Operating Characteristic Curves for Acceptance Sampling

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PASS Sample Size Software NCSS com, Operating Characteristic Curves for Acceptance Sampling for Attributes. Technical details, Define N to be the lot size possibly infinite n as the size of the sample to be drawn and c to be the acceptance. number the highest number of nonconforming units for which the lot will still be accepted Let X denote the number. of nonconforming units in the sample If the lot size is assumed to be infinite the probability of acceptance Pa for a. given lot proportion defective p is given by, If the lot size is finite the hypergeometric distribution is used where for each X. where M Np,The probability of acceptance is given by. Procedure Options, This section describes the options that are specific to this procedure These are located on the Design tab For.
more information about the options of other tabs go to the Procedure Window chapter. Design Tab, The Design tab contains the parameters associated with this test such as the proportions sample sizes alpha and. Lot Size N, Specify the total number of units in the lot that is subject to quality inspection If the lot size is infinite or. continuous select Infinite for the Lot Size In this case the binomial distribution is used for calculations. If the lot size is set to any value other than infinite the hypergeometric distribution is used in the calculations. You can choose a value from the drop down or you can enter a value directly. NCSS LLC All Rights Reserved,PASS Sample Size Software NCSS com. Operating Characteristic Curves for Acceptance Sampling for Attributes. Sample Size and Acceptance Number,Sample Size n, Enter one or more values for the sample size n This is the number of elements from the lot that will be. randomly sampled and examined You can enter a single value such as 100 or a series of values such as. 50 60 70 80 90 100 or 100 to 150 by 10 The Sample Size should be less than the Lot Size. Acceptance Number c, This cutoff value is the largest number of nonconforming defective items from the sample of size n for which the.
lot should still be accepted You can enter a single value such as 1 or a series of values such as 1 2 5 10 or. 0 to 5 by 1 The Acceptance Number should be less than the Sample Size. Range and Increment of Proportion Defective,Proportion Defective Range. This is the series of values for the lot proportion defective You can enter the range of values directly or you can. use the button with the three arrows at the end of the box The range is entered using the first and last values of. the range followed by the amount to increment between each value For example you may enter 0 to 0 5 by 0 01. The full range of possible values is a series of values between 0 and 1 Typically the Probability of Acceptance. drops down to 0 long before the Proportion Defective reaches 1 We recommend that you run the procedure a few. times until you have selected a Proportion Defective range that has a Probability of Acceptance near 0 at the end. of the range For example you may try 0 to 0 5 by 0 01 on the first run and then settle on 0 to 0 2 by 0 002 for the. NCSS LLC All Rights Reserved,PASS Sample Size Software NCSS com. Operating Characteristic Curves for Acceptance Sampling for Attributes. Example 1 Generating an Operating Characteristic Curve. Suppose a quality engineer is to receive a lot of 500 units The engineer is considering sampling 50 units and. would like to examine the operating characteristic curve for an acceptance number of 3 To begin the engineer. will examine the full range of lot proportion defectives 0 to 1. This section presents the values of each of the parameters needed to run this example First from the PASS Home. window load the Operating Characteristic Curves for Acceptance Sampling for Attributes procedure. window by clicking on Quality Control and then clicking on Operating Characteristic Curves for Acceptance. Sampling for Attributes You may then make the appropriate entries as listed below or open Example 1 a or b. by going to the File menu and choosing Open Example Template. Option Value,Design Tab,Lot Size N 500,Sample Size n 50. Acceptance Number c 3,Proportion Defective Range 0 to 1 by 0 01. Annotated Output, Click the Calculate button to perform the calculations and generate the following output.
Chart Section,NCSS LLC All Rights Reserved,PASS Sample Size Software NCSS com. Operating Characteristic Curves for Acceptance Sampling for Attributes. Numeric Results, Numeric Results for Operating Characteristic Curves for Acceptance Sampling for Attributes. Lot Size N 500,Sample Acceptance Proportion Probability of. Size n Number c Defective Acceptance,50 3 0 0000 1 00000. 50 3 0 0100 0 99959,50 3 0 0200 0 98814,50 3 0 0300 0 94723.
50 3 0 0400 0 87112,50 3 0 0500 0 76708,50 3 0 0600 0 64824. 50 3 0 0700 0 52769,50 3 0 0800 0 41537,50 3 0 0900 0 31727. 50 3 0 1000 0 23586,50 3 0 1100 0 17108,50 3 0 1200 0 12134. 50 3 0 1300 0 08430,50 3 0 1400 0 05744,50 3 0 1500 0 03844. 50 3 0 1600 0 02528,50 3 0 1700 0 01636, Each line gives the probability of acceptance based on the corresponding proportion defective.
