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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Larson Nomogram – iSixSigma

Both the binomial nomograph and the Thorndike chart give the same sample size and acceptance number. A Nomograph is a paper slide rule that helps to simplify certain computations.

The L is moved across the chart until one of the acceptance number curves goes through both the a value on the inside vertical scale and the R value on the inside horizontal scale. Sampling plans are hypothesis tests regarding product that has been submitted for an appraisal and subsequent acceptance or rejection.

Find the closest sample size and acceptance number to the intersection point. Draw a line from the AQL. There are some minor differences. Although the hypergeometric may be used when the lot sizes are small, the binomial and Poisson are by far the most popular distributions to use when constructing sampling plans.

Incoming quality is denoted by p. Audit sampling is used where the manufacturing quality controls are known to be working correctly.

One hundred percent checking is a sorting operation to separate good product from defective product. The decision is based on the specified criteria and the amount of defects or defective units found in the sample. In acceptance sampling, the risks of making a wrong decision are known.

The unscientific sampling technique, known as the constant percentage sample, is a very popular procedure. The values for the operating characteristic OC curve are obtained directly from the nomograph. By using this site, you agree to the Terms of Use and Privacy Policy.


It is represented by the symbol P a. This procedure is done on a lot by lot basis. Like the binomial nomograph, it may also be used to determine sample sizes and acceptance numbers for sampling plan applications.


The following nomogranm are used for the binomial nomograph and Thorndike chart examples:. Selecting product for appraising quality characteristics can be done by a number of different methods. In some cases, incoming materials from various suppliers may not be inspected because the supplier has demonstrated outstanding quality capabilities. The chart shows the inspector what decision to make after each sample is inspected.

As processes become more refined and the process capabilities are known, the need for inspection becomes less important. A periodic audit to verify that conditions have not changed is a recommended practice when products are not checked on a routine basis.

This page was last edited on 13 Octoberat Copies nompgramm the binomial nomograph and Thorndike chart are included in the appendix.

At this time, one out of X shall be inspected. They may be determined by your customer, special studies, or past experience. The probability of 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. A chart like the one shown below is specified for various sequential sampling plans. If the number of defects or defectives in the sample exceed the acceptance number c or ANnomoggamm entire lot is rejected. The curved lines in the body of the chart represent the cumulative number of occurrences or successes that are of interest.

This is sometimes referred to as sampling with replacement although the parts are not physically replaced.

The L may be modified for any value nimogramm b. The following other wikis use this file: A sample is selected and checked for various characteristics. Two parameters are specified in a continuous sampling plan. The rejected lots may be submitted for re-inspection. The Thorndike chart, which will be discussed later, is a valuable aid in the construction of sampling plans using the Poisson distribution. The probability of acceptance is larsonn probability that the number of defects or defective units in the sample is equal to or less than the acceptance number of the sampling plan.


It is a nomograph of the cumulative Poisson probability distribution.

The required quality levels determine the acceptance, rejection, and continue sampling regions on the chart. The advantage of this type of sampling plan is that a decision could be made based on a relatively small sample. The Thorndike chart is used for the following sampling plans:. It is also used to approximate the binomial probabilities involving the number of defective parts when the sample n is large and p is very small.

This is called sampling without replacement.

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. These distributions were covered in the Basic Probability chapter and are reviewed here. 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 lot single sampling plans being the no,ogramm popular.

NPTEL :: Management – Six Sigma

The letter n represents the sample size. The abscissa on the Thorndike chart is np. If the number of defects or defectives in the first sample do not exceed c 1the lot is accepted and a second sample is not taken. When the risks involved are known, this technique will result in significant savings and increased product velocity. This screenshot either does not contain copyright-eligible parts or visuals of copyrighted software, or the author has released it under a free license which should be indicated beneath this noticeand as such follows the licensing guidelines for screenshots of Wikimedia Commons.