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Sampling Standards and Plans, Lecture notes of Computational and Statistical Data Analysis

Stanford UniversityComputational and Statistical Data Analysis

Again, let's use the ANSI/ASQ Z1.4 standard to demonstrate how to find your acceptance number using your AQL and Sample Size Code Letter. For this example, ...

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Sampling Standards and Plans
Alright, are you ready for the second part of this chapter which is the actual sampling
standards and plans themselves.
This includes a review of basic sampling plans such as single, double, multiple, sequential,
and continuous sampling plans.
Then we will review the more complex sampling schemes in ANSI/ASQ Z1.4 and Z1.9
standards. Lastly, we will finish this part with a brief description of the Dodge-Romig
sampling tables.
Let’s start with the simple concepts of single sampling plan and double/multiple sampling
plans.
Single Sampling Plans
A single sampling plan is the easiest and most common sampling plan where an entire lot is
accepted or rejected based on the inspection results of a single sample group of size n, taken
from the entire lot (population - N).
Single sampling plans are defined by three parameters:
N = Total Lot Size, n = sample size, c = the acceptance number (derived from
AQL)
The total lot size is designed as N, and the Sample Size (n) is the number of samples to be
inspected.
I’ll jump ahead to the ANSI/ASQ Z1.4 standard to give you an example of what this looks like
in practice.
Most normal inspections use General Inspection Level II, and let’s say that your Total Lot
Size (N) is 5,000, then your sample size is determined by the Sample Size Code Letter, L.
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Sampling Standards and Plans

Alright, are you ready for the second part of this chapter which is the actual sampling standards and plans themselves. This includes a review of basic sampling plans such as single, double, multiple, sequential, and continuous sampling plans. Then we will review the more complex sampling schemes in ANSI/ASQ Z1.4 and Z1. 9 standards. Lastly, we will finish this part with a brief description of the Dodge-Romig sampling tables. Let’s start with the simple concepts of single sampling plan and double/multiple sampling plans. Single Sampling Plans A single sampling plan is the easiest and most common sampling plan where an entire lot is accepted or rejected based on the inspection results of a single sample group of size n, taken from the entire lot (population - N). Single sampling plans are defined by three parameters : N = Total Lot Size, n = sample size, c = the acceptance number (derived from AQL) The total lot size is designed as N, and the Sample Size (n) is the number of samples to be inspected. I’ll jump ahead to the ANSI/ASQ Z1.4 standard to give you an example of what this looks like in practice. Most normal inspections use General Inspection Level II , and let’s say that your Total Lot Size (N) is 5,000, then your sample size is determined by the Sample Size Code Letter, L.

The Acceptance Number (c) is the maximum number of non-conformances allowed within the sample. The acceptance number is derived from a combination of the AQL you select for the attribute being inspected for, and the sample size. Again, let’s use the ANSI/ASQ Z1.4 standard to demonstrate how to find your acceptance number using your AQL and Sample Size Code Letter. For this example, let’s say your AQL is 1.0. So, you start by finding your AQL across the top, and your sample size code letter (L in this case) along the side, and you find their intersection in the matrix. It’s also important to know that this table also specifies the number of samples you should be using during inspection. So you can see that for a sample size code letter of L, you should be inspecting 200 samples (n) , and the acceptance number (c) is 5 , and the rejection number is 6.

A lot can be accepted within the 1st^ sample if the actual number of non-conformances is less than the acceptance number (c). Similarly, a lot can be rejected if the actual number of non- conformances is greater than the reject number. If the number of non-conformances observed is greater than that the 1 st^ acceptance number (c 1 ) but less than the 1 st^ rejection number (r 1 ) then the sampling continues with the second sample, n 2. Double Sampling Example Let’s say you want to turn that previous example into double sampling, using the same AQL and starting with the same lot size. If the overall lot size (N) does change, then the sample size code letter also won’t change, L. Executing this sampling plan means taking the initial sample (n 1 ) of 125 units and inspecting for non-conformances. Let’s review quickly how to respond to the various outcomes of this first sample:

  • If 2 or fewer non-conformances (c 1 , acceptance number ) are found in this initial 125 units, then the entire lot is accepted.
  • If 5 or more non-conformances (r 1 , rejection number) are found in this initial 125 units, then the entire lot is rejected. If, let’s say three non-conformances is found in this initial 125 units, then we move on to the second sample of another 125 samples (n 2 ). Then the results of both samples are combined to make a final decision, so let’s review those possible outcomes:
  • If, a combined total of 7 non-conformances are found between both samples (250 total), then the lot is rejected.
  • If, a combined total of 6 (or fewer) non-conformances are found between both sample groups, then the lot is accepted. Remember, the final decision at the end of the second sample is cumulative. You must combine the non-conformances found in the first and second sample and compare that against r 2. Multiple Sampling Plans A multiple sampling plan is simply an extension of the double sampling plan, where sampling can go on for up 7 to different samples. Similar to the double sampling plan, each sample taken has its own accept(c) and reject (r) requirements. Let’s look at the multiple sampling plan for sample size code letter L, with an AQL of 1.. Similarly, to the double sampling plan, over time, these plans have shown to have a lower average sampling number (ASN), when compared to a double or single sampling plan. The downside is that it these plans can be difficult to administer and create waste (muda) in the form of excess motion when picking samples. Sequential Sampling Plans The sequential sampling plan is a further extension of the multiple sampling plan where sampling can go on indefinitely until the entire lot is inspected.