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Lot-by-Lot%20Acceptance%20Sampling%20for%20Attributes

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Title: Lot-by-Lot%20Acceptance%20Sampling%20for%20Attributes


1
Chapter 14
  • Lot-by-Lot Acceptance Sampling for Attributes

2
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

3
14-1. The Acceptance-Sampling Problem
  • Three approaches to lot sentencing
  • Accept with no inspection
  • 100 inspection
  • Acceptance sampling

4
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

5
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

6
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

7
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.

8
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.

9
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.

10
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.

11
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.

12
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

13
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.

14
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

15
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

16
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.

17
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

18
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.

19
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.

20
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.

21
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.
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