Chapter 6: Sampling Plans in Quality Engineering and Management

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

Abstract:

A sampling plan is a method for selecting a subset of items from a population for inspection or research. It helps to ensure that the sample is representative of the population. 

When to use sampling plans

Quality control: To determine how many items to inspect, and how to decide whether to accept or reject a lot 

Research: To select individuals to represent a target population 

Surveys: To select a sample of people to survey 

What to consider when creating a sampling plan

Target audience: Who the survey is intended for 

Sample size: How many items or people to include in the sample 

Sampling method: How to select the sample, such as stratified, systematic, or cluster sampling 

Non-response bias: How to account for people who don't respond to the survey 

Acceptance Quality Limit (AQL): The percentage of defects that consumers are willing to accept 

Some types of sampling plans

Single sampling

A random sample from the lot is used to decide whether to accept or reject the lot 

Stratified sampling

The population is divided into subpopulations so that each subgroup is represented in the sample 

Systematic sampling

A random selection point is chosen, and then other items are selected at a fixed interval 

Cluster sampling

The population is divided into clusters, and then a sample is drawn from each cluster 

Keywords:

Sampling Plans, Systematic Sampling, Cluster Sampling, Single Sampling, Acceptance Quality Limit (AQL), When to use sampling plans

Learning Outcomes:

After undergoing this article you will be able to understand the following:

Sampling Plans, Systematic Sampling, Cluster Sampling, Single Sampling, Acceptance Quality Limit (AQL), When to use sampling plans

Here is the complete Chapter 6: Sampling Plans:

Chapter 6: Sampling Plans

6.1 Introduction to Sampling Plans

Sampling plans are systematic approaches used to select a subset (sample) of items from a population for inspection, evaluation, or testing. Instead of inspecting an entire population, which is often time-consuming or costly, sampling allows for efficient decision-making while maintaining a high level of confidence in the results.

Sampling plans are extensively used in quality control to determine whether a batch or lot meets the required specifications. They are key tools in ensuring that products conform to customer requirements while optimizing resource use.

6.2 Objectives of Sampling Plans

  • To ensure quality standards are met without inspecting every item.
  • To identify defective products or processes.
  • To reduce inspection costs and time.
  • To support decisions about accepting or rejecting a batch.

6.3 Types of Sampling Plans

Sampling plans can be classified based on the inspection method, purpose, and sample size.

6.3.1 Attribute Sampling Plans

Attribute sampling involves classifying items as conforming or nonconforming based on set criteria. It is used when data is binary (e.g., pass/fail, defective/non-defective).

  1. Single Sampling Plan:

    • A single sample is taken, and the batch is accepted or rejected based on the number of defective items found.
    • Key parameters:
      • Sample size ()
      • Acceptance number (): Maximum number of defects allowed for acceptance.

  2. Double Sampling Plan:

    • Two samples are taken if necessary. The first sample determines acceptance, rejection, or the need for a second sample.

  3. Multiple Sampling Plan:

    • More than two samples are taken, reducing the risk of erroneous decisions and allowing for greater flexibility.

6.3.2 Variable Sampling Plans

Variable sampling is used for measurable data (e.g., dimensions, weight). It determines whether the average and variability of the sample meet specified criteria.

  • Advantages: Requires smaller sample sizes compared to attribute sampling.
  • Applications: Used when continuous measurements are available, such as in manufacturing tolerances.

6.3.3 Acceptance Sampling Plans

Acceptance sampling plans determine whether to accept or reject a lot based on sample inspection results.

  1. Lot-by-Lot Sampling: Inspect samples from each lot.
  2. Continuous Sampling: Inspect items sequentially in a continuous production process.

6.4 Parameters of a Sampling Plan

Several parameters influence the design and interpretation of sampling plans:

  1. Lot Size (): Total number of items in a batch.
  2. Sample Size (): Number of items selected for inspection.
  3. Acceptance Number (): Maximum number of defective items allowed for lot acceptance.
  4. Rejection Number (): Number of defects at which the lot is rejected.

