Designation E1994 − 09 (Reapproved 2013) An American National Standard Standard Practice for Use of Process Oriented AOQL and LTPD Sampling Plans1 This standard is issued under the fixed designation E[.]
Designation: E1994 − 09 (Reapproved 2013) An American National Standard Standard Practice for Use of Process Oriented AOQL and LTPD Sampling Plans1 This standard is issued under the fixed designation E1994; the number immediately following the designation indicates the year of original adoption or, in the case of revision, the year of last revision A number in parentheses indicates the year of last reapproval A superscript epsilon (´) indicates an editorial change since the last revision or reapproval INTRODUCTION This standard is an abbreviated compilation of the sampling plans presented by H.F Dodge and H.G Romig in their classic development of sampling plans for use with the process associated with a continuing supply of products The so called AOQL plans provide a means for disposition of product whether or not the process is in control as well as incentives for process improvement in terms of reduced sample size as the process average percent defective is lowered In addition, so called LTPD plans are provided for use with individual lots of product, not necessarily associated with a process stream The sampling plans and parts of the text given here are taken from the Wiley Classics Library Edition of the Dodge-Romig tables (copyright 1998) Additional tables and detailed discussion of the plans, OC curves, and their derivation will be found in that text.2 The theoretical development of the Dodge-Roming plans will be found in Volumes and 20 of the Bell System Technical Journal3,4 and an amplification of the plans is given in Acceptance Sampling in Quality Control.5 Scope Terminology 1.1 This practice is primarily a statement of principals for the guidance of ASTM technical committees and others in the use of Average Outgoing Quality Limit, AOQL, and Lot Tolerance Percent Defective, LTPD, sampling plans for determining acceptable of lots of product 3.1 Definitions—Terminology E456 provides a more extensive list of terms in E11 standards 3.2 average quality protection—a type of protection in which there is prescribed some chosen value of average percent defective in the product after inspection (average outgoing quality limit (AOQL), that shall not be exceeded in the long run no matter what may be the level of percent defective in the product submitted to the inspector 3.3 average outgoing quality (AOQ)—the average percent defective of outgoing product including all accepted lots or batches, after any defective units found in them are replaced by acceptable units, plus all lots or batches which are not accepted after such lots or batches have been effectively 100 % inspected and all defective units replaced by acceptable units 3.4 average outgoing quality limit (AOQL)—the maximum of the AOQs for all possible incoming percentages defective for the process, for a given acceptance sampling plan 3.5 lot quality protection—a type of protection in which there is prescribed some chosen value of limiting percent defective in a lot (lot tolerance percent defective, (LTPD)) and also some chosen value for the probability (called the consumer’s risk) of accepting a submitted lot that has a percent defective equal to the lot tolerance percent defective 3.6 lot tolerance percent defective (LTPD)—for purposes of acceptance sampling, the percentage of defective units in a lot for which the consumer has a stated low probability of acceptance of the lot Referenced Documents 2.1 ASTM Standards:6 E178 Practice for Dealing With Outlying Observations E456 Terminology Relating to Quality and Statistics This practice is under the jurisdiction of ASTM Committee E11 on Quality and Statistics and is the direct responsibility of Subcommittee E11.30 on Statistical Quality Control Current edition approved April 1, 2013 Published April 2013 Originally approved in 1998 Last previous edition approved in 2009 as E1994 – 09 DOI: 10.1520/E1994-09R13 Available from John Wiley and Sons, Inc., 605 Third Ave., New York, NY 10158 Dodge, H F and Romig, H G., “A Method of Sampling Inspection,” The Bell System Technical Journal, Vol , No 10, 1924, pp 613–631 Dodge, H F and Romig, H G., “Single Sampling and Double Sampling Inspection Tables,” The Bell System Technical Journal, Vol 20, No 1, 1941, pp 1–61 Schilling, E G., Acceptance Sampling in Quality Control, Marcel Dekker Inc., NY, 1982, pp 372–399 For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org For Annual Book of ASTM Standards volume information, refer to the standard’s Document Summary page on the ASTM website Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959 United States E1994 − 09 (2013) sampling This results in the selection of one of the appended tables The second step is to determine whether the quality of product is good enough to warrant the introduction of sampling The economies of sampling will be realized, of course, only insofar as the percent defective in submitted product is such that the acceptance criteria of the selected sampling plan will be met A statistical analysis of past inspection results should first be made, therefore, in order to determine existing levels and fluctuations in the percent defective for the characteristic or the group of characteristics under consideration This provides information with respect to the degree of control as well as the usual level of percent defective to be expected under existing conditions Determine a value from this and other information for the process average percent defective that should be used in applying the selected sampling table, if sampling is to be introduced 3.7 Definitions of Terms Specific to This Standard: 3.7.1 consumer’s risk—the probability that a lot whose percentage defective is equal to the LTPD will be accepted by the plan Significance and Use 4.1 Two general types of tables (Note 1) are given, one based on the concept of lot tolerance, LTPD, and the other on AOQL The broad conditions under which the different types have been found best adapted are indicated below 4.1.1 For each of the types, tables are provided both for single sampling and for double sampling Each of the individual tables constitutes a collection of solutions to the problem of minimizing the over-all amount of inspection Because each line in the tables covers a range of lot sizes, the AOQL values in the LTPD tables and the LTPD values in the AOQL tables are often conservative Procedure NOTE 1—Tables in Annex A1-Annex A4 and parts of the text are reproduced by permission of John R Wiley and Sons More extensive tables and discussion of the methods will be found in that text 5.1 Two distinct methods of inspection are employed, single sampling and double sampling In single sampling only one sample is permitted before a decision is reached regarding the disposition of the lot, and the acceptance criterion is expressed as an acceptance number, c In double sampling, a second sample is permitted and two acceptance numbers are used; the first, c1, applying to the observed number of defectives for the first sample alone and the second, c2, applying to the observed number of defectives for the first and second samples combined The specific procedures assumed in the development of the tables are as follows: 5.1.1 Single Sampling Inspection Procedure: 5.1.1.1 Inspect a sample of n pieces 5.1.1.2 If the number of defectives found in the sample does not exceed c, the acceptance number, accept the lot 5.1.1.3 If the number of defectives found in the sample exceeds c, inspect all the pieces in the remainder of the lot 5.1.1.4 Regardless of whether or not the lot was accepted, correct or replace all defective pieces found in the sample as well as in any subsequent inspection of the remainder of the lot 5.1.2 Double Sampling Inspection Procedure: 5.1.2.1 Inspect a first sample of n1 pieces 5.1.2.2 If the number of defectives found in the first sample does not exceed c1, the acceptance number for the first sample, accept the lot 5.1.2.3 If the number of defectives found in the first sample exceeds c2, the acceptance number for the combined first and second samples, inspect all the pieces in the remainder of the lot 5.1.2.4 If the number of defectives found in the first sample exceeds c1, but does not exceed c2, inspect a