BINOMIAL NOMOGRAPH PDF

The observed value is found in one of these ranges, and the tick mark used on that scale is found immediately above it. Then the curved scale used for the expected value is selected based on the range. For example, an observed value of 9 would use the tick mark above the 9 in range A, and curved scale A would be used for the expected value. An observed value of 81 would use the tick mark above 81 in range E, and curved scale E would be used for the expected value. This allows five different nomograms to be incorporated into a single diagram.

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A sample size n is selected randomly from the lot. If the number of defects or defectives in the sample exceed the acceptance number c or AN , the entire lot is rejected. If the number of defects or defectives in the sample do not exceed the acceptance number, the entire lot is accepted. In some cases the lot may be scrapped. Accepted lots and screened rejected lots are sent to their destination. The rejected lots may be submitted for re-inspection. Two sample sizes n1, n2 and two acceptance numbers c1, c2 or AN1, AN2 are specified.

A first sample of size n1 is taken. If the number of defects or defectives in the first sample exceed c2 , the lot is rejected and a second sample is not taken. If the number of defects or defectives in the first sample do not exceed c1, the lot is accepted and a second sample is not taken.

If the number of defects or defectives in the first sample are more than c1 but less than or equal to c2, a second sample n2 is selected and inspected. If a second sample is inspected: a and defects or defectives in combined first and second sample do not exceed c2, the lot is accepted. Two parameters are specified in a continuous sampling plan. The first is the frequency of checking f and the second is the clearing number i.

At this time, one out of X shall be inspected. The sampling will continue until a defect is found. The part is classified as good or defective. A chart like the one shown below is specified for various sequential sampling plans. The required quality levels determine the acceptance, rejection, and continue sampling regions on the chart. The chart shows the inspector what decision to make after each sample is inspected. The lot will either be accepted rejected or another sample will be taken.

This procedure is done on a lot by lot basis. The advantage of this type of sampling plan is that a decision could be made based on a relatively small sample. Accepted and screened rejected lots are sent to their destination. Each sampling plan has a unique OC curve.

The sample size and acceptance number define the OC curve and determine its shape. The acceptance number is the maximum allowable defects or defective parts in a sample for the lot to be accepted. The OC curve shows the probability of acceptance for various values of incoming quality.

An OC curve is developed by determining the probability of acceptance for several values of incoming quality. Incoming quality is denoted by p. 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.

There are three probability distributions that may be used to find the probability of acceptance. These distributions were covered in the Basic Probability chapter and are reviewed here. The hypergeometric distribution The binomial distribution The Poisson distribution 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. It can be defined as the true basic probability distribution of attribute data but the calculations could become quite cumbersome for large lot sizes.

The probability of exactly x defective parts in a sample n: 4. For large lots, the non-replacement of the sampled product does not affect the probabilities. The hypergeometric takes into consideration that each sample taken affects the probability associated with the next sample.

This is called sampling without replacement. The binomial assumes that the probabilities associated with all samples are equal. This is sometimes referred to as sampling with replacement although the parts are not physically replaced. The binomial is used extensively in the construction of sampling plans. The sampling plans in the Dodge-Romig Sampling Tables were derived from the binomial distribution. The probability of exactly x defective parts in a sample n: The symbol p represents the value of incoming quality expressed as a decimal.

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. When n is large and p is small, the Poisson distribution formula may be used to approximate the binomial. Using the Poisson to calculate probabilities associated with various sampling plans is relatively simple because the Poisson tables can be used.

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 exactly x defects or defective parts in a sample n: The letter e represents the value of the base of the natural logarithm system.

The probability of acceptance is usually expressed as a decimal rather than as a percentage. It is represented by the symbol Pa.

The letter n represents the sample size.

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BINOMIAL NOMOGRAPH PDF

The number of trials refers to the number of attempts in a binomial experiment. The number of trials is equal to the number of successes plus the number of failures. Suppose that we conduct the following binomial experiment. We flip a coin and count the number of Heads. In this experiment, Heads would be classified as success; tails, as failure. If we flip the coin 3 times, then 3 is the number of trials.

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Binomial data and statistics are presented to us daily. For example, in the election of political officials we may be asked to choose between two candidates. This fictitious election pits Mr. Gubinator vs.

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Vonris Since computers are not allowed at the CQE exam, the nomographs may come in handy. A sample is selected and checked for various characteristics. The product may be grouped into lots or may be single pieces from a continuous operation. Sampling plans are hypothesis tests regarding product that has been submitted for an appraisal and subsequent acceptance or rejection. Calculator apparatus with annuity switch for bunomial begin-and end-period annuity calculations. Accepted and screened rejected lots are sent to their destination.

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Moramar The intersection will yield the sample size and acceptance number. When the process capability and the product quality level is not known, no checking usually results in increased costs for reworking defective product. Pin 20 is preset in slot 4 to the value of 3, namely 0. USA — Device for the graphical solution of simultaneous equations — Google Patents The probability of accepting a lot is the probability of c or fewer defective parts. It is a nomograph of the cumulative Poisson probability distribution. 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.

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