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ASTM E2234-08
Standard Practice for Sampling a Stream of Product by Attributes Indexedby AQL
Standard Practice for Sampling a Stream of Product by Attributes Indexedby AQL
E2234-08
ASTM|E2234-08|en-US
Standard Practice for Sampling a Stream of Product by Attributes Indexedby AQL
Standard
E2234 Standard Practice for Sampling a Stream of Product by Attributes Indexedby AQL>
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BOS Vol. 14.01 Committee E11
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Significance and Use
Written Procedures—Written procedures are ordinarily developed and made available for the customer’s review, upon request. When the written procedures indicate use of this standard, they shall comply with the requirements of this practiceand reference appropriate parts as necessary.
Nonconformance—The extent of nonconformance of product shall be expressed either in terms of percent defective or in terms of defects per hundred units.
Formation and Identification of Lots or Batches—The product shall be assembled into identifiable lots, sublots, batches, or in such other manner as may be prescribed. Each lot or batch shall, as far as is practicable, consist of units of product of a single type, grade, class, size, and composition, manufactured under essentially the same conditions, and at essentially the same time. The lots or batches shall be identified by the contractor and shall be kept intact in adequate and suitable storage space.
AQL:
AQL Use—The AQL, together with the Sample Size Code Letter, is used for indexing the sampling plans provided herein.
Limitation—The selection or use of an AQL shall not imply that the contractor has the right to supply any defective unit of product.
Choosing AQLs—Different AQLs may be chosen for groups of defects considered collectively, or for individual defects. An AQL for a group of defects may be chosen in addition to AQLs for individual defects, or subgroups, within that group. AQL values of 10.0 or less may be expressed either in percent defective or in defects per hundred units; those over 10.0 shall be expressed in defects per hundred units only.
Sampling:
Representative (Stratified) Sampling—When appropriate, the number of units in the sample shall be selected in proportion to the size of sublots or sub-batches, or parts of the lot or batch, identified by some rational criterion. When representative sampling is used, the units from each sublot, sub-batch or part of the lot or batch shall be selected at random.
Time of Sampling—A sample may be drawn after all the units comprising the lot or batch have been assembled, or sample units may be drawn during assembly of the lot or batch, in which case the size of the lot or batch will be determined before any sample units are drawn. If the sample units are drawn during assembly of the lot or batch, and if the rejection number is reached before the lot is completed, that portion of the lot already completed shall be rejected. The cause of the defective product shall be determined and corrective action taken, after which a new lot or batch shall be begun.
Double or Multiple Sampling—When double or multiple sampling is to be used, each sample shall be selected over the entire lot or batch.
Inspection Procedures—Normal inspection will be used at the start of inspection. Normal, tightened or reduced inspection shall continue unchanged for each class of defects or defectives on successive lots or batches except where the switching procedures given below require change. The switching procedures shall be applied to each class of defects or defectives independently.
Switching Procedures:
Normal to Tightened—When normal inspection is in effect, tightened inspection shall be instituted when 2 out of 2, 3, 4, or 5 consecutive lots or batches have been rejected on original inspection (that is, ignoring resubmitted lots or batches for this procedure).
Tightened to Normal—When tightened inspection is in effect, normal inspection shall be instituted when 5 consecutive lots or batches have been considered acceptable on original inspection.
Normal to Reduced—When normal inspection is in effect, reduced inspection shall be instituted provided that all of the following conditions are satisfied:
The preceding 10 lots or batches (or more, as indicated by the note to Table VIII) have been on normal inspection and all have been accepted on original inspection; and
The total number of defectives (or defects) in the samples from the preceding 10 lots or batches (or such other number as was used for condition 4.7.3.1 above) is equal to or less than the applicable number given in Table VIII. If double or multiple sampling is in use, all samples inspected should be included, not “first” samples only; and
Production is at a steady rate; and
Reduced inspection is considered desirable.
Reduced to Normal—When reduced inspection is in effect, normal inspection shall be instituted if any of the following occur on original inspection:
A lot or batch is rejected; or
A lot or batch is considered acceptable under the procedures of 4.10.1.4, or
Production becomes irregular or delayed; or
Other conditions warrant that normal inspection shall be instituted.
Discontinuation of Inspection. If the cumulative number of lots not accepted in a sequence of consecutive lots on original tightened inspection reaches five, the acceptance procedures of this practiceshall be discontinued. Inspection under the provisions of this practiceshall not be resumed until corrective action has been taken. Tightened inspection shall then be used as if 4.7.1 had been invoked.
