HRN ISO , Larson nomogram, operating characteristic curve of the acceptance plan, statistical quality control attribute acceptance plans, sampling. Fortunately, Larson has determined a nomograph (a graphical calculating Larson’s nomograph can be used as follows: the vertical line on the left-hand side is. From the Larson nomogram, the binomial plan satisfying these specifications is n1⁄, c1⁄ Using the Lieberman and Owen () tables for D1 1⁄(20).

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The Thorndike chart, which will be discussed later, is a valuable aid in the construction of sampling plans using the Poisson distribution. Summary [ edit ] Description Larson.

If the larzon of defects or defectives in the sample exceed the acceptance number c or ANthe entire lot is rejected.

It permits direct solution of some problems not otherwise directly solvable except by approximation or computer. This is because they are easier to administer and implement than the other plans and they are very effective. Find the closest sample size and acceptance number to the intersection point. Two parameters are specified nomogrramm a continuous sampling plan.

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Retrieved from ” https: If c is in terms number of defects, the AIQ or abscissa on the OC curve is in terms of defects per unit. The probability parson acceptance is usually expressed as a decimal rather than as a percentage. The sample size and acceptance number define the OC curve and determine its shape. Random spot-checking may sometimes be used when a process is in statistical control. The sampling risks are not known, so this method will not oarson that the outgoing quality will be at an acceptable level.


The AOQL is approximately. It can be defined as the true basic probability distribution of attribute data but the calculations could become quite cumbersome for large lot sizes. Audit sampling is sampling that is done on a routine basis, but acceptance criterion is not specified.


The chart shows the inspector what decision to make after each sample is inspected. A quality report is issued and the manufacturing organization will determine what action is to be taken if the material is not acceptable.

In acceptance sampling, the risks of making a wrong decision are known.

The inspection accuracy is not achieved for small lots and too much time and effort may be spent on large lots. When the process capability and the product quality level is not known, no checking usually results in increased costs for reworking defective product. For this example, the lot size is pieces.

The sample size is determined as follows: The curve represents the acceptance number c for the plan. The manufacturing department, as part of the process or quality control program, may also use sampling techniques.

Sampling plans are hypothesis tests regarding product that has been submitted for an appraisal and subsequent acceptance or rejection.

The abscissa on the Thorndike chart is np. As the number of quality characteristics being checked increases, the effectiveness of the inspector decreases. The sampling plan will have a 1 – a chance of being accepted when the incoming quality is at the AQL level and a b chance of being accepted when the incoming quality is at the RQL level.

When n is large and p is small, the Poisson distribution formula may be used to approximate the binomial. From Wikimedia Commons, the free media repository. The random check is used to verify that the process is in control and to report the product quality level. The binomial is used extensively in the construction of sampling plans. The sampling will continue until a defect is found.


The AOQ and OC curve, when used together, describe the characteristics of the sampling plan and the risks involved. Both the sample size and acceptance numbers must be integers. If the number of defects or defectives in the sample do not exceed the acceptance number, the entire lot is accepted.

Using the Poisson to calculate probabilities associated with various sampling plans is relatively simple because the Poisson tables can be used. Also, the sampling risks involved are not known.

Larson Nomogram

They are also included in various textbooks. When inspection is performed by attributes, product is classified as good or defective four types of acceptance sampling plans may be used, with lot by lason single sampling plans being the most popular.

An easy way to find the sample size and acceptance number is to use a the binomial nomograph or the cumulative Poisson nomograph called the Thorndike chart.

If the number of defects or defectives in the first sample do not exceed nomogrammm 1the lot is accepted and a second sample is not taken. The AOQL is the outgoing quality level at the crest of the curve.

Like the binomial nomograph, it may also be used to determine sample sizes and acceptance numbers for sampling plan applications. The OC curve shows the probability of acceptance for various momogramm of incoming quality.

The lot will either be accepted rejected or another sample will be taken. In the construction of a lot by lot single sampling plan, four parameters must be determined prior to determining the sample size and acceptance number.