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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

Chapter 9

Lot-by-Lot Acceptance Sampling for Attributes

acceptance sampling problem
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
acceptance sampling problem3
Acceptance-Sampling Problem
  • Three approaches to lot sentencing:
    • Accept with no inspection
    • 100% inspection
    • Acceptance sampling
acceptance sampling problem4
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
acceptance sampling problem5
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
acceptance sampling problem6
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
acceptance sampling problem7
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.
acceptance sampling problem8
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.
single sampling plans for attributes
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.
single sampling plans for attributes10
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.
single sampling plans for attributes11
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.
single sampling plans for attributes12
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
single sampling plans for attributes13
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.
military standard 105e ansi asqc z1 4 iso 2859
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
military standard 105e ansi asqc z1 4 iso 285915
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
military standard 105e ansi asqc z1 4 iso 285916
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.
military standard 105e ansi asqc z1 4 iso 285917
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
military standard 105e ansi asqc z1 4 iso 285918
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.
military standard 105e ansi asqc z1 4 iso 285919
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.
military standard 105e ansi asqc z1 4 iso 285920
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.
military standard 105e ansi asqc z1 4 iso 285921
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.