Sampling Plans:
Inspection Level—The inspection level determines the relationship between the lot or batch size and the sample size. The inspection level to be used for any particular requirement will be as prescribed by the contractor’s written procedures. Three inspection levels: I, II, and III, are given in Table I for general use (see 4.1). Normally, Inspection Level II is used. However, Inspection Level I may be used when less discrimination is needed, or Level III may be used for greater discrimination. Four additional special levels: S-1, S-2, S-3, and S-4, are given in the same table and may be used where relatively small sample sizes are necessary and large sampling risks can or must be tolerated.
Note 1—In the selection of inspection levels S-1 to S-4, care must be exercised to avoid AQLs inconsistent with these inspection levels. In other words, the purpose of the special inspection levels is to keep samples sma11 when necessary. For instance, the code letters under S-1 go no further than D, equivalent to a single sample of size 8, but it is of no use to choose S-1 if the AQL is 0.10 percent for which the minimum sample is 125.
Code Letters—Sample sizes are designated by code letters. Table I shall be used to find the applicable code letter for the particular lot or batch size and the prescribed inspection level.
Obtaining Sampling Plan—The AQL and the code letter shall be used to obtain the sampling plan from Tables II, III, or IV. When no sampling plan is available for a given combination of AQL and code letter, the tables direct the user to a different letter. The sample size to be used is given by the new code letter, not by the original letter. If this procedure leads to different sample sizes for different classes of defects, the code letter corresponding to the largest sample size derived may be used for all classes of defects. As an alternative to a single sampling plan with an acceptance number of 0, the plan with an acceptance number of 1 with its correspondingly larger sample size for a designated AQL (where available), may be used.
Types of Sampling Plans—Three types of sampling plans; Single, Double, and Multiple, are given in Tables II, III, and IV, respectively. When several types of plans are available for a given AQL and code letter, any one may be used. A decision as to type of plan, either single, double, or multiple, when available for a given AQL and code letter, will usually be based upon the comparison between the administrative difficulty and the average sample sizes of the available plans. The average sample size of multiple plans is less than for double (except in the case corresponding to single acceptance number 1) and both of these are always less than a single sample size (see Table IX). Usually the administrative difficulty for single sampling and the cost per unit of the sample are less than for double or multiple.
Determination of Acceptability:
Percent Defective Inspection—To determine acceptability of a lot or batch under percent defective inspection, the applicable sampling plan shall be used in accordance with 4.10.1.1-4.10.1.4.
Single Sampling Plan—The number of sample units inspected shall be equal to the sample size given by the plan. If the number of defectives found in the sample is equal to or less than the acceptance number, the lot or batch shall be considered acceptable. If the number of defectives is equal to or greater than the rejection number, the lot or batch shall be rejected.
Double Sampling Plan—A number of sample units equal to the first sample size given by the plan shall be inspected. If the number of defectives found in the first sample is equal to or less than the first acceptance number, the lot or batch shall be considered acceptable. If the number of defectives found in the first sample is equal to or greater than the first rejection number, the lot or batch shall be rejected. If the number of defectives found in the first sample is between the first acceptance and rejection numbers, a second sample of the same size shall be inspected. The number of defectives found in the first and second samples shall be accumulated. If the cumulative number of defectives is equal to or less than the second acceptance number, the lot or batch shall be considered acceptable. If the cumulative number of defectives is equal to or greater than the second rejection number, the lot or batch shall be rejected.
Multiple Sample Plan—Under multiple sampling, the procedure shall be similar to that specified in 4.10.1.2, except that the number of successive samples required to reach a decision may be as many as seven.
Special Procedure for Reduced Inspection—Under reduced inspection, when the number not accepted falls in the gap between Ac and Re, the sampling procedure may terminate without either acceptance or rejection criteria having been met. In these circumstances, the lot or batch will be considered acceptable, but normal inspection will be reinstated starting with the next lot or batch (see 4.7.4.2).
Defects per Hundred Units Inspection. To determine the acceptability of a lot or batch under defects per hundred units inspection, the procedure specified for percent defective inspection above shall be used, except that the word “defects” shall be substituted for “defectives”.