second sample of n2 pieces 5.1.2.5 If the total number of defectives found in the first and second samples combined does not exceed c2, accept the lot 5.1.2.6 If the total number of defectives found in the first and second samples combined exceeds c2, inspect all the pieces in the remainder of the lot 4.2 The sampling tables based on lot quality protection (LTPD) (the tables in Annex A1 and Annex A2) are perhaps best adapted to conditions where interest centers on each lot separately, for example, where the individual lot tends to retain its identity either from a shipment or a service standpoint These tables have been found particularly useful in inspections made by the ultimate consumer or a purchasing agent for lots or shipments purchased more or less intermittently 4.3 The sampling tables based on average quality protection (AOQL) (the tables in Annex A3 and Annex A4) are especially adapted for use where interest centers on the average quality of product after inspection rather than on the quality of each individual lot and where inspection is, therefore, intended to serve, if necessary, as a partial screen for defective pieces The latter point of view has been found particularly helpful, for example, in consumer inspections of continuing purchases of large quantities of a product and in manufacturing process inspections of parts where the inspection lots tend to lose their identity by merger in a common storeroom from which quantities are withdrawn on order as needed 4.4 The plans based on average quality protection (AOQL) consider the degree to which the entire inspection procedure screens out defectives in the product submitted to the inspector Lots accepted by sample undergo a partial screening through the elimination of defectives found in samples Lots that fail to be accepted by sample are completely cleared of defectives Obviously, this requires a nondestructive test The over-all result is some average percent defective in the product as it leaves the inspector, termed the average outgoing quality, which depends on the level of percent defective for incoming product and the proportion of total defectives that are screened out 4.5 Given a specific problem of replacing a 100 % screening inspection by a sampling inspection, the first step is to decide on the type of protection desired, to select the desired limit of percent defective lot tolerance (LTPD) or AOQL value for that type of protection, and to choose between single and double E1994 − 09 (2013) a continuing supply of product, especially in consumer’s acceptance inspections and in producer’s receiving, process, and final inspections 5.3.3.2 Choose AOQL for a percent defective that will almost always be safely met by the running average quality of product after inspection 5.3.3.3 Choose LTPD for a percent defective that will almost always be met by each lot (This will be a much more pessimistic figure than the AOQL value of the plan) 5.3.3.4 As a manufacturer trying to meet a consumer’s stated AQL (Note 2), use for final inspection an AOQL plan with an AOQL value equal to the specified AQL value, in order to provide good assurance that outgoing quality will be found acceptable by the consumer (or set the AOQL at one and one third times the AQL for reasonably good assurance) 5.1.2.7 Regardless of whether or not the lot was accepted, correct or replace all defective pieces found in either sample as well as any in subsequent inspection or the remainder of the lot 5.2 In choosing a sampling plan for a particular application, a number of decisions must be made which depend on the conditions under which the plan is to be used The accompanying Sequence of Steps gives an outline of a typical procedure These steps are shown in the following numbered paragraphs 5.3 Sequence of Steps: 5.3.1 Decide what characteristics will be included in the inspection 5.3.1.1 If advantageous, use a separate sampling plan for a single characteristic or selected group of characteristics of like importance Sampling need not wait until all characteristics have good quality 5.3.1.2 If one or two characteristics give an outstandingly high number of defective units, treat them separately (using 100 percent inspection; also, if possible, concentrate on correcting the causes of trouble) and include the rest collectively in the sampling inspection 5.3.1.3 If all characteristics have satisfactory quality, include all of them collectively in the sampling inspection 5.3.1.4 In general, combine at one inspection station characteristics subject to essentially similar inspection operations, for example, all visual inspection items together, all gauging, or all testing Visual and gauging inspection operations often combine well 5.3.1.5 Include in any group characteristics of essentially the same degree of seriousness If two degrees of seriousness are involved, say major and minor, keep all majors together in one group and all minors in a second group 5.3.1.6 Consider these plans applicable to all basic types of inspection for manufactured products receiving, process, and final and to the inspection of administrative and clerical products as in paper-work quality control 5.3.2 Decide what is to constitute a lot for purposes of sampling inspection 5.3.2.1 So far as practicable, require that individual lots presented for acceptance comprise essentially homogeneous material from a common source 5.3.2.2 If presented material comes from two or more direct sources not under a common system of control, arrange to have each presented lot comprise material from only one of those sources; otherwise have source identification information furnished with each lot 5.3.2.3 To minimize the amount of inspection, make the lots as large as practicable, considering the limitations of available storage space, delays in shipment, difficulty in handling large rejected lots, etc 5.3.3 Choose between lot quality (LTPD) and average outgoing quality (AOQL) protection 5.3.3.1 Choose AOQL if interest centers on the general level of quality of product after inspection AOQL plans have been found generally more useful than LTPD plans in inspections of NOTE 2—AQL = Acceptable Quality Level, as used to index certain systems of sampling plans, signifying what the consumer feels to be the maximum percent defective that, for sampling purposes, can be considered satisfactory as a process average 5.3.3.5 When producer and consumer of a product are two departments of the same company, use AOQL plans with the provision that the producer perform the 100 percent inspection of rejected lots Close interchange of quality findings will expedite good process control of quality 5.3.3.6 Wherever practicable, make arrangements for the producer to perform the 100 percent inspection of rejected lots under procedures acceptable to the consumer and to provide suitable certifications of work performed 5.3.4 Choose a suitable figure of quality (LTPD or AOQL) for the sampling plan 5.3.4.1 For LTPD, choose the value of percent defective for lot acceptance not more than 10 % of the time (that is, reject at least 90 % of the time) 5.3.4.2 For AOQL, choose the value of average percent defective in product after inspection that should not be exceeded 5.3.4.3 In choosing a value of LTPD (or AOQL), consider and compare the cost of inspection with the economic loss that would ensue if quality as bad as the LTPD were accepted often (or if the average level of percent defective were greater than the AOQL) Even though the evaluation of economic loss may be difficult, relative values for different levels of percent defective may often be determined 5.3.5 Choose between single sampling and double sampling 5.3.5.1 In general, for economy in overall inspection effort, use double sampling rather than single sampling 5.3.5.2 In general, for minimum variation in the inspector’s workload, use single sampling 5.3.5.3 Consider adopting double sampling as the normal standard for sampling plans in a given plant, with a view to effecting overall economies 5.3.5.4 In a particular case, for a given AOQL and given process average, compare the OC curves of the two sampling plans (single sampling and double sampling) as an aid in making a choice (Note 3) NOTE 3—See the Dodge-Romig text for OC curves E1994 − 09 (2013) those units whose serial numbers correspond to the numbers in some section of a listing of random numbers are included in the