References and Report Definitions,References, Montgomery D C 2013 Introduction to Statistical Quality Control 7th Edition John Wiley Sons. Kenett Ron S and Zacks Shelemyahu 2014 Modern Industrial Statistics 2nd Edition John Wiley Sons West. Sussex United Kingdom,Report Definitions, Sample Size n is the size of the sample drawn from the lot. c the acceptance number is the largest number of nonconforming items from the sample of size n for which the. lot should still be accepted, Proportion Defective is the proportion of the items of the lot that is assumed to be defective. Probability of Acceptance is probability that the lot will be accepted given the corresponding sample size. acceptance number and assumed proportion defective. These reports give some text references as well as the definitions for each column. Since the probability of acceptance is close to 0 when the lot proportion defective reaches 0 2 the Proportion. Defective Range is changed to 0 to 0 2 by 0 002 and the procedure is run again. NCSS LLC All Rights Reserved,PASS Sample Size Software NCSS com. Operating Characteristic Curves for Acceptance Sampling for Attributes. Chart Section, This second chart gives a nice range for the Lot Proportion Defective relative to the Probability of Acceptance.
NCSS LLC All Rights Reserved,PASS Sample Size Software NCSS com. Operating Characteristic Curves for Acceptance Sampling for Attributes. Example 2 OC Curves for Various Acceptance Numbers. Continuing with Example 1 suppose the quality engineer would like to see various curves for different values of. the acceptance number In particular the engineer would like to examine acceptance numbers of 0 1 2 3 4 5. This section presents the values of each of the parameters needed to run this example First from the PASS Home. window load the Operating Characteristic Curves for Acceptance Sampling for Attributes procedure. window by clicking on Quality Control and then clicking on Operating Characteristic Curves for Acceptance. Sampling for Attributes You may then make the appropriate entries as listed below or open Example 2 by. going to the File menu and choosing Open Example Template. Option Value,Design Tab,Lot Size N 500,Sample Size n 50. Acceptance Number c 0 1 2 3 4 5,Proportion Defective Range 0 to 0 3 by 0 002. Click the Calculate button to perform the calculations and generate the following output. This plot shows the operating characteristic curve for each acceptance number. NCSS LLC All Rights Reserved,PASS Sample Size Software NCSS com. Operating Characteristic Curves for Acceptance Sampling for Attributes. Example 3 Validation using Kenett and Zacks 2014, Kenett and Zacks 2014 pp 260 261 give an operating characteristic curve example in which the sample size is.
50 and the acceptance number is 1, This section presents the values of each of the parameters needed to run this example First from the PASS Home. window load the Operating Characteristic Curves for Acceptance Sampling for Attributes procedure. window by clicking on Quality Control and then clicking on Operating Characteristic Curves for Acceptance. Sampling for Attributes You may then make the appropriate entries as listed below or open Example 3 by. going to the File menu and choosing Open Example Template. Option Value,Design Tab,Lot Size N Infinite,Sample Size n 50. Acceptance Number c 1,Proportion Defective Range 0 to 0 18 by 0 001. Click the Calculate button to perform the calculations and generate the following output. This plot matches the plot shown in Kenett and Zacks 2014. NCSS LLC All Rights Reserved,PASS Sample Size Software NCSS com. Operating Characteristic Curves for Acceptance Sampling for Attributes. Example 4 Validation using Montgomery 2013, Montgomery 2013 p 657 gives an operating characteristic curve example in which the sample size is 89 and.
the acceptance numbers are 0 1 and 2, This section presents the values of each of the parameters needed to run this example First from the PASS Home. window load the Operating Characteristic Curves for Acceptance Sampling for Attributes procedure. window by clicking on Quality Control and then clicking on Operating Characteristic Curves for Acceptance. Sampling for Attributes You may then make the appropriate entries as listed below or open Example 4 by. going to the File menu and choosing Open Example Template. Option Value,Design Tab,Lot Size N Infinite,Sample Size n 89. Acceptance Number c 0 1 2,Proportion Defective Range 0 to 0 08 by 0 001. Click the Calculate button to perform the calculations and generate the following output. This plot matches the plot shown in Montgomery 2013. window load the Operating Characteristic Curves for Acceptance Sampling for Attributes procedure window by clicking on Quality Control and then clicking on Operating Characteristic Curves for Acceptance Sampling for Attributes You may then make the appropriate entries as listed below or open Example 1 a or b

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