Limiting Quality Protection. The sampling plans and associated procedures given in this publication were designed for use where the units of product are produced in a continuing series of lots or batches over a period of time. However, if the lot or batch is of an isolated nature, it is desirable to limit the selection of sampling plans to those, associated with a designated AQL value, that provide not less than a specified limiting quality protection. Sampling plans for this purpose can be selected by choosing a Limiting Quality (LQ) and a consumer’s risk to be associated with it. Tables VI and VII give values of LQ for the commonly used consumer's risks of 10 percent and 5 percent respectively. If a different value of consumer's s risk is required, the operating characteristic (OC) curves and their tabulated values may be used. The concept of LQ may also be useful in specifying the AQL and Inspection Levels for a series of lots or batches, thus fixing minimum sample size where there is some reason for avoiding (with more than a given consumer’s risk) more than a limiting proportion of defectives (or defects) in any single lot or batch.
Curves:
Operating Characteristic Curves—The operating characteristic curves for normal inspection, shown in Table X, indicate the percentage of lots or batches which may be expected to be accepted under the various sampling plans for a given process quality. The curves shown are for single sampling; curves for double and multiple sampling are matched as closely as practicable. The OC curves shown for AQLs greater than 10.0 are based on the Poisson distribution and are applicable for defects per hundred units inspection; those for AQLs of 10.0 or less and sample sizes of 80 or less are based on the binomial distribution and are applicable for percent defective inspection; those for AQLs of 10.0 or less and sample sizes larger than 80 are based the Poisson distribution and are applicable either for defects per hundred units inspection, or for percent defective inspection (the Poisson distribution being an adequate approximation to the binomial distribution under these conditions). Tabulated values, corresponding to selected values or probabilities of acceptance (Pa, in percent) are given for each of the curves shown, and, in addition, for tightened inspection, and for defects per hundred units for AQLs of 10.0 or less and sample sizes of 80 or less.
Average Sample Size Curves—Average sample size curves for double and multiple sampling are in Table IX. These show the average sample sizes which may be expected to occur under the various sampling plans for given levels of process quality. The curves assume no curtailment of inspection and are approximate to the extent that they are based upon the Poisson distribution, and that the sample sizes for double and multiple sampling are assumed to be 0.631n and 0.25n respectively, where n is the equivalent single sample size.
Operation:
This practicepreserves the structure of MIL-STD-105E for use in applications in which that standard is prescribed, or where its use is desirable, for example, where it is called out as part of the procedure contained in another standard.
This practiceis a sampling system primarily intended for use with a stream of lots where an upper limit on the process fraction defective is specified. This is the Acceptance Quality Limit (AQL). Protection against the process levels greater than the AQL is accomplished by switching among prescribed plans so that the rate of rejection of lots becomes more and more intolerable as the process average increases beyond the AQL. It is important to note that a relatively large proportion of lots will be accepted when the process average is less than or equal to the AQL.
When sampling a stream of lots, the standard is employed as follows:
Determine the lot size and set the AQL (see 4.4).
Determine the inspection level (see 4.9.1). Use Inspection Level II if none is specified.
Decide if single, double, or multiple sampling is to be used (see 4.10).
Enter Table I to determine the sample size code letter (see 4.9.2).
Enter Table II (single), Table III (double), or Table IV (multiple) with the lot size and code letter to determine a set of normal, tightened or reduced sampling plans which will be used in applying this sampling scheme.
Apply the switching rules to determine which of the three plans to apply to the next lot (see 4.6-4.8).
The switching rules must be used in application of the procedure to a stream of lots.
When an isolated lot, apart from a stream, the standard may be applied as follows:
Determine the AQL as above. A single lot of AQL quality will have a high probability of acceptance very often around 95 % (see 4.4).
Set a limiting quality level (LQ) that will have a low consumer’s risk (risk of acceptance) of 10 % or 5 % as desired (see 4.11).
Enter Table VI or Table VII as appropriate to the consumer’s risk and defect type. For a particular AQL, go down the column until a value of LQ less than or equal to the desired LQ is found. Read the corresponding code letter and AQL. Using the Normal sampling tables (Tables IIA, IIIA, or IVA) determine the sampling plan for this code letter and AQL.
Apply the sampling plan to the isolated lot.
Parameters of the sampling plans
The operating characteristic curves for individual plans are given in Table X (see 4.12).
The AOQL values for individual plans are given in Table V (see 3.1.2 and 3.1.3).
ASN curves for the double and multiple plans are given in Table IX (see 4.12.2).
Limit Numbers for Reduced Inspection used in the switching rules are given in Table VIII (see 4.10.1.4).
Scope
1.1 Purpose—This practice establishes lot or batch sampling plans and procedures for inspection by attributes using MIL-STD-105E as a basis for sampling a steady stream of lots indexed by AQL. The tabled calculations are based on the probabilistic theory of recurrent events when a series of lots or batches are produced in a stable environment.
1.2 Application—Sampling plans