sample 5.3.10.2 If a double sampling plan has been chosen, consider selecting sample units for both samples at the same time 5.3.11 Follow the sampling inspection procedure for single sampling or double sampling, whichever was chosen 5.3.11.1 Inspect each unit in the sample for all the characteristics decided on in Section 5.3 5.3.11.2 If single sampling is being used, inspect all units in the sample even though the acceptance number is exceeded before all units have been inspected This facilitates estimation of the process average 5.3.11.3 If double sampling is being used, inspect all units in the first sample; if desired, discontinue inspection of the second sample when the acceptance number, c2, is exceeded 5.3.12 Keep a running check on the process average and change the sampling plan if the process average changes sufficiently 5.3.12.1 Adopt a definite plan for making periodic estimates of the process average, every 20 or 50 lots or every month, quarter, or six months, depending on the production rate and the quality history 5.3.12.2 Keep the producing organization informed of the running quality of presented product, preferably in control chart form, and furnish prompt information regarding any sudden adverse shifts in quality 5.3.12.3 Change from one sampling plan to another within a sampling table, as the process average changes from one general level to another This provides a general basis for tightened and reduced inspection while holding to a given AOQL or LTPD If, with stable quality at an excellent level, it is desired to reduce inspection even further, use a larger AOQL or LTPD value, twice as large as the basic AOQL or LTPD 5.3.6 Select the proper sampling table in Annex A1-Annex A4, on the basis of the above choices 5.3.7 Obtain an estimate of process average percent defective 5.3.7.1 Use recent data to estimate the process average 5.3.7.2 Use rough estimates at the start, if little or no actual data are available; a poor estimate merely prevents getting the most economical plan but keeps the same (LTPD or AOQL) protection 5.3.7.3 As more data are collected, make improved estimates of process average 5.3.7.4 Omit wild and obviously nonrepresentative sets of data in making estimates and adopt some suitable rule for discarding data (see Practice E178) 5.3.8 Choose a sampling plan for the given lot size and the estimated process average 5.3.8.1 If the estimated process average percent defective, PA, falls within the range of PA values in the selected table, choose the sampling plan corresponding to the PA value and to the given lot size 5.3.8.2 If the PA is unknown or is estimated to be larger than the largest PA value given in the table, choose the sampling plan corresponding to the largest PA in the table (last column) and to the given lot size 5.3.8.3 Under 5.3.8.2, obtain revised estimates of the PA from the lot-by-lot data and use a sampling plan with a smaller sample size as soon as a revised estimate of the PA permits 5.3.8.4 If, for single sampling, the sampling plan given by the table has c = 0, consider whether it would be preferable to use a plan with c = to avoid making rejections on finding a single defective There is no such problem for double sampling, since c2 always equals or more 5.3.8.5 If inspection includes two classes of defects, major and minor, with two AOQL values, choose the two sampling plans from the appropriate tables in the Annexes and use them simultaneously 5.3.9 Check the OC curve of the chosen plan(s) (Note 4) Precision and Bias 6.1 The use of this standard assumes that test methods are used with sufficient precision and accuracy that test results can be safely translated into attribute (go-no go) results NOTE 4—See the Dodge–Romig text for OC Curves 5.3.10 From the lot, select sample units by means of a random procedure 5.3.10.1 Consider the use of random numbers as the preferred way of selecting sample units at random Each unit in the lot is assigned a serial number usually on paper, and then Keywords 7.1 average outgoing quality limit; lot tolerance percent defective; sampling; sampling plans E1994 − 09 (2013) ANNEXES (Mandatory Information) A1 SINGLE SAMPLING TABLES FOR STATED VALUES OF LOT TOLERANCE PERCENT DEFECTIVE (LTPD) WITH CONSUMER’S RISK OF 0.10, 0.5 % LTPD, 1.0 % LTP, 2.0 % LTP, 5.0 % LTPD, 10.0 % LTPD A1.1 Tables A1.1-A1.5 illustrate single sampling stated values of lot tolerance percent TABLE A1.1 Single Sampling Table for Lot Tolerance Percent Defective (LTPD) = 0.5 % NOTE 1—n = sample size; c = acceptance number; AOQL = average outgoing quality limit; “all” indicates that each piece in the lot is to be inspcted 1–180 181–210 211–250 Process Average to 0.005 % AOQL n c % all 0 180 0.02 210 0.03 Process Average 0.006 to 0.050 % AOQL n c % all 0 180 0.02 210 0.03 Process Average 0.051 to 0.100 % AOQL n c % all 0 180 0.02 210 0.03 Process Average 0.101 to 0.150 % AOQL n c % all 0 180 0.02 210 0.03 Process Average Process Average 0.151 to 0.200 % 0.201 to 0.250 % AOQL AOQL n c n c % % all 0 all 0 180 0.02 180 0.02 210 0.03 210 0.03 251–300 301–400 401–500 240 275 300 0 0.03 0.04 0.05 240 275 300 0 0.03 0.04 0.05 240 275 300 0 0.03 0.04 0.05 240 275 300 0 0.03 0.04 0.05 240 275 300 0 0.03 0.04 0.05 240 275 300 0 0.03 0.04 0.05 501–600 601–800 801–1000 320 350 365 0 0.05 0.06 0.06 320 350 365 0 0.05 0.06 0.06 320 350 365 0 0.05 0.06 0.06 320 350 365 0 0.05 0.06 0.06 320 350 365 0 0.05 0.06 0.06 320 350 365 0 0.05 0.06 0.06 1001–2000 2001–3000 3001–4000 410 430 440 0 0.07 0.07 0.07 410 430 440 0 0.07 0.07 0.07 410 705 730 1 0.07 0.09 0.09 670 705 985 1 0.08 0.09 0.10 670 955 1230 0.08 670 0.10 955 0.11 1230 0.08 0.10 0.11 4001–5000 5001–7000 7001–10 000 445 450 455 0 0.08 0.08 0.08 740 750 760 1 0.10 0.10 0.10 1000 1020 1040 2 0.11 0.12 0.12 1000 1280 1530 0.11 0.12 0.14 1250 1510 1790 0.12 1480 0.13 1760 0.14 2240 0.12 0.14 0.16 10 001–20 000 20 001–50 000 50 001–100 000 460 775 780 1 0.08 0.11 0.11 775 1050 1060 2 0.10 0.13 0.13 1330 1600 1840 0.14 0.15 0.17 1820 2080 2590 5 0.16 0.18 0.19 2300 3060 3780 10 13 0.17 2780 0.20 4200 0.22 5140 15 19 0.18 0.22 0.24 Lot Size E1994 − 09 (2013) TABLE A1.2 Single Sampling Table for Lot Tolerance Percent Defective (LTPD) = 1.0 % NOTE 1—n = sample size; c = acceptance number; AOQL = average outgoing quality limit; “all” indicates that each piece in the lot is to be inspcted 1–120 121–150 151–200 Process Average to 0.010 % AOQL n c % all 0 120 0.06 140 0.08 Process Average 0.011 to 0.10 % AOQL n c % all 0 120 0.06 140 0.08 Process Average 0.11 to 0.20 % AOQL n c % all 0 120 0.06 140 0.08 Process Average 0.21 to 0.30 % AOQL n c % all 0 120 0.06 140 0.08 Process Average Process Average 0.31 to 0.40 % 0.41 to 0.50 % AOQL AOQL n c n c % % all 0 all 0 120 0.06 120 0.06 140 0.08 140 0.08 201–300 301–400 401–500 165 175 180 0 0.10 0.12 0.13 165 175 180 0 0.10 0.12 0.13 165 175 180 0 0.10 0.12 0.13 165 175 180 0 0.10 0.12 0.13 165 175 180 0 0.10 0.12 0.13 165 175 180 0 0.10 0.12 0.13 501–600 601–800 801–1000 190 200 205 0 0.13 0.14 0.14 190 200 205 0 0.13 0.14 0.14 190 200 205 0 0.13 0.14 0.14 190 330 335 1 0.13 0.15 0.17 190 330 335 1 0.13 0.15 0.17 305 330 335 1 0.14 0.15 0.17 1001–2000 2001–3000 3001–4000 220 220 225 0 0.15 0.15 0.15 220 375 380 1 0.15 0.20 0.20 360 505 510 2 0.19 0.23 0.24 490 630 645 3 0.21 0.24 0.25 490 745 880 0.21 610 0.26 870 0.28 1000 0.22 0.26 0.29 4001–5000 5001–7000 7001–10 000 225 230 230 0 0.16 0.15 0.16 380 385 520 1 0.20 0.21 0.25 520 655 660 3 0.24 0.27 0.28 770 780 910 4 0.28 0.29 0.32 895 1020 1150 0.29 1120 0.32 1260 0.34 1500 10 0.31 0.34 0.37 10 001–20 000 20 001–50 000 50 001–100 000 390 390 390 1 0.21 0.21 0.21 525 530 670 2 0.26 0.26 0.29 785 920 1040 0.31 0.34 0.36 1040 1300 1420 0.35 0.39 0.41 1400 1890 2120 13 15 0.39 1980 0.44 2570 0.47 3150 14 19 23 0.43 0.48 0.50 Lot Size TABLE A1.3 Single Sampling Table for Lot Tolerance Percent Defective (LTPD ) = 2.0 % NOTE 1—n = sample size; c = acceptance number; AOQL = average outgoing quality limit; “all” indicates that each piece in the lot is to be inspcted Lot Size Process Average to 0.02 % Process Average 0.03 to 0.20 % Process Average 0.21 to 0.40 % Process Average 0.41 to 0.60 % Process Average 0.61 to 0.80 % Process Average 0.81 to 1.00 % n c AOQL % n c AOQL % n c AOQL % n c AOQL % n c AOQL % n c AOQL % 1–75 76–100 101–200 all 70 85 0 0 0.16 0.25 all 70 85 0 0 0.16 0.25 all 70 85 0 0 0.16 0.25 