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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Since computers are not allowed at the CQE exam, the nomographs may come in handy. A chart like the one shown below is specified for various sequential sampling plans.

Larson Nomogram

Sampling plans may be developed to meet certain criteria and to insure that the specified outgoing quality levels are met. Using the Poisson to calculate probabilities associated with various sampling plans is bomogramm simple because the Poisson tables can be used. The six methods listed below are widely used. The product may be grouped into lots or may be single pieces from a continuous operation. The letter p is the incoming quality level AIQ and P a is the probability of acceptance. Both the binomial nomograph and the Thorndike chart give the same sample size and acceptance number.

The inspection accuracy is not achieved for small lots and too much time and effort may be spent on large lots. It may also be used to approximate binomial probabilities and compute the probability of acceptance for fraction defective sampling plans. A periodic audit to verify that conditions have no,ogramm changed is a recommended practice when products are not checked on a routine basis.

As processes become more refined and the process capabilities are known, the need for inspection becomes less important. The AOQL is the outgoing quality level at the crest of the curve.

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.

As the number of quality characteristics being checked increases, the effectiveness of the inspector decreases. Find the closest sample size and acceptance number to the intersection point.


If the process or quality controls have broken down, the sampling procedures will prevent defective products from going any farther. The values for the operating characteristic OC larsno are obtained directly from the nomograph. The curved lines also represent the acceptance numbers in a sampling plan.

It is nomogrammm by the symbol P a. Accepted and screened rejected lots are sent to their destination. If the number of defects or defectives in the first sample do not exceed c 1the lot larzon accepted and a second sample is not taken. There are three probability distributions that may be used to find the probability of acceptance. This is sometimes referred to as sampling with replacement although the parts are not physically replaced.

This type of sampling may be used when a supplier has been certified as providing excellent quality products over some length of time or the process capability is so good that other methods of inspection are not necessary. Sampling at the end of a manufacturing process provides a check on the adequacy of the quality control procedures of the manufacturing department. The binomial assumes that the probabilities associated with all samples are equal.

Also a straight line can be dropped from R to the pn scale. The semi vertical lines on the nomograph represent the sample sizes and the semi horizontal lines are the acceptance numbers. The required quality levels determine the acceptance, rejection, and continue sampling regions on the chart.

Larson Nomogram – iSixSigma

The value of pn is 8. In addition, one hundred percent checking cannot be used when lrason destructive test is made. If a second sample is inspected: Views View Edit History. 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.

Each sampling plan has a unique OC nomgoramm.


The advantage of this type of sampling plan is that a decision could be made based on a relatively small sample. At the corner of the L where the value is 1, drop a straight line to the pn scale on the abscissa of the Thorndike chart. The Operating characteristic curve is a picture of a sampling plan. The acceptance number is the maximum allowable defects or defective parts in a sample for the lot to be accepted.


The value of pn is 2. The probability of acceptance is the 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. For this example, the differences increase slightly as the curve approaches the tail. A quality report is issued and the manufacturing organization will determine what action is to be taken if the material is not acceptable. Sampling plans will be constructed using both the binomial nomograph and the Thorndike chart.

The sample size is determined as follows: At this time, one out of X shall be inspected. For this example, the lot size is pieces. If the number of defects or defectives in the first sample are more than c 1 but less than or equal to c 2a second sample n 2 is selected and inspected.

From Wikimedia Commons, the free media repository. When n is large and p is small, the Poisson distribution formula may be used to approximate the binomial. One hundred percent checking is a sorting operation to separate good product from defective product. Accepting or rejecting a lot is analogous to not rejecting or rejecting the null hypothesis in a hypothesis test.

The objective is to find a sample size and acceptance number whose OC curve meets the above parameters.

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The part is classified as good or defective. If the number of defects or defectives in the first sample exceed c 2the lot is rejected and a second sample is not taken. The abscissa on the Thorndike chart is np.