6.5 Operating Characteristic (OC) Curve

The Operating Characteristic (OC) Curve illustrates the performance of a sampling plan. It shows the probability of accepting a lot as a function of the proportion of defective items in the lot.

Key Points on the OC Curve:

  1. Producer’s Risk (): Probability of rejecting a good lot.
  2. Consumer’s Risk (): Probability of accepting a defective lot.
  3. Acceptable Quality Level (AQL): Maximum defect level considered acceptable.
  4. Lot Tolerance Percent Defective (LTPD): Defect level at which a lot is rejected with high confidence.

6.6 Designing a Sampling Plan

  1. Define Objectives: Understand the purpose of sampling (e.g., detecting defects, reducing risk).
  2. Determine Parameters: Establish lot size, sample size, AQL, and acceptance number.
  3. Select the Sampling Plan: Choose between single, double, or multiple sampling based on efficiency and risk tolerance.
  4. Construct the OC Curve: Evaluate the sampling plan's performance to ensure it meets the required risks.
  5. Implement and Monitor: Use the sampling plan consistently and adjust if necessary.

6.7 Advantages and Limitations of Sampling Plans

Advantages:

  • Cost-Effective: Reduces inspection costs by sampling instead of full inspection.
  • Time-Saving: Speeds up quality assessment processes.
  • Reduced Fatigue: Lessens inspector fatigue, improving reliability.
  • Efficient for Large Batches: Suitable for large-scale production.

Limitations:

  • Risk of Error: Sampling may not detect all defects, leading to incorrect decisions.
  • Assumes Randomness: Effectiveness depends on the randomness of the sampling process.
  • Not Suitable for Critical Applications: May not be appropriate for high-risk products requiring 100% inspection.

6.8 Case Study: Sampling Plan for a Manufacturing Process

Scenario: A company produces bolts in batches of 1,000 units. The acceptable quality level (AQL) is 2%, and the company uses a single sampling plan.

  1. Lot Size (): 1,000 units.
  2. Sample Size (): 50 units.
  3. Acceptance Number (): 2 defective units.

Implementation:

  • Inspect 50 bolts randomly selected from the batch.
  • Accept the batch if there are 2 or fewer defective bolts.
  • Reject the batch if there are more than 2 defective bolts.

Analysis:

  • If 2 bolts are defective, the batch is acceptable, assuming the defect rate does not exceed the AQL.
  • An OC Curve can be used to evaluate the probability of accepting batches with various defect levels.

6.9 Sampling Plans in Industry

6.9.1 Automotive Industry

Sampling plans are used for inspecting components like gears, tires, and engine parts to ensure they meet strict safety and performance standards.

6.9.2 Pharmaceutical Industry

Sampling plans are critical for ensuring drug quality, including content uniformity and packaging integrity.

6.9.3 Food Industry

Used to inspect raw materials, packaging, and finished products for compliance with food safety regulations.

6.10 Conclusion

Sampling plans are essential tools in quality control, enabling efficient and cost-effective inspection while maintaining high-quality standards. By selecting the appropriate sampling plan, organizations can balance inspection efforts with acceptable levels of risk.

Mastery of sampling techniques and their application ensures that businesses deliver reliable products, meet customer expectations, and maintain a competitive edge.

Prof. (Dr.) D. G. Mahto is a multifaceted professional, serving as a Director, Professor, Philanthropist, HEI Builder, prolific writer, international consultant, reviewer, and expert career advisor at "Career Education for Success—Discover, Apply, Succeed!" He has guided countless individuals, products, and brands in discovering their true potential through insightful content, purposeful concepts, and motivational writing. With a deep sense of leadership and a commitment to community upliftment, he inspires others with his success stories and takes on the challenge of driving technological transformation, redefining social impact, and fostering interpersonal relationships for a more meaningful, balanced life. Prof. Mahto is dedicated to bridging the gap between dreams and reality for young people, striving for qualitative change in their lives. To explore his articles, books, and international journal contributions, visit his blogs at Career Education Success Now, Career Edus, and Discover Knowledge Wisely. You can also reach out to him via email.

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