all 70 85 0 0 0.16 0.25 all 70 85 0 0 0.16 0.25 all 70 85 0 0 0.16 0.25 201–300 301–400 401–500 95 100 105 0 0.26 0.28 0.28 95 100 105 0 0.26 0.28 0.28 95 100 105 0 0.26 0.28 0.28 95 160 165 1 0.26 0.32 0.34 95 160 165 1 0.26 0.32 0.34 95 160 165 1 0.26 0.32 0.34 501–600 601–800 801–1000 105 110 115 0 0.29 0.29 0.28 105 110 115 0 0.29 0.29 0.28 175 180 185 1 0.34 0.36 0.37 175 240 245 2 0.34 0.40 0.42 175 240 305 0.34 0.40 0.44 235 300 305 3 0.36 0.41 0.44 1001–2000 2001–3000 3001–4000 115 115 115 0 0.30 0.31 0.31 190 190 195 1 0.40 0.41 0.41 255 260 330 2 0.47 0.48 0.54 325 385 450 0.50 0.58 0.63 380 450 510 0.54 0.60 0.65 440 565 690 0.56 0.64 0.70 4001–5000 5001–7000 7001–10 000 195 195 195 1 0.41 0.42 0.42 260 265 265 2 0.50 0.50 0.50 335 335 395 3 0.54 0.55 0.62 455 515 520 6 0.63 0.69 0.69 575 640 760 10 0.69 750 0.73 870 0.79 1050 10 12 15 0.74 0.80 0.86 10 001–20 000 20 001–50 000 50 001–100 000 200 200 200 1 0.42 0.42 0.42 265 335 335 3 0.51 0.58 0.58 460 520 585 0.67 0.73 0.76 650 710 770 10 0.77 0.81 0.84 885 1060 1180 12 15 17 0.86 1230 0.93 1520 0.97 1690 18 23 26 0.94 1.0 1.1 E1994 − 09 (2013) TABLE A1.4 Single Sampling Table for Lot Tolerance Percent Defective (LTPD) = 5.0 % NOTE 1—n = sample size; c = acceptance number; AOQL = average outgoing quality limit; “all” indicates that each piece in the lot is to be inspcted Lot Size Process Average to 0.05 % Process Average 0.06 to 0.50 % Process Average 0.51 to 1.00 % Process Average 1.01 to 1.50 % Process Average 1.51 to 2.00 % Process Average 2.01 to 2.50 % n c AOQL % n c AOQL % n c AOQL % n c AOQL % n c AOQL % n c AOQL % 1–30 31–50 51–100 101–200 all 30 37 40 0 0 0.49 0.63 0.74 all 30 37 40 0 0 0.49 0.63 0.74 all 30 37 40 0 0 0.49 0.63 0.74 all 30 37 40 0 0 0.49 0.63 0.74 all 30 37 40 0 0 0.49 0.63 0.74 all 30 37 40 0 0 0.49 0.63 0.74 201–300 301–400 401–500 43 44 45 0 0.74 0.74 0.75 43 44 75 0 0.74 0.74 0.95 70 70 100 1 0.92 0.99 1.1 70 100 100 2 0.92 1.0 1.1 95 120 125 3 0.99 1.1 1.2 95 145 150 4 0.99 1.1 1.2 501–600 601–800 801–1000 45 45 45 0 0.76 0.77 0.78 75 75 75 1 0.98 1.0 1.0 100 100 105 2 1.1 1.2 1.2 125 130 155 3 1.2 1.2 1.4 150 175 180 5 1.3 1.4 1.4 175 200 225 1.3 1.4 1.5 1001–2000 2001–3000 3001–4000 45 75 75 1 0.80 1.1 1.1 75 105 105 2 1.0 1.3 1.3 130 135 160 3 1.4 1.4 1.5 180 210 210 6 1.6 1.7 1.7 230 280 305 10 1.7 1.9 2.0 280 370 420 13 15 1.8 2.1 2.2 4001–5000 5001–7000 7001–10 000 75 75 75 1 1.1 1.1 1.1 105 105 105 2 1.3 1.3 1.3 160 185 185 5 1.5 1.7 1.7 235 260 260 8 1.8 1.9 1.9 330 350 380 11 12 13 2.0 2.2 2.2 440 490 535 16 18 20 2.2 2.4 2.5 10 001–20 000 20 001–50 000 50 001–100 000 75 75 75 1 1.1 1.1 1.1 135 135 160 3 1.4 1.4 1.6 210 235 235 7 1.8 1.9 1.9 285 305 355 10 12 2.0 2.1 2.2 425 470 515 15 17 19 2.3 2.4 2.5 610 700 770 23 27 30 2.6 2.7 2.8 TABLE A1.5 Single Sampling Table for Lot Tolerance Percent Defective (LTPD) = 10.0 % NOTE 1—n = sample size; c = acceptance number; AOQL = average outgoing quality limit; “all” indicates that each piece in the lot is to be inspcted Lot Size Process Average to 0.10 % n c 1–20 all 21–50 51–100 101–200 17 20 22 201–300 301–400 401–500 AOQL % Process Average 0.11 to 1.00 % n c all 0 0 1.3 1.5 1.5 17 20 22 23 23 23 0 1.5 1.5 1.5 501–600 601–800 801–1000 23 23 39 0 1001–2000 2001–3000 3001–4000 39 39 39 4001–5000 5001–7000 7001–10 000 10 001-20 000 20 001–50 000 50 001–100 000 AOQL % Process Average 1.01 to 2.00 % n c all 0 0 1.3 1.5 1.5 17 20 35 38 38 38 1 1.9 2.0 2.0 1.5 1.6 2.1 38 38 50 1 1 2.1 2.1 2.1 50 50 50 39 39 39 1 2.1 2.1 2.2 39 39 39 1 2.2 2.2 2.2 AOQL % Process Average 2.01 to 3.00 % n c all 0 1.3 1.5 2.0 17 33 48 50 50 50 2 2.3 2.4 2.5 2.1 2.1 2.6 65 65 65 3 2 2.6 2.6 2.6 80 80 90 50 65 65 3 2.6 3.0 3.0 65 80 95 3.0 3.2 3.3 AOQL % Process Average 3.01 to 4.00 % n c all 0 1.3 1.7 2.2 17 33 48 65 65 75 3 2.4 2.5 2.8 2.7 2.8 2.8 80 90 90 5 4 3.1 3.1 3.4 105 115 130 90 105 105 6 3.5 3.6 3.6 120 120 130 7 3.7 3.7 4.0 AOQL % Process Average 4.01 to 5.00 % AOQL % n c all 0 1.3 1.7 2.2 17 33 60 1.3 1.7 2.4 75 90 90 5 2.6 2.7 2.9 85 100 110 2.7 2.9 3.2 3.0 3.1 3.2 100 100 115 6 3.2 3.3 3.4 125 140 150 10 3.3 3.4 3.7 3.4 3.7 3.8 140 165 190 11 13 3.9 4.1 4.4 195 230 255 14 17 19 4.4 4.7 4.8 130 140 150 10 3.9 4.1 4.2 200 200 210 14 14 15 4.5 4.6 4.7 270 295 315 20 22 24 4.9 5.0 5.2 150 165 180 10 11 12 4.3 4.4 4.4 240 260 270 17 19 20 4.8 5.0 5.1 340 380 380 26 30 30 5.4 5.7 5.7 E1994 − 09 (2013) A2 DOUBLE SAMPLING TABLES FOR STATED VALUES OF LOT TOLERANCE PERCENT DEFECTIVE (LTPD) WITH CONSUMER RISK OF 0.10, 0.5 % LTPD, 1.0 % LTPD, 2.0 % LTPD, 5.0 % LTPD, 10.0 % LTPD A2.1 Tables A2.1-A2.5 illustrate double sampling stated values of lot tolerance percent TABLE A2.1 Double Sampling Table for Lot Tolerance Percent Defective (LTPD) = 50 % Lot Size A Process Average to 0.005 % Trial 2B n n + n2 c C Trial n1 all 180 c1 0 Process Average 0.006 to 0.050 % Trial n n + n2 c Trial n1 all 180 c1 0 Process Average 0.051 to 0.100 % Trial AOQLC n2 n1 + n2 c2 in % 0.02 1–180 181–210 Trial n1 c1 allD 180 211–250 251–300 301–400 210 240 275 0 0.03 0.03 0.04 210 240 275 0 0.03 0.03 0.04 210 240 275 0 0.03 0.03 0.04 401–450 451–500 501–550 290 340 350 0 110 130 450 480 1 0.04 0.04 0.05 290 340 350 0 110 130 450 480 1 0.04 0.04 0.05 290 340 350 0 110 130 450 480 1 0.04 0.04 0.05 551–600 601–800 801–1000 360 400 430 0 150 185 200 510 585 630 1 0.05 0.06 0.07 360 400 430 0 150 185 200 510 585 630 1 0.05 0.06 0.07 360 400 430 0 150 185 200 510 585 630 1 0.05 0.06 0.07 1001–2000 2001–3000 3001–4000 490 520 530 0 265 290 310 755 810 840 1 0.08 0.09 0.09 490 520 530 0 265 290 570 755 810 1100 1 0.08 0.09 0.11 490 520 530 0 265 755 530 1050 570 1100 2 0.08 0.10 0.11 4001–5000 5001–7000 7001–10 000 540 545 550 0 305 315 330 845 860 880 1 0.09 0.10 0.10 540 545 550 0 580 615 620 1120 1160 1170 2 0.11 0.11 0.12 540 545 550 0 830 1370 865 1410 1130 1680 3 0.12 0.12 0.14 10 001–20 000 20 001–50 000 50 001–100 000 555 560 560 0 0.10 0.12 0.12 555 560 560 0 0.13 0.14 0.15 555 900 905 1 Lot Size 345 900 650 1210 650 1210 Process Average 0.101 to 0.150 % Trial 2B n n + n2 c AOQL in % 0.02 925 1480 940 1500 1210 1770 Process Average 0.151 to 0.200 % Trial n n + n2 c AOQL in % 0.02 1185 1740 0.15 1400 2300 0.16 1655 2560 0.17 Process Average 0.201 to 0.250 % Trial AOQL n2 n1 + n2 c2 in % 0.02 1–180 181–210 Trial 1A c1 n1 allD 180 211–250 251–300 301–400 210 240 275 0 0.03 0.03 0.04 210 240 275 0 0.03 0.03 0.04 210 240 275 0 0.03 0.03 0.04 401–450 451–500 501–550 290 340 350 0 110 130 450 480 1 0.04 0.04 0.05 290 340 350 0 110 130 450 480 1 0.04 0.04 0.05 290 340 350 0 110 130 450 480 1 0.04 0.04 0.05 551–600 601–800 801–1000 360 400 430 0 150 185 200 510 585 630 1 0.05 0.06 0.07 360 400 430 0 150 185 200 510 585 630 1 0.05 0.06 0.07 360 400 430 0 150 185 200 510 585 630 1 0.05 0.06 0.07 1001–2000 2001–3000 3001–4000 490 520 530 0 500 530 810 990 1050 1340 2 0.09 0.10 0.11 490 520 530 0 500 760 1030 990 1280 1560 0.09 0.11 0.12 490 520 840 0 500 990 980 1500 1160 2000 0.09 0.11 0.13 4001–5000 5001–7000 7001–10 000 540 545 880 0 1060 1105 1300 1600 1650 2180 4 0.13 0.13 0.15 845 860 880 1 1205 1490 1770 2050 2350 2650 0.14 0.15 0.16 845 860 1170 1 1425 2270 1700 2560 2160 3330 11 0.14 0.16 0.17 10 001–20 000 20 001–50 000 50 001–100 000 900 1210 1210 2 1840 2330 2590 2740 3540 3800 11 12 0.18 0.20 0.21 1200 1500 1770 2250 2980 3690 3450 4480 5460 11 15 19 0.19 0.22 0.23 1740 2300 2560 2620 4360 4240 6540 5420 7980 15 24 30 0.21 0.24 0.26 AOQLC in % 0.02 Trial n1 all 180 c1 0 A Trial 1: n1 = first sample size; c1 = acceptance number for first sample Trial 2: n2 = second sample size; c2 = acceptance number for first and second samples combined C AOQL = Average Outgoing Quality Limit D “all” indicates that each piece in the lot is to be inspected B AOQL in % 0.02 Trial n1 all 180 c1 0 E1994 − 09 (2013) TABLE A2.2 Double Sampling Table for Lot Tolerance Percent Defective (LTPD) = 1.0 % Lot Size 1–120 Process Average to 0.010 % Trial 1A Trial 2B c1 n n + n2 c n1 allD AOQLC in % Process Average 0.011 to 0.10 % Trial Trial n1 c1 n n + n2 c all AOQL in % Trial n1 c1 all Process Average 0.11 to 0.20 % Trial n n + n2 c AOQL in % 121–150 151–200 201–260 120 140 165 0 0.06 0.08 0.10 120 140 165 0 0.06 0.08 0.10 120 140 165 0 0.06 0.08 0.10 261–300 301–400 401–500 180 200 215 0 75 90 100 255 290 315 1 0.10 0.12 0.14 180 200 215 0 75 90 100 255 290 315 1 0.10 0.12 0.14 180 200 215 0 75 90 100 255 290 