Lot-by-Lot Acceptance Sampling for Attributes

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Chapter 14

• Lot-by-Lot Acceptance Sampling for Attributes

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14-1. The 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
• Accept and Reject Lots (does not achieve quality
  improvement) Lot sentencing
• Audit tool

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14-1. The Acceptance-Sampling Problem

• Three approaches to lot sentencing
• Accept with no inspection
• 100 inspection
• Acceptance sampling

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14-1. The 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

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14-1. The Acceptance-Sampling Problem

• 14-1.1 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

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14-1. The Acceptance-Sampling Problem

• 14-1.2 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

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14-1. The Acceptance-Sampling Problem

• 14-1.3 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.

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14-1. The Acceptance-Sampling Problem

• 14-1.4 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.

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14-2. Single-Sampling Plans For
Attributes

• 14-2.1 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.

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14-2. Single-Sampling Plans For
Attributes

• 14-2.2 The OC Curve
• The operating-characteristic (OC) curve measures
  the performance of an acceptance-sampling plan.
• The OC curve plots the probability of accepting
  the lot versus the lot fraction defective.
• The OC curve shows the probability that a lot
  submitted with a certain fraction defective will
  be either accepted or rejected.

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14-2. Single-Sampling Plans For
Attributes

• 14-2.3 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.

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14-2. Single-Sampling Plans For
Attributes

• 14-2.3 Designing a Single-Sampling Plan with a
  Specified OC Curve
• The sample size n and acceptance number c are the
  solution to

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14-2. 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.

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14-4. Military Standard 105E (ANSI/ASQC
Z1.4 ISO 2859)

• 14-4.1 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

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14-4. Military Standard 105E (ANSI/ASQC
Z1.4 ISO 2859)

• 14-4.1 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

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14-4. Military Standard 105E (ANSI/ASQC
Z1.4 ISO 2859)

• 14-4.1 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.

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14-4. Military Standard 105E (ANSI/ASQC
Z1.4 ISO 2859)

• 14-4.1 Description of the Standard
• Switching Rules
• Normal to tightened
• Tightened to normal
• Normal to reduced
• Reduced to normal
• Discontinuance of inspection

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14-4. Military Standard 105E (ANSI/ASQC
Z1.4 ISO 2859)

• 14-4.2 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.

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14-4. 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.

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14-4. Military Standard 105E (ANSI/ASQC
Z1.4 ISO 2859)

• 14-4.3 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.

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14-4. Military Standard 105E (ANSI/ASQC
Z1.4 ISO 2859)

• 14-4.3 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.