Learning Objectives

Acceptance sampling is an important form of inspection applied to lots or batches of items before or after a process, to judge conformance with predetermined standards. Similarly Sampling plans are the plans that specify lot size, sample size, number of samples, and acceptance/rejection criteria

  • Single-sampling
  • Double-sampling
  • Multiple-sampling

Single Sampling Characteristics

  • One random is drawn from each lot.
  • Every item in the sample is examined
  • Each item after examination is classified good or defective.
  • If the sample contains more than a specified number of defectives say c, then that lot is rejected.

Double Sampling Plan Characteristics

  • Takes care of limitation of Single Sampling Plan by taking another sample if results of the initial sample are inconclusive.
  • If results from second sample also indicate poor quality than the lot is rejected or otherwise decision reached on the basis of both samples.
  • A double sampling plan specifies the lot size, the size of the initial sample, accept/reject criteria for the initial sample, the size of the second sample and a single acceptance number.
  • With double sampling plan, 2 values are specified for number of defective items, a lower level c1 and an upper level c2. E.g. if we have c1 equal to 2 and c2 to 7, if number of defects is smaller than c1 than sampling is terminated and lot is accepted.
  • If defects are greater than c2, than lot is rejected.
  • If it’s between c1 and c2 then second sample is selected and compared to a third value c3 which can be 8 and if the cumulative defects from 1 and 2 does not exceeds c3, the lot is accepted.

Choosing a Plan

  • Cost and time are prime determinants of choosing a plan.
  • Primary considerations are number of samples needed and total number of observations required.
  • Single sample has only one sample but large sample size.
  • Where the cost to obtain a sample is high than cost of analyzing the sample, single sample plan is followed.
  • Where inspection costs are higher than costs of obtaining the sample, multiple samples are carried to ensure that a good or bad result can help terminate the sample testing thus ensuring savings in inspection cost.

Multiple Sampling Plans

  • Similar to double sampling plan but allows more than two samples.
  • A sampling plan will specify each sample size and two limits for each sample.
  • The values increase with number of samples.
  • If the cumulative number of defects ( in current and previous samples) exceed the upper limit, then sampling is terminated and the lot is rejected.

• If defects les than permissible, lot is accepted.

Operating Characteristic Curve

Important criteria of sampling plan are how it discriminates between lots of high and low quality.

  • The ability of a Sampling Plan to discriminate is described by its OC.
  • The degree to which a sampling plan discriminates between good and bad lots is a function of steepness of the curve
  • The ideal plan would require 100 % inspection of each lot.

OC Curves

production and operations management  ACCEPTANCE SAMPLING

The Perfect OC Curve

production and operations management  ACCEPTANCE SAMPLING

OC Curve Terms

  • Acceptable Quality Level (AQL): Percentage of defective items a customer is willing to accept from you (a property of mfg. process)
  • Lot Tolerance Percent Defective (LTPD): Upper limit on the percentage of defects a customer is willing to accept ( a property of the consumer)
  • Average Outgoing Quality (AOQ):Average of rejected lots and accepted lots
  • Average Outgoing Quality Limit (AOQL):Maximum AOQ for a range of fractions defective


The curve shows the probability that use of the sampling plan will result in lots with various fractions defective being accepted. The graph shows that the lot with 3 percent defects ( a fraction of 0.03) would have a probability of about 0.9 being accepted , 90%. And 1-0.9 =0.1 ( 10% being rejected)

As the lot quality decreases, the probability of acceptance decreases, although the relationship is not linear.

OC Definitions on the Curve

production and operations management  ACCEPTANCE SAMPLING



Probability of accepting








0.1 0

production and operations management  ACCEPTANCE SAMPLING

Lot quality (fraction

Decision Criteria

production and operations management  ACCEPTANCE SAMPLING

Sampling Terms

  • Acceptance quality level (AQL): the percentage of defects at which consumers are willing to accept lots as “good”
  • Lot tolerance percent defective (LTPD): the upper limit on the percentage of defects that a consumer is willing to accept
  • Consumer’s risk: the probability that a lot contained defectives exceeding the LTPD will be accepted
  • Producer’s risk: the probability that a lot containing the acceptable quality level will be rejected


production and operations management  ACCEPTANCE SAMPLING

Average Quality is the Average outgoing quality (AOQ): Average of inspected lots (100%) and un inspected lots

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