315 1 0.10 0.12 0.14 501–600 601–800 801–1000 225 235 245 0 115 125 135 340 360 380 1 0.15 0.16 0.17 225 235 245 0 115 125 135 340 360 380 1 0.15 0.16 0.17 225 235 245 0 115 125 250 340 360 495 1 0.15 0.16 0.19 1001–2000 2001–3000 3001–4000 265 270 275 0 155 160 160 420 430 435 1 0.18 0.19 0.19 265 270 275 0 155 300 305 420 570 580 2 0.18 0.22 0.22 265 270 275 0 285 420 435 550 690 710 3 0.21 0.25 0.25 4001–5000 5001–7000 7001–10 000 275 275 280 0 165 170 320 440 445 600 1 0.19 0.20 0.24 275 275 280 0 310 315 460 585 590 740 2 0.23 0.23 0.26 275 275 280 0 565 580 590 840 855 870 4 0.28 0.29 0.30 10 001–20 000 20 001–50 000 50 001–100 000 280 280 280 0 0.24 0.25 0.25 280 280 280 0 0.27 0.30 0.30 450 450 450 1 Lot Size 1–120 325 605 325 605 325 605 Process Average 0.21 to 0.30 % Trial 1A Trial 2B c1 n2 n1 + n c2 n1 allD AOQLC in % 465 745 605 885 605 885 Process Average 0.31 to 0.40 % Trial Trial n1 c1 n2 n1 + n c2 all AOQL in % Trial n1 c1 all 700 1150 830 1280 960 1410 Process Average 0.41 to 0.50 % Trial n2 n1 + n c2 0.33 0.36 0.38 AOQL in % 121–150 151–200 201–260 120 140 165 0 0.06 0.08 0.10 120 140 165 0 0.06 0.08 0.10 120 140 165 0 0.06 0.08 0.10 261–300 301–400 401–500 180 200 215 0 75 90 100 255 290 315 1 0.10 0.12 0.14 180 200 215 0 75 90 100 255 290 315 1 0.10 0.12 0.14 180 200 215 0 75 90 100 255 290 315 1 0.10 0.12 0.14 501–600 601–800 801–1000 225 235 245 0 115 230 250 340 465 495 2 0.15 0.18 0.19 225 235 245 0 115 230 250 340 465 495 2 0.15 0.18 0.19 225 235 245 0 205 230 250 430 465 495 2 0.16 0.18 0.19 1001–2000 2001–3000 3001–4000 265 270 435 0 405 545 645 670 815 1080 0.23 0.26 0.29 265 430 435 1 515 620 865 780 1050 1300 0.24 0.28 0.30 265 430 580 515 830 940 780 1260 1520 10 0.24 0.30 0.33 4001–5000 5001–7000 7001–10 000 440 445 450 1 660 785 920 1100 1230 1370 0.30 0.33 0.35 440 590 600 2 1000 1440 990 1580 1240 1840 10 12 0.33 0.36 0.39 585 730 870 1075 1190 1540 1660 1920 2410 11 13 17 0.35 0.38 0.41 10 001–20 000 20 001–50 000 50 001–100 000 605 605 605 2 1035 1295 1545 1640 1900 2150 10 12 14 0.39 0.42 0.44 745 885 885 4 1485 2230 1845 2730 2085 2970 15 19 21 0.43 0.47 0.49 1150 1280 1410 1990 2600 3280 3140 3880 4690 23 29 36 0.44 0.52 0.55 A Trial 1: n1 = first sample size; c1 = acceptance number for first sample Trial 2: n2 = second sample size; c2 = acceptance number for first and second samples combined C AOQL = Average Outgoing Quality Limit D “all” indicates that each piece in the lot is to be inspected B E1994 − 09 (2013) TABLE A2.3 Double Sampling Table for Lot Tolerance Percent Defective (LTPD) = 2.0 % 1–75 76–100 101–200 Process Average to 0.02 % Trial 1A Trial 2B c1 n n + n2 c n1 allD 70 85 201–300 301–400 401–500 115 120 125 0 50 60 65 165 180 190 1 0.29 0.32 0.33 115 120 125 0 50 60 65 165 180 190 1 0.29 0.32 0.33 115 120 125 0 50 60 120 165 180 245 1 0.29 0.32 0.37 501–600 601–800 801–1000 125 130 135 0 70 75 75 195 205 210 1 0.34 0.35 0.36 125 130 135 0 70 75 140 195 205 275 1 0.34 0.35 0.42 125 130 135 0 130 125 140 255 265 275 2 0.39 0.41 0.42 1001–2000 2001–3000 3001–4000 135 140 140 0 85 85 85 220 225 225 1 0.38 0.39 0.40 135 140 140 0 155 155 225 290 295 365 2 0.45 0.46 0.52 135 140 140 0 220 285 290 355 425 430 4 0.50 0.56 0.57 4001–5000 5001–7000 7001–10 000 140 140 140 0 160 160 160 300 300 300 2 0.47 0.48 0.48 140 140 140 0 230 230 235 370 370 375 3 0.53 0.54 0.54 140 140 225 0 360 365 350 500 505 575 5 0.61 0.62 0.66 10 001–20 000 20 001–50 000 50 001–100 000 140 140 140 0 2 0.49 0.49 0.49 140 140 140 0 0.54 0.59 0.60 225 225 225 1 0.71 0.75 0.78 AOQLC in % 0.16 0.25 415 640 480 705 545 770 Process Average 0.81 to 1.00 % Trial Trial n1 c1 n2 n1 + n all 70 85 c2 AOQL in % 0.16 0.25 Lot Size AOQLC in % 0.16 0.25 Process Average 0.03 to 0.20 % Trial Trial n1 c1 n n + n2 all 70 85 c2 c2 AOQL in % 0.16 0.25 1–75 76–100 101–200 165 305 165 305 165 305 Process Average 0.41 to 0.60 % Trial 1A Trial 2B c1 n n1 + n c2 n1 allD 70 85 201–300 301–400 401–500 115 120 125 0 50 115 120 165 235 245 2 0.29 0.34 0.37 115 120 125 0 50 115 120 165 235 245 2 0.29 0.34 0.37 115 120 125 0 50 115 120 165 235 245 2 0.29 0.34 0.37 501–600 601–800 801–1000 125 130 135 0 130 195 200 255 325 335 3 0.39 0.44 0.46 125 130 135 0 185 250 255 310 380 390 4 0.41 0.45 0.48 125 130 210 0 185 250 290 310 380 500 0.41 0.45 0.54 1001–2000 2001–3000 3001–4000 135 225 225 1 285 385 455 420 610 680 0.54 0.65 0.69 220 295 295 2 375 435 555 595 730 850 11 0.62 0.69 0.74 220 360 365 3 485 535 715 705 895 12 1080 15 0.65 0.72 0.77 4001–5000 5001–7000 7001–10 000 225 300 300 2 460 450 520 685 750 820 10 0.70 0.74 0.77 300 370 375 3 620 920 680 1050 735 1110 12 14 15 0.77 0.82 0.85 435 505 575 775 935 1055 1210 17 1440 21 1630 24 0.81 0.89 0.95 10 001–20 000 20 001–50 000 50 001–100 000 305 305 305 2 645 715 830 950 1020 1135 12 13 15 0.83 0.86 0.90 375 445 510 935 1310 1045 1490 1150 1660 18 21 24 0.92 0.98 1.0 640 705 770 1240 1635 1850 1880 28 2340 36 2620 41 1.0 1.1 1.2 Lot Size 235 375 305 445 305 445 Process Average 0.61 to 0.80 % Trial Trial n1 c1 n2 n1 + n c2 all 70 85 AOQL in % 0.16 0.25 Process Average 0.21 to 0.40 % Trial Trial n1 c1 n n + n2 all 70 85 A Trial 1: n1 = first sample size; c1 = acceptance number for first sample Trial 2: n2 = second sample size; c2 = acceptance number for first and second samples combined AOQL = Average Outgoing Quality Limit D “all” indicates that each piece in the lot is to be inspected B C 10 AOQL in % 0.16 0.25 E1994 − 09 (2013) TABLE A2.4 Double Sampling Table for Lot Tolerance Percent Defective (LTPD) = 5.0 % Lot Size 1–30 31–50 Process Average to 0.05 % Trial 1A Trial 2B c1 n2 n1 + n c2 n1 allD 30 AOQLC in % 0.49 Process Average 0.06 to 0.50 % Trial Trial n1 c1 n n + n2 c all 30 AOQL in % 0.49 Process Average 0.51 to 1.00 % Trial Trial AOQL in % n1 c1 n n + n2 c all 30 0.49 51–75 76–100 101–200 38 44 49 0 21 26 65 75 1 0.59 0.64 0.84 38 44 49 0 21 26 65 75 1 0.59 0.64 0.84 38 44 49 0 21 26 65 75 0.59 0.64 0.84 201–300 301–400 401–500 50 55 55 0 30 30 30 80 85 85 1 0.91 0.92 0.93 50 55 55 0 30 55 55 80 110 110 2 0.91 1.1 1.1 50 55 55 0 55 55 80 105 110 135 2 1.0 1.1 1.2 501–600 601–800 801–1000 55 55 55 0 30 35 35 85 90 90 1 0.94 0.95 0.96 55 55 55 0 60 65 65 115 120 120 2 1.1 1.1 1.1 55 55 55 0 85 85 115 140 140 170 3 1.2 1.3 1.4 1001–2000 2001–3000 3001–4000 55 55 55 0 35 65 65 90 120 120 2 0.98 1.2 1.2 55 55 55 0 95 95 95 150 150 150 3 1.3 1.3 1.3 55 55 90 0 120 150 140 175 205 230 1.4 1.5 1.6 4001–5000 5001–7000 7001–10 000 55 55 55 0 65 65 65 120 120 120 2 1.2 1.2 1.2 55 55 55 0 95 95 120 150 150 175 3 1.4 1.4 1.5 90 90 90 1 165 165 190 255 255 280 7 1.6 1.8 1.9 10 001–20 000 20 001–50 000 50 001–100 000 55 55 55 0 55 55 55 0 1.5 1.7 1.7 90 90 90 1 190 280 215 305 240 330 Process Average 2.01 to 2.50 % Trial Trial n1 c1 n n + n2 all 30 10 1.9 2.0 2.1 c2 AOQL in % 0.49 65 120 65 120 65 120 Process Average 1.01 to 1.50 % Trial 2B Trial 1A c n n + n2 c n1 allD 30 2 1.2 1.2 1.2 AOQLC in % 0.49 51–75 76–100 101–200 38 44 49 0 21 51 65 100 0.59 0.64 0.91 38 44 49 0 21 51 65 100 0.59 0.64 0.91 38 44 49 0 21 51 65 100 0.59 0.64 0.91 201–300 301–400 401–500 50 55 55 0 55 80 105 105 135 160 1.0 1.1 1.3 50 55 85 0 80 100 120 130 155 205 1.1 1.2 1.4 50 85 85 1 100 105 140 150 190 225 1.1 1.3 1.4 501–600 601–800 801–1000 55 90 90 1 110 125 150 165 215 240 1.3 1.5 1.5 85 90 90 1 145 170 200 230 260 290 1.4 1.5 1.6 85 120 120 2 165 185 210 250 305 10 330 11 1.5 1.6 1.7 1001–2000 2001–3000 3001–4000 90 120 120 2 185 180 210 275 300 330 10 1.7 1.9 2.0 120 150 150 3 225 270 295 345 420 445 11 14 15 1.9 2.1 2.3 175 205 230 260 375 420 435 15 580 21 650 24 2.0 2.3 2.4 4001–5000 5001–7000 7001–10 000 120 120 120 2 255 260 285 375 380 405 12 12 13 2.1 2.1 2.1 150 150 175 3 345 370 370 495 520 545 17 18 19 2.3 2.3 2.4 255 255 280 7 445 495 540 700 26 750 28 820 31 2.5 2.6 2.7 10 001–20 000 20 001–50 000 50 001–100 000 120 120 120 2 310 335 360 430 455 480 14 15 16 2.2 2.2 2.3 175 205 205 5 420 485 555 595 690 760 21 25 28 2.4 2.5 2.6 280 305 330 10 660 745 810 940 36 1050 41 1140 45 2.8 2.9 3.0 Lot Size 1–30 31–50 120 175 150 205 150 205 Process Average 1.51 to 2.00 % Trial Trial n1 c1 n n + n2 c all 30 A Trial 1: n1 = first sample size; c1 = acceptance number for first sample Trial 2: n2 = second sample size; c2 = acceptance number for first and second samples combined C AOQL = Average Outgoing Quality Limit D “all” indicates that each piece in