Chapter 8: Acceptance Sampling

Prof.(Dr.) D G Mahto, Founder & CEO -

Abstract 

Acceptance sampling is a statistical quality control method where a random sample from a production lot is inspected to decide whether to accept or reject the entire batch, balancing inspection costs with quality assurance by avoiding 100% testing, especially when testing is costly or destructive. A pre-defined sampling plan dictates the sample size and acceptance criteria (e.g., number of defects allowed), leading to lot acceptance or rejection, common in supply chains for balancing producer/consumer risks, 
 
How it works
  1. Sampling Plan: A plan specifies sample size (n) and acceptance number (c) for a given lot size.
  2. Random Sample: A representative sample is drawn from the lot.
  3. Inspection: The sample is inspected for defects.
  4. Decision: If the number of defects is below 'c', the lot is accepted; otherwise, it's rejected. 
Key concepts
  • AQL (Acceptable Quality Level): The maximum percentage of defects considered acceptable.
  • OC Curve (Operating Characteristic Curve): Shows the probability of accepting lots with varying defect levels.
  • Types of Plans: Includes single, double, and multiple sampling plans. 
Why it's used
  • Cost Reduction: Cheaper than inspecting every item.
  • Efficiency: Faster than 100% inspection.
  • Destructive Testing: Necessary when testing destroys the product (e.g., light bulbs).
  • Balancing Risk: Manages risks for both producers (rejecting good lots) and consumers (accepting bad lots

So let's dive into the chapter 8 Acceptance Sampling for more details 

8.1 Introduction

Acceptance sampling is a statistical quality control technique used to decide whether to accept or reject a lot based on the inspection of a sample rather than the entire lot. It is especially useful when 100% inspection is costly, time-consuming, or destructive.

Unlike SPC, which focuses on process control, acceptance sampling focuses on product disposition. This chapter explains the principles, types, and applications of acceptance sampling.

8.2 Inspection and Sampling

8.2.1 Types of Inspection

  1. 100% Inspection

    • All items are inspected

    • Costly and prone to inspection fatigue

  2. Sampling Inspection

    • Only a sample is inspected

    • Economical and practical

8.2.2 Purpose of Acceptance Sampling

  • To decide acceptance or rejection of a lot

  • To protect consumer and producer

  • To maintain outgoing quality levels

Acceptance sampling does not improve process quality; it only screens output.

8.3 Basic Terminology in Acceptance Sampling

  • Lot: A collection of units submitted for inspection

  • Sample: Subset of units selected from the lot

  • Acceptance Number (c): Maximum allowable defects for lot acceptance

  • Sample Size (n): Number of units inspected

8.4 Types of Acceptance Sampling Plans

8.4.1 Single Sampling Plan

  • One sample of size n is taken

  • Lot accepted if number of defectives ≤ c

  • Otherwise, lot is rejected

8.4.2 Double Sampling Plan

  • Decision may be made after one or two samples

  • Reduces average inspection effort

8.4.3 Multiple Sampling Plan

  • Extension of double sampling

  • Decisions made using several small samples

8.5 Risks in Acceptance Sampling

8.5.1 Producer’s Risk (α)

  • Probability of rejecting a good lot

  • Related to Acceptable Quality Level (AQL)

8.5.2 Consumer’s Risk (β)

  • Probability of accepting a bad lot

  • Related to Lot Tolerance Percent Defective (LTPD)

8.6 Operating Characteristic (OC) Curve

The OC curve shows the probability of accepting a lot versus the fraction defective.

Uses:

  • Evaluates effectiveness of a sampling plan

  • Compares different sampling plans

  • Assesses producer’s and consumer’s risks

8.7 Average Outgoing Quality (AOQ)

AOQ represents the average quality of outgoing lots after inspection.

[
AOQ = P_a \times p
]

Where:

  • (P_a) = Probability of acceptance

  • (p) = Incoming fraction defective

8.8 Average Outgoing Quality Limit (AOQL)

The AOQL is the maximum value of AOQ for a given sampling plan and represents the worst outgoing quality.

8.9 Sampling Plans Based on Attributes

Attribute sampling plans assume:

  • Items are classified as defective or non-defective

  • Defects follow binomial or Poisson distribution

Standard tables (e.g., MIL-STD, ISO) are commonly used.

8.10 Acceptance Sampling vs SPC

Acceptance SamplingSPC
Product-orientedProcess-oriented
Detects defectsPrevents defects
Reactive approachProactive approach
Used at receiving/endUsed during production

8.11 Applications of Acceptance Sampling

  • Incoming material inspection

  • Final product inspection

  • Supplier quality assurance

  • Regulatory compliance

8.12 Limitations of Acceptance Sampling

  • Does not improve process quality

  • Sampling errors possible

  • Not suitable for continuous production monitoring

8.13 Learning Objectives

After studying this chapter, the learner will be able to:

  • Explain the concept of acceptance sampling

  • Differentiate between sampling plans

  • Understand producer’s and consumer’s risks

  • Interpret OC curves and AOQ

8.14 Review Questions

  1. What is acceptance sampling?

  2. Differentiate between AQL and LTPD.

  3. Explain producer’s and consumer’s risks.

  4. What is an OC curve?

  5. Compare acceptance sampling and SPC.

8.15 Short Answer Questions (Exam Oriented)

  1. Define acceptance number.

  2. What is AOQL?

  3. State one advantage of acceptance sampling.

  4. What is single sampling plan?

8.16 Summary

This chapter discussed acceptance sampling as a decision-making tool for accepting or rejecting lots based on sample inspection. While acceptance sampling helps control outgoing quality, it should be complemented with SPC for long-term process improvement.


Prof. (Dr.) D. G. Mahto: A Visionary Director, Professor, Leader & Educator With over 25 years of excellence, Prof. (Dr.) D. G. Mahto is a Director, Professor, Philanthropist, HEI Builder, writer, consultant, reviewer, and career advisor at "Career Education for Success—Discover, Apply, Succeed!" He has empowered individuals, brands, and institutions through insightful content, innovation, and mentorship. Holding a Ph.D. in Engineering from NIT Jamshedpur, he has pursued Post-Doctoral Programs at IITs, NITs, and IIITs, reinforcing his expertise. A member of prestigious global organizations like NPA (USA), IET (UK), ASME, IAENG, and MRSI, he actively contributes to engineering, research, and education. An accomplished writer and researcher, he shares knowledge via Career Education Success Now, Career Edus, and Discover Knowledge Wisely. His vision integrates technology, innovation, and leadership, bridging gaps between aspirations and achievements. Connect with him for insights into education, research, and professional growth.

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