Reduced damage • Reduces the amount of inspection error Disadvantages • Risk of accepting “bad” lots, rejecting “good” lots. • Less information generated • Requires planning and documentation

  6. Acceptance-Sampling Problem Types of Sampling Plans • There are variables sampling plans and attribute sampling plans (this chapter concentrates on attributes) • Single sampling plan • Double-sampling plan • Multiple-sampling plan • Sequential-sampling

  7. Acceptance-Sampling Problem Lot Formation • Considerations before inspection: • Lots should be homogeneous • Larger lots more preferable than smaller lots • Lots should be conformable to the materials-handling systems used in both the vendor and consumer facilities.

  8. Acceptance-Sampling Problem Random Sampling • The units selected for inspection should be chosen at random. • Random samples are not used, bias can be introduced. • If any judgment methods are used to select the sample, the statistical basis of the acceptance-sampling procedure is lost.

  9. Single-Sampling Plans For Attributes Definition of a Single-Sampling Plan • A single sampling plan is defined by sample size, n, and the acceptance number c. Say there are N total items in a lot. Choose n of the items at random. If at least c of the items are unacceptable, reject the lot. • N = lot size • n = sample size • c = acceptance number • d = observed number of defectives • The acceptance or rejection of the lot is based on the results from a single sample - thus a single-sampling plan.

  10. Single-Sampling Plans For Attributes The OC Curve • The operating-characteristic (OC) curvemeasures the performance of an acceptance-sampling plan. • The OC curve plots the probability of accepting the lot versus the lot fraction defective.

  11. Single-Sampling Plans For Attributes Designing a Single-Sampling Plan with a Specified OC Curve • Let the probability of acceptance be 1 -  for lots with fraction defective p1. • Let the probability of acceptance be  for lots with fraction defective p2. • Assume binomial sampling (with type-B OC curves) is appropriate.

  12. Single-Sampling Plans For Attributes Designing a Single-Sampling Plan with a Specified OC Curve • The sample size n and acceptance number c are the solution to

  13. Single-Sampling Plans For Attributes Example • Consider constructing a sampling plan for which • p1 = 0.01 •  = 0.05 • p2 = 0.06 •  = 0.10 • N = 1000 • Using computer software or a graphical approach (using an appropriate binomial nomograph) it can be shown that the necessary values of n and c are 85 and 2, respectively.

  14. Military Standard 105E (ANSI/ASQC Z1.4 ISO 2859) Description of the Standard • Developed during World War II • MIL STD 105E is the most widely used acceptance-sampling system for attributes • Gone through four revisions since 1950. • MIL STD 105E is a collection of sampling schemes making it an acceptance-sampling system

  15. Military Standard 105E (ANSI/ASQC Z1.4 ISO 2859) Description of the Standard • Three types of sampling are provided for: • Single • Double • Multiple • Provisions for each type of sampling plan include • Normal inspection • Tightened inspection • Reduced inspection

  16. Military Standard 105E (ANSI/ASQC Z1.4 ISO 2859) Description of the Standard • The acceptable quality level (AQL) is a primary focal point of the standard • The AQL is generally specified in the contract or by the authority responsible for sampling. • Different AQLs may be designated for different types of defects. • Defects include critical defects, major defects, and minor defects. • Tables for the standard provide are used to determine the appropriate sampling scheme.

  17. Military Standard 105E (ANSI/ASQC Z1.4 ISO 2859) Description of the Standard • Switching Rules • Normal to tightened • Tightened to normal • Normal to reduced • Reduced to normal • Discontinuance of inspection

  18. Military Standard 105E (ANSI/ASQC Z1.4 ISO 2859) Procedure • Choose the AQL • Choose the inspection level • Determine the lot size • Find the appropriate sample size code letter from Table 14-4 • Determine the appropriate type of sampling plan to use (single, double, multiple) • Enter the appropriate table to find the type of plan to be used. • Determine the corresponding normal and reduced inspection plans to be used when required.

  19. Military Standard 105E (ANSI/ASQC Z1.4 ISO 2859) Example • Suppose a product is submitted in lots of size N = 2000. The AQL is 0.65%. Say we wanted to generate normal single-sampling plans. • For lots of size 2000, (and general inspection level II) Table 14-4 indicates the appropriate sample size code letter is K. • From Table 14-5 for single-sampling plans under normal inspection, the normal inspection plan is n = 125, c = 2.

  20. Military Standard 105E (ANSI/ASQC Z1.4 ISO 2859) Discussion • There are several points about the standard that should be emphasized: • MIL STD 105E is AQL-oriented • The sample sizes selected for use in MIL STD 105E are limited • The sample sizes are related to the lot sizes. • Switching rules from normal to tightened and from tightened to normal are subject to some criticism. • A common abuse of the standard is failure to use the switching rules at all.

  21. Military Standard 105E (ANSI/ASQC Z1.4 ISO 2859) Discussion • ANSI/ASQC Z1.4 or ISO 2859 is the civilian standard counterpart of MIL STD 105E. • Differences include: • Terminology “nonconformity”, “nonconformance”, and “percent nonconforming” is used. • Switching rules were changed slightly to provide an option for reduced inspection without the use of limit numbers • Several tables that show measures of scheme performance were introduced • A section was added describing proper use of individual sampling plans when extracted from the system. • A figure illustrating switching rules was added.

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