the lot is to be inspected B 11 AOQL in % 0.49 E1994 − 09 (2013) TABLE A2.5 Double Sampling Table for Lot Tolerance Percent Defective (LTPD) = 10.0 % Lot Size Process Average to 0.10 % Trial 2B n2 n1 + n c2 13 38 15 42 Process Average 0.11 to 1.00 % Trial n n + n2 c 13 38 15 42 Process Average 1.01 to 2.00 % Trial Trial AOQL in % n1 c1 n n + n2 c all 17 1.3 25 13 38 1.6 27 28 55 2.1 1–20 21–50 51–100 101–200 Trial 1A c1 n1 allD 17 25 27 201–300 301–400 401–500 27 27 28 0 16 17 16 43 44 44 1 1.9 1.9 1.9 27 27 28 0 30 33 32 57 60 60 2 2.2 2.2 2.3 27 27 28 0 43 43 57 70 70 85 3 2.4 2.5 2.7 501–600 601–800 801–1000 28 28 28 0 17 17 32 45 45 60 1 1.9 2.0 2.3 28 28 28 0 32 47 47 60 75 75 3 2.3 2.6 2.6 28 28 28 0 57 57 72 85 85 100 4 2.8 2.9 3.0 1001–2000 2001–3000 3001–4000 28 28 28 0 32 32 32 60 60 60 2 2.4 2.4 2.4 28 28 28 0 47 47 62 75 75 90 3 2.7 2.7 2.9 45 45 45 1 70 85 85 115 130 130 7 3.3 3.5 3.5 4001–5000 5001–7000 7001–10 000 28 28 28 0 32 32 32 60 60 60 2 2.4 2.4 2.5 28 28 28 0 62 62 62 90 90 90 4 3.0 3.0 3.0 45 45 45 1 95 95 95 140 140 140 8 3.7 3.8 3.8 10 001–20 000 20 001–50 000 50 001–100 000 28 28 28 0 28 28 28 0 3.0 3.3 3.8 45 45 45 1 110 155 120 165 135 180 Process Average 4.01 to 5.00 % Trial Trial n1 c1 n n + n2 all 10 11 3.9 3.9 4.2 c2 AOQL in % AOQLC in % 1.3 1.6 1.8 n1 all 17 25 27 Trial c1 0 0 32 60 32 60 32 60 Process Average 2.01 to 3.00 % Trial 1A Trial 2B c n n + n2 c n1 allD 2 2.5 2.5 2.5 AOQLC in % 21–50 51–100 101–200 17 25 27 0 24 38 49 65 1.3 1.8 2.3 17 25 27 0 24 53 49 80 1.3 1.8 2.4 17 25 27 0 24 53 49 80 1.3 1.8 2.4 201–300 301–400 401–500 27 44 44 1 53 66 76 80 110 120 2.7 2.9 3.1 43 44 44 1 62 86 101 105 130 145 2.8 3.1 3.3 43 60 60 2 82 90 105 125 150 10 165 11 3.0 3.2 3.4 501–600 601–800 801–1000 45 45 45 1 75 90 90 120 135 135 8 3.3 3.5 3.5 60 60 60 2 100 110 125 160 170 185 10 11 12 3.4 3.7 3.9 75 75 90 3 115 140 150 190 13 215 15 240 17 3.6 3.9 4.1 1001–2000 2001–3000 3001–4000 60 60 60 2 105 130 130 165 190 190 10 12 12 3.9 4.1 4.2 75 75 90 3 150 175 170 225 250 260 15 17 18 4.3 4.4 4.6 115 130 130 7 200 235 255 315 23 365 27 385 29 4.8 5.0 5.1 4001–5000 5001–7000 7001–10 000 60 60 60 2 140 140 155 200 200 215 13 13 14 4.3 4.4 4.4 90 90 90 4 180 205 220 270 295 310 19 21 22 4.7 4.9 5.0 140 140 140 8 270 315 340 410 31 455 35 480 37 5.2 5.3 5.4 10 001–20 000 20 001–50 000 50 001–100 000 60 75 75 3 165 165 200 225 240 275 15 16 19 4.4 4.5 4.8 100 100 115 5 230 280 285 330 380 400 24 28 30 5.1 5.2 5.3 155 165 165 10 10 370 405 440 525 41 570 45 605 48 5.6 5.7 6.2 Lot Size 1–20 62 90 72 100 72 100 Process Average 3.01 to 4.00 % Trial Trial n1 c1 n n + n2 c all AOQL in % 1.3 1.6 1.8 A Trial 1: n1 = first sample size; c1 = acceptance number for first sample Trial 2: n2 = second sample size; c2 = acceptance number for first and second samples combined AOQL = Average Outgoing Quality Limit D “all” indicates that each piece in the lot is to be inspected B C 12 AOQL in % E1994 − 09 (2013) A3 SINGLE SAMPLING TABLES FOR STATED VALUES OF AVERAGE OUTGOING QUALITY LIMIT (AOQL) 0.1 % AOQL, 0.5 % AOQL, 1.0 % AOQL, 2.0 % AO, 5.0 % AOQL, 10.0 % AOQL A3.1 Tables A3.1-A3.6 illustrate single sampling for stated values of average outgoing quality limit (AOQL) TABLE A3.1 Single Sampling Table for Average Outgoing Quality Limit (AOQL) = 0.1 % Lot Size 1–75 Process Average to 0.002 % nA c ptB % C all Process Average 0.003 to 0.020 % n c pt % all Process Average 0.021 to 0.040 % n c pt % all Process Average 0.041 to 0.060 % n c pt % all Process Average 0.061 to 0.080 % n c pt % all Process Average 0.081 to 0.100 % n c pt % all 76–95 96–130 131–200 75 95 130 0 1.5 1.4 1.2 75 95 130 0 1.5 1.4 1.2 75 95 130 0 1.5 1.4 1.2 75 95 130 0 1.5 1.4 1.2 75 95 130 0 1.5 1.4 1.2 75 95 130 0 1.5 1.4 1.2 201–300 301–400 401–500 165 190 210 0 1.1 0.96 0.91 165 190 210 0 1.1 0.96 0.91 165 190 210 0 1.1 0.96 0.91 165 190 210 0 1.1 0.96 0.91 165 190 210 0 1.1 0.96 0.91 165 190 210 0 1.1 0.96 0.91 501–600 601–800 801–1000 230 250 270 0 0.86 0.81 0.76 230 250 270 0 0.86 0.81 0.76 230 250 270 0 0.86 0.81 0.76 230 250 270 0 0.86 0.81 0.76 230 250 270 0 0.86 0.81 0.76 230 250 270 0 0.86 0.81 0.76 1001–2000 2001–3000 3001–4000 310 330 340 0 0.71 0.67 0.64 310 330 340 0 0.71 0.67 0.64 310 330 340 0 0.71 0.67 0.64 310 330 695 0 0.71 0.67 0.59 310 330 695 0 0.71 0.67 0.59 310 655 695 1 0.71 0.64 0.59 4001–5000 5001–7000 7001–10 000 345 350 355 0 0.62 0.61 0.60 345 350 355 0 0.62 0.61 0.60 345 750 775 1 0.62 0.51 0.49 720 750 775 1 0.54 0.51 0.49 720 750 775 1 0.54 0.51 0.49 720 750 1210 1 0.54 0.51 0.44 10 001–20 000 20 001–50 000 50 001–100 000 360 365 365 0 0.59 0.58 0.58 810 830 835 1 0.48 0.47 0.46 810 1330 1350 2 0.48 0.41 0.40 1280 1870 2480 0.42 1280 0.37 2420 0.33 3070 0.42 0.34 0.32 1770 2980 4270 0.38 0.33 0.30 A n = sample size; c = acceptance number pt = lot tolerance per cent defective with a Consumer’s Risk (Pc) of 0.10 C “all” indicates that each piece in the lot is to be inspected B 13 E1994 − 09 (2013) TABLE A3.2 Single Sampling Table for Average Outgoing Quality Limit (AOQL) = 0.5 % Process Average to 0.010 % nA c ptB % allC Process Average 0.011 to 0.10 % n c pt % all Process Average 0.11 to 0.20 % n c pt % all Process Average 0.21 to 0.30 % n c pt % all Process Average 0.31 to 0.40 % n c pt % all Process Average 0.41 to 0.50 % n c pt % all 31–50 51–100 101–200 30 42 55 0 5.0 4.2 3.6 30 42 55 0 5.0 4.2 3.6 30 42 55 0 5.0 4.2 3.6 30 42 55 0 5.0 4.2 3.6 30 42 55 0 5.0 4.2 3.6 30 42 55 0 5.0 4.2 3.6 201–300 301–400 401–500 60 60 65 0 3.4 3.5 3.3 60 60 65 0 3.4 3.5 3.3 60 60 65 0 3.4 3.5 3.3 60 60 65 0 3.4 3.5 3.3 60 60 65 0 3.4 3.5 3.3 60 60 125 0 3.4 3.5 2.9 501–600 601–800 801–1000 65 65 70 0 3.3 3.4 3.2 65 65 70 0 3.3 3.4 3.2 65 65 70 0 3.3 3.4 3.2 65 140 145 1 3.3 2.6 2.6 130 140 145 1 2.7 2.6 2.6 130 140 145 1 2.7 2.6 2.6 1001–2000 2001–3000 3001–4000 70 70 70 0 3.2 3.3 3.3 70 70 160 0 3.2 3.3 2.4 155 160 160 1 2.5 2.4 2.4 155 160 255 1 2.5 2.4 2.1 155 250 255 2 2.5 2.1 2.1 240 250 355 2 2.2 2.1 1.9 4001–5000 5001–7000 7001–10 000 75 75 75 0 3.0 3.0 3.1 165 165 165 1 2.4 2.4 2.4 165 265 265 2 2.4 2.0 2.0 260 265 375 2 2.0 2.0 1.8 360 370 485 3 1.9 1.8 1.7 460 475 595 4 1.7 1.7 1.6 10 001–20 000 20 001–50 000 50 001–100 000 75 170 170 1 3.1 2.3 2.3 165 275 275 2 2.4 1.9 1.9 270 390 510 1.9 1.7 1.6 380 625 755 1.7 1.5 1.4 615 875 1290 10 1.5 1.3 1.2 855 1410 2130 11 16 1.4 1.2 1.1 Lot Size 1–30 A B C n = sample size; c = acceptance number pt = lot tolerance per cent defective with a Consumer’s Risk (Pc) of 0.10 “all” indicates that each piece in the lot is to be inspected TABLE A3.3 Single Sampling Table for Average Outgoing Quality Limit (AOQL) = 1.0 % Process Average to 0.02 % c ptB % n C all Process Average 0.03 to 0.20 % n c pt % all Process Average 0.21 to 0.40 % n c pt % all Process Average 0.41 to 0.60 % n c pt % all Process Average 0.61 to 0.80 % n c pt % all Process Average 0.81 to 1.00 % n c pt % all 26–50 51–100 101–200 22 27 32 0 7.7 7.1 6.4 22 27 32 0 7.7 7.1 6.4 22 27 32 0 7.7 7.1 6.4 22 27 32 0 7.7 7.1 6.4 22 27 32 0 7.7 7.1 6.4 22 27 32 0 7.7 7.1 6.4 201–300 301–400 401–500 33 34 35 0 6.3 6.1 6.1 33 34 35 0 6.3 6.1 6.1 33 34 35 0 6.3 6.1 6.1 33 70 70 1 6.3 4.6 4.7 33 70 70 1 6.3 4.6 4.7 65 70 70 1 5.0 4.6 4.7 501–600 601–800 801–1000 35 35 35 0 6.1 6.2 6.3 35 35 35 0 6.1 6.2 6.3 75 75 80 1 4.4 4.4 4.4 75 75 80 1 4.4 4.4 4.4 75 75 120 1 4.4 4.4 4.3 75 120 120 2 4.4 4.2 4.3 1001–2000 2001–3000 3001–4000 36 36 36 0 6.2 6.2 6.2 80 80 80 1 4.5 4.6 4.7 80 80 135 1 4.5 4.6 3.9 130 130 135 2 4.0 4.0 3.9 130 185 185 3 4.0 3.6 3.6 180 235 295 3.7 3.3 3.1 4001–5000 5001–7000 7001–10 000 36 37 37 0 6.2 6.1 6.2 85 85 85 1 4.6 4.6 4.6 135 135 135 2 3.9 3.9 3.9 190 190 245 3 3.5 3.5 3.2 245 305 310 5 3.2 3.0 3.0 300 420 430 7 3.1 2.8 2.7 10 001–20 000 20 001–50 000 50 001–100 000 85 85 85 1 4.6 4.6 4.6 135 135 135 2 3.9 3.9 3.9 195 255 255 4 3.4 3.1 3.1 250 380 445 3.2 2.8 2.6 435 575 790 12 2.7 2.5 2.3 635 990 1520 10 15 22 2.4 2.1 1.9 Lot Size A 1–25 A B C n = sample size; c = acceptance number pt = lot tolerance per cent defective with a Consumer’s Risk (Pc) of 0.10 “all” indicates that each piece in the lot is to be inspected 14 E1994 − 09 (2013) TABLE A3.4 Single Sampling Table for Average Outgoing Quality Limit (AOQL) = 2.0 % Process Average to 0.04 % nA c ptB % allC Process Average 0.05 to 0.40 % n c pt % all Process Average 0.41 to 0.80 % n c pt % all Process Average 0.81 to 1.20 % n c pt % all Process Average 1.21 to 1.60 % n c pt % all Process Average 1.61 to 2.00 % n c pt % all 16–50 51–100 101–200 14 16 17 0 13.6 12.4 12.2 14 16 17 0 13.6 12.4 12.2 14 16 17 0 13.6 12.4 12.2 14 16 17 0 13.6 12.4 12.2 14 16 35 0 13.6 12.4 10.5 14 16 35 0 13.6 12.4 10.5 201–300 301–400 401–500 17 18 18 0 12.3 11.8 11.9 17 18 18 0 12.3 11.8 11.9 17 38 39 1 12.3 10.0 9.8 37 38 39 1 10.2 10.0 9.8 37 38 60 1 10.2 10.0 8.6 37 60 60 2 10.2 8.5 8.6 501–600 601–800 801–1000 18 18 18 0 11.9 11.9 12.0 18 40 40 1 11.9 9.6 9.6 39 40 40 1 9.8 9.6 9.6 39 65 65 2 9.8 8.0 8.1 60 65 65 2 8.6 8.0 8.1 60 85 90 3 8.6 7.5 7.4 1001–2000 2001–3000 3001–4000 18 18 18 0 12.0 12.0 12.0 41 41 42 1 9.4 9.4 9.3 65 65 65 2 8.2 8.2 8.2 65 95 95 3 8.2 7.0 7.0 95 120 155 7.0 6.5 6.0 120 180 210 6.5 5.8 5.5 4001–5000 5001–7000 7001–10 000 18 18 42 0 12.0 12.0 9.3 42 42 70 1 9.3 9.3 7.5 70 95 95 3 7.5 7.0 7.0 125 125 155 4 6.4 6.4 6.0 155 185 220 6.0 5.6 5.4 245 280 350 11 5.3 5.1 4.8 10 001–20 000 20 001–50 000 50 001–100 000 42 42 42 1 9.3 9.3 9.3 70 70 95 2 7.6 7.6 7.0 95 125 160 7.0 6.4 5.9 190 220 290 5.6 5.4 4.9 290 395 505 12 15 4.9 4.5 4.2 460 720 955 14 21 27 4.4 3.9 3.7 Lot Size 1–15 A B C n = sample size; c = acceptance number pt = lot tolerance per cent defective with a Consumer’s Risk (Pc) of 0.10 “all” indicates that each piece in the lot is to be inspected TABLE A3.5 Single Sampling Table for Average Outgoing Quality Limit (AOQL) = 5.0 % Lot Size Process Average to 0.10 % c ptB % n C all A 1–5 A B C Process Average 0.11 to1.00 % n c pt % all Process Average 1.01 to 2.00 % n c pt % all Process Average 2.01 to 3.00 % n c pt % all Process Average 3.01 to 4.00 % n c pt % all Process Average 4.01 to 5.00 % n c pt % all 6–50 51–100 101–200 7 0 30.5 27.0 27.5 7 0 30.5 27.0 27.5 16 0 30.5 27.0 24.0 14 16 1 30.5 26.5 24.0 14 16 1 30.5 26.5 24.0 14 24 30.5 26.5 21.5 201–300 301–400 401–500 7 0 27.5 27.5 27.5 16 16 16 1 24.0 24.0 24.0 16 16 16 1 24.0 24.0 24.0 16 26 26 2 24.0 20.0 20.0 25 26 36 2 21.0 20.0 18.3 25 35 46 21.0 18.8 17.0 501–600 601–800 801–1000 7 0 28.0 28.0 28.0 16 16 17 1 24.0 24.0 22.5 26 27 27 2 20.0 19.4 19.5 26 37 37 3 20.0 17.9 17.9 37 48 48 4 17.9 16.3 16.3 47 60 70 16.6 15.2 14.3 1001–2000 2001–3000 3001–4000 7 17 0 28.0 28.0 23.0 17 17 27 1 23.0 23.0 19.6 27 38 39 3 19.6 17.6 17.0 38 50 60 17.6 15.8 15.4 60 75 85 15.3 13.9 13.8 85 125 140 10 11 13.7 12.3 11.8 4001–5000 5001–7000 7001–10 000 17 17 17 1 23.0 23.0 23.0 27 27 27 2 19.6 19.7 19.7 39 39 50 3 17.0 17.1 15.9 65 75 75 6 14.2 13.9 14.0 100 115 130 10 12.9 12.3 12.0 155 185 225 12 14 17 11.6 11.0 10.4 10 001–20 000 20 001–50 000 50 001–100 000 17 17 17 1 23.0 23.0 23.0 27 39 39 3 19.7 17.1 17.1 50 65 75 15.9 14.3 14.0 90 115 145 11 13.1 12.3 11.6 170 215 275 13 16 20 11.0 10.4 9.8 305 400 450 22 28 31 9.6 9.0 8.8 n = sample size; c = acceptance number pt = lot tolerance per cent defective with a Consumer’s Risk (Pc) of 0.10 “all” indicates that each piece in the lot is to be inspected 15 E1994 − 09 (2013) TABLE A3.6 Single Sampling Table for Average Outgoing Quality Limit (AOQL) = 10.0 % Lot Size 1–3 A B C Process Average to 0.04 % nA c ptB % allC Process Average 0.05 to 0.40 % n c pt % all Process Average 0.41 to 0.80 % n c pt % all Process Average 0.81 to 1.20 % n c pt % all Process Average 1.21 to 1.60 % n c pt % all Process Average 1.61 to 2.00 % n c pt % all 4–50 51–100 101–200 4 0 52.5 43.0 43.5 0 52.5 43.0 40.0 8 1 52.5 40.0 40.0 13 52.5 40.0 35.5 13 52.5 40.0 35.5 12 18 43.5 37.5 33.0 201–300 301–400 401-500 4 0 43.5 43.5 43.5 8 1 40.5 40.5 40.5 13 13 2 40.5 35.5 36.0 13 13 19 2 35.5 35.5 31.6 18 24 24 4 33.0 30.0 30.0 23 29 30 5 32.0 30.0 29.5 501–600 601–800 801–1000 4 0 43.5 43.5 44.0 8 1 40.5 40.5 40.5 13 13 14 2 36.0 36.0 33.5 19 19 25 3 31.5 31.5 30.0 24 31 37 30.5 29.5 28.0 36 42 49 28.5 27.5 26.5 1001–2000 2001–3000 3001–4000 8 1 40.5 40.5 40.5 14 14 14 2 33.5 33.5 33.5 19 19 25 3 32.0 32.0 30.0 31 31 38 5 30.0 30.0 27.5 44 50 65 10 26.5 26.0 24.0 65 85 100 10 13 15 23.5 22.5 21.5 4001–5000 5001–7000 7001–10 000 8 1 40.5 40.5 40.5 14 14 14 2 33.5 33.5 33.5 25 25 32 4 30.0 30.0 29.0 44 44 50 27.5 27.0 26.0 65 80 85 10 12 13 24.0 22.5 22.5 120 135 160 18 20 23 20.5 19.8 19.2 10 001–20 000 20 001–50 000 50 001–100 000 8 14 1 40.5 40.5 33.5 19 19 19 3 32.0 32.0 32.0 32 38 44 29.0 27.5 27.0 60 70 80 11 12 24.5 23.0 22.5 110 130 155 16 19 22 21.0 19.7 19.0 190 225 260 27 31 35 18.3 17.5 16.9 n = sample size; c = acceptance number pt = lot tolerance per cent defective with a Consumer’s Risk (Pc) of 0.10 “all” indicates that each piece in the lot is to be inspected A4 DOUBLE SAMPLING TABLES FOR STATED VALUES OF AVERAGE OUTGOING QUALITY LIMIT (AOQL) 0.1 % AOQL, 0.5 % AOQL, 1.0 % AOQL, 2.0- % AOQL, 5.0 % AOQL, 10.0 % AOQL A4.1 Tables A4.1-A4.6 illustrate double sampling for stated values of average outgoing quality limit (AOQL) 16 E1994 − 09 (2013) TABLE A4.1 Double Sampling Table for Average Outgoing Quality Limit (AOQL) = 0.1 % Process Average to 0.002 % Trial 1A Trial 2B c2 n n + n2 c n1 all 75 ptC % 1.5 Trial n1 all 75 96–130 131–200 201–300 95 130 165 0 1.4 1.2 1.1 95 130 165 0 301–350 351–400 401–500 190 225 250 0 95 120 320 370 1 0.96 0.86 0.80 190 225 250 0 95 120 501–600 601–800 801–1000 275 310 350 0 130 155 185 405 465 535 1 0.77 0.71 0.66 275 310 350 0 1001–2000 2001–3000 3001–4000 430 465 495 0 240 265 285 670 730 780 1 0.58 0.56 0.54 430 465 495 4001–5000 5001–7000 7001–10 000 505 520 540 0 295 320 335 800 840 875 1 0.53 0.52 0.51 10 001–20 000 20 001–50 000 50 001–100 000 555 660 670 0 345 760 770 900 1420 1440 2 0.50 0.42 0.42 Lot Size 1–75 76–95 Lot Size 1–75 76–95 Trial 1A n1 c1 all 75 Process Average 0.041 to 0.060 % Trial 2B n n + n2 c pt % 1.5 Process Average 0.021 to 0.040 Trial Trial n1 c1 n n + n2 c all 75 pt % 1.5 1.4 1.2 1.1 95 130 165 0 1.4 1.2 1.1 320 370 1 0.96 0.86 0.80 190 225 250 0 95 120 320 370 1 0.96 0.86 0.80 130 155 185 405 465 535 1 0.77 0.71 0.66 275 310 350 0 130 155 185 405 465 535 1 0.77 0.71 0.66 0 240 265 285 670 730 780 1 0.58 0.56 0.54 430 465 540 0 240 265 570 670 730 1110 1 0.58 0.56 0.49 505 520 625 0 295 320 715 800 840 1340 1 0.53 0.52 0.44 555 590 625 0 615 660 715 1170 1250 1340 2 0.48 0.46 0.44 650 660 740 0 750 760 1230 1400 1420 1970 2 0.43 0.42 0.38 720 770 805 0 1150 1700 1725 1870 2470 2530 4 0.38 0.36 0.35 pt pt 1.5 Process Average 0.081 to 0.100 % Trial Trial n1 c1 n n + n2 c all 75 1.5 Trial n1 all 75 ptC c1 0 c1 0 Process Average 0.003 to 0.020 Trial n n + n2 c Process Average 0.061 to 0.080 % Trial n n + n2 c 1.5 96–130 131–200 201–300 95 130 165 0 1.4 1.2 1.1 95 130 165 0 1.4 1.2 1.1 95 130 165 0 1.4 1.2 1.1 301–350 351–400 401–500 190 225 250 0 95 120 320 370 1 0.96 0.86 0.80 190 225 250 0 95 120 320 370 1 0.96 0.86 0.80 190 225 250 0 95 120 320 370 1 0.96 0.86 0.80 501–600 601–800 801–1000 275 310 350 0 130 155 185 405 465 535 1 0.77 0.71 0.66 275 310 350 0 130 155 185 405 465 535 1 0.77 0.71 0.66 275 310 350 0 130 155 185 405 465 535 1 0.77 0.71 0.66 1001–2000 2001–3000 3001–4000 430 520 540 0 240 530 570 670 1050 1110 2 0.58 0.50 0.49 430 520 540 0 240 530 570 670 1050 1110 2 0.58 0.50 0.49 475 520 585 0 450 530 885 925 1050 1470 2 0.54 0.50 0.45 4001–5000 5001–7000 7001–10 000 555 655 700 0 615 1045 1120 1170 1700 1820 3 0.48 0.41 0.39 605 655 700 0 935 1045 1120 1540 1700 1820 3 0.44 0.41 0.39 605 680 1250 0 935 1360 1780 1540 2040 3030 0.44 0.40 0.35 740 1400 1460 1530 2170 3060 2270 3570 4520 0.37 0.32 0.31 1350 1450 2330 1 2020 3030 4910 3370 4480 7240 12 0.33 0.31 0.26 1400 2230 3690 2420 3820 4650 6880 7580 11270 12 19 0.32 0.27 0.24 10 001–20 000 20 001–50 000 50 001–100 000 A Trial 1: n1 = first sample size; c1 = acceptance number for first sample Trial 2: n2 = second sample size; c2 = acceptance number for first and second samples combined C pt = lost tolerance percent defective with a Consumer’s Risk (Pc) of 0.10 B 17 E1994 − 09 (2013) TABLE A4.2 Double Sampling Table for Average Outgoing Quality Limit (AOQL) = 0.5 % Lot Size 1–30 31–50 51–75 A Trial c1 n1 allD 30 40 Process Average to 0.010 % Trial 2B n n + n2 c C pt % 5.0 4.6 Trial n1 c1 all 30 40 Process Average 0.011 to 0.10 % Trial n n + n2 c pt % 5.0 4.6 Trial n1 c1 all 30 40 Process Average 0.11 to 0.20 % Trial n n + n2 c pt % 5.0 4.6 76–100 101–150 151–200 47 60 70 0 23 30 35 70 90 105 1 4.4 3.8 3.3 47 60 70 0 23 30 35 70 90 105 1 4.4 3.8 3.3 47 60 70 0 23 30 35 70 90 105 1 4.4 3.8 3.3 201–300 301–400 401–500 80 85 90 0 45 50 55 125 135 145 1 3.0 2.9 2.8 80 85 90 0 45 50 55 125 135 145 1 3.0 2.9 2.8 80 85 90 0 45 50 55 125 135 145 1 3.0 2.9 2.8 501–600 601–800 801–1000 95 100 100 0 55 55 60 150 155 160 1 2.8 2.7 2.7 95 100 100 0 55 55 60 150 155 160 1 2.8 2.7 2.7 95 110 115 0 55 115 125 150 225 240 2 2.8 2.4 2.3 1001–2000 2001–3000 3001–4000 105 110 110 0 60 60 65 165 170 175 1 2.6 2.6 2.5 125 130 130 0 135 145 155 260 275 285 2 2.2 2.1 2.1 125 145 145 0 135 235 240 260 380 385 3 2.2 1.9 1.9 4001–5000 5001–7000 7001–10 000 135 135 135 0 150 155 160 285 290 295 2 2.1 2.1 2.1 135 135 135 0 150 155 160 285 290 295 2 2.1 2.1 2.1 150 155 175 0 240 245 375 390 400 550 3 1.9 1.8 1.6 10 001–20 000 20 001–50 000 50 001–100 000 140 140 140 0 160 165 170 300 305 310 2 2.0 2.0 2.0 155 155 155 0 250 255 260 405 410 415 3 1.8 1.8 1.8 185 185 325 0 500 505 495 685 690 820 5 1.5 1.5 1.4 Lot Size 1–30 31–50 51–75 Trial 1A n1 c1 allD 30 40 Process Average 0.21 to 0.30 % Trial 2B n n + n2 c 5.0 4.6 Trial n1 c1 all 30 40 ptC % Process Average 0.31 to 0.40 % Trial n n + n2 c 5.0 4.6 Trial n1 c1 all 30 40 pt % Process Average 0.41 to 0.50 % Trial n n + n2 c2 pt % 5.0 4.6 76–100 101–150 151–200 47 60 70 0 23 30 35 70 90 105 1 4.4 3.8 3.3 47 60 70 0 23 30 35 70 90 105 1 4.4 3.8 3.3 47 60 70 0 23 30 35 70 90 105 1 4.4 3.8 3.3 201–300 301–400 401–500 80 85 100 0 45 50 100 125 135 200 1 3.0 2.9 2.6 80 95 100 0 45 90 100 125 185 200 2 3.0 2.7 2.6 80 95 100 0 45 90 100 125 185 200 2 3.0 2.7 2.6 501–600 601–800 801–1000 105 110 115 0 105 115 125 210 225 240 2 2.5 2.4 2.3 105 110 125 0 105 115 185 210 225 310 2 2.5 2.4 2.2 105 120 125 0 105 180 185 210 300 310 3 2.5 2.2 2.2 1001–2000 2001–3000 3001–4000 135 145 155 0 220 235 325 355 380 480 3 2.0 1.9 1.8 135 150 280 0 220 320 415 355 470 695 2.0 1.8 1.6 145 275 295 1 295 475 600 440 750 895 1.9 1.6 1.5 4001–5000 5001–7000 7001–10 000 165 175 300 0 345 455 460 510 630 760 1.7 1.6 1.5 300 310 465 1 525 670 785 825 980 1250 10 1.5 1.4 1.3 430 460 620 2 700 860 1120 1130 10 1320 11 1740 14 1.4 1.3 1.2 10 001–20 000 20 001–50 000 50 001–100 000 320 350 505 1 680 930 1075 1000 1280 10 1580 12 1.4 1.3 1.2 495 680 680 3 1175 1490 1810 1670 13 2170 16 2490 19 1.2 1.1 1.1 740 925 1550 1420 2085 3410 2160 18 3010 24 4960 38 1.2 1.1 0.99 A Trial 1: n1 = first sample size; c1 = acceptance number for first sample Trial 2: n2 = second sample size; c2 = acceptance number for first and second samples combined C pt = lot tolerance percent defective with a Consumer’s Risk (Pc) of 0.10 D “all” indicates that each piece in the lot is to be inspected B 18 E1994 − 09 (2013) TABLE A4.3 Double Sampling Table for Average Outgoing Quality Limit (AOQL) = 1.0 % Lot Size 1–25 A Trial c1 n1 allD Process Average to 0.02 % Trial 2B n2 n + n2 c2 Process Average 0.03 to 0.20 % Trial n2 n + n2 c2 pt % Trial n1 c1 all 7.7 6.9 5.8 22 33 43 0 17 22 Trial n1 c1 all 7.7 6.9 5.8 22 33 43 0 17 22 22 33 43 0 17 22 201–300 301–400 401–500 47 49 50 0 28 31 30 75 80 80 1 5.5 5.4 5.4 47 49 50 0 28 31 30 75 80 80 1 5.5 5.4 5.4 47 55 55 0 501–600 601–800 801–1000 50 50 55 0 30 35 30 80 85 85 1 5.4 5.3 5.2 50 60 60 0 30 70 75 80 130 135 2 5.4 4.5 4.4 60 60 60 1001–2000 2001–3000 3001–4000 55 65 70 0 35 80 80 90 145 150 2 5.1 4.2 4.1 65 65 70 0 75 80 80 140 145 150 2 4.3 4.2 4.1 4001–5000 5001–7000 7001–10 000 70 70 70 0 80 80 80 150 150 150 2 4.1 4.1 4.1 70 75 80 0 80 125 125 150 200 205 3 10 001–20 000 20 001–50 000 50 001–100 000 70 75 75 0 80 80 80 150 155 155 2 4.1 4.0 4.0 80 80 85 0 130 135 180 210 215 265 3 1–25 A Trial n1 c1 allD Process Average 0.41 to 0.60 % Trial 2B n n + n2 c Process Average 0.61 to 0.80 % Trial n n + n2 c Trial n1 c1 all 50 65 7.7 6.9 5.8 22 33 43 0 17 22 ptC % 50 65 7.7 6.9 5.8 28 60 65 75 115 120 2 5.5 4.8 4.7 0 65 70 75 125 130 135 2 4.6 4.5 4.4 75 75 80 0 120 125 175 195 200 255 3 3.8 3.7 3.5 4.1 3.7 3.6 80 80 85 0 180 180 180 260 260 265 4 3.4 3.4 3.3 3.6 3.6 3.3 90 95 170 0 230 300 380 320 395 550 3.2 2.9 2.6 50 65 7.7 6.9 5.8 22 33 47 0 17 43 0 17 22 201–300 301–400 401–500 55 55 55 0 50 60 65 105 115 120 2 4.9 4.8 4.7 55 55 60 0 50 60 95 105 115 155 2 4.9 4.8 4.3 55 60 60 0 501–600 601–800 801–1000 60 65 65 0 65 105 110 125 170 175 3 4.6 4.1 4.0 65 65 70 0 100 105 150 165 170 220 3 4.2 4.1 3.8 65 70 125 1001–2000 2001–3000 3001–4000 80 80 85 0 165 170 220 245 250 305 4 3.7 3.6 3.3 135 150 160 1 200 265 330 335 415 490 3.3 3.0 2.8 4001–5000 5001–7000 7001–10 000 145 155 165 1 225 285 355 370 440 520 3.1 2.9 2.7 225 235 250 2 375 440 585 600 10 675 11 835 13 10 001–20 000 20 001–50 000 50 001–100 000 175 250 275 2 415 490 700 590 740 11 975 14 2.6 2.4 2.2 325 340 420 3 655 910 1050 980 15 1250 19 1470 22 Trial 1: n1 = first sample size; c1 = acceptance number for first sample Trial 2: n2 = second sample size; c2 = acceptance number for first and second samples combined pt = lot tolerance percent defective with a Consumer’s Risk (Pc) of 0.10 D “all” indicates that each piece in the lot is to be inspected C 19 Process Average 0.81 to 1.00 % Trial n n + n2 c Trial n1 c1 all pt % 22 33 43 B pt % 50 65 26–50 51–100 101–200 A Process Average 0.21 to 0.40 % Trial n2 n1 + n c2 pt % 26–50 51–100 101–200 Lot Size 50 65 C pt % 50 90 7.7 6.9 5.4 50 80 95 105 140 155 3 4.9 4.5 4.3 0 100 140 180 165 210 305 4.2 3.9 3.5 140 215 225 2 245 355 455 385 570 10 680 12 3.2 2.8 2.7 2.7 2.6 2.4 240 310 385 595 665 785 835 14 975 16 1170 19 2.5 2.4 2.3 2.3 2.2 2.1 520 610 770 980 1410 1850 1500 24 2020 32 2620 41 2.2 2.1 2.0 E1994 − 09 (2013) TABLE A4.4 Double Sampling Table for Average Outgoing Quality Limit (AOQL) = 2.0 % Lot Size 1–15 A Trial c1 n1 allD Process Average to 0.04 % Trial 2B n n + n2 c Process Average 0.05 to 0.40 % Trial n n + n2 c pt % Trial n1 c1 all 13.6 11.7 11.0 14 21 24 0 12 13 pt % Trial n1 c1 all 13.6 11.7 11.0 14 21 24 0 12 13 0 12 13 201–300 301–400 401–500 26 26 27 0 15 16 16 41 42 43 1 10.4 10.3 10.3 26 26 30 0 15 16 35 41 42 65 1 10.4 10.3 9.0 29 30 30 0 31 35 35 60 65 65 2 9.1 9.0 9.0 501–600 601–800 801–1000 27 27 27 0 16 17 17 43 44 44 1 10.3 10.2 10.2 31 31 32 0 34 39 38 65 70 70 2 8.9 8.8 8.7 35 35 36 0 55 60 59 90 95 95 3 7.9 7.7 7.6 1001–2000 2001–3000 3001–4000 33 34 34 0 37 41 41 70 75 75 2 8.5 8.2 8.2 33 34 38 0 37 41 62 70 75 100 2 8.5 8.2 7.3 37 41 41 0 63 84 89 100 125 130 4 7.5 7.0 6.9 4001–5000 5001–7000 7001–10 000 34 35 35 0 41 40 40 75 75 75 2 8.2 8.1 8.1 38 38 38 0 62 62 62 100 100 100 3 7.3 7.3 7.3 42 44 45 0 88 116 115 130 160 160 5 6.9 6.4 6.3 10 001–20 000 20 001–50 000 50 001–10 000 35 35 35 0 40 40 45 75 75 80 2 8.1 8.1 8.0 39 43 43 0 66 92 92 105 135 135 4 7.2 6.6 6.6 45 47 85 0 115 148 185 160 195 270 6.3 6.0 5.2 1–15 Trial n1 c1 allD Process Average 0.81 to 1.20 % Trial 2B n n + n2 c 33 55 Process Average 1.21 to 1.60 % Trial n n + n2 c Trial n1 c1 all 13.6 11.7 9.6 14 21 27 0 12 28 ptC % 13.6 11.7 9.6 14 23 27 0 23 28 pt % 14 21 27 0 12 28 201–300 301–400 401–500 29 33 34 0 31 52 56 60 85 90 3 9.1 8.2 7.9 32 33 36 0 48 52 74 80 85 110 3 8.4 8.2 7.5 32 36 60 0 48 69 90 80 105 150 8.4 7.6 7.0 501–600 601–800 801–1000 35 38 38 0 55 82 87 90 120 125 4 7.9 7.3 7.2 37 38 70 0 78 82 100 115 120 170 4 7.4 7.3 6.5 65 70 70 1 95 120 145 160 190 215 6.8 6.4 6.2 1001–2000 2001–3000 3001–4000 43 75 80 1 112 115 140 155 190 220 6.5 6.1 5.8 80 115 120 2 160 195 255 240 310 10 375 12 5.8 5.3 5.0 110 160 235 205 310 415 315 11 470 15 650 20 5.5 4.7 4.3 4001–5000 5001–7000 7001–10 000 80 85 85 1 175 205 210 255 290 295 9 5.5 5.3 5.2 125 125 165 2 285 320 335 410 13 445 14 500 15 4.9 4.8 4.5 275 280 320 6 475 575 645 750 23 855 26 965 29 4.2 4.1 4.0 10 001–20 000 20 001–50 000 50 001–100 000 90 130 135 2 260 300 345 350 11 430 13 480 14 5.1 4.7 4.5 170 205 250 425 515 615 595 18 720 22 865 26 4.4 4.3 4.1 395 480 11 580 13 835 1090 1460 1230 37 1570 46 2040 58 3.9 3.7 3.5 Trial 1: n1 = first sample size; c1 = acceptance number for first sample Trial 2: n2 = second sample size; c2 = acceptance number for first and second samples combined pt = lot tolerance percent defective with a Consumer’s Risk (Pc) of 0.10 D “all” indicates that each piece in the lot is to be inspected B C 20 46 55 13.6 11.7 11.0 16–50 51–100 101–200 A 33 55 Process Average 1.61 to 2.00 % Trial n n + n2 c Trial n1 c1 all pt % 33 37 pt % 14 21 24 A 33 37 Process Average 0.41 to 0.80 % Trial n n + n2 c 16–50 51–100 101–200 Lot Size 33 37 C 13.6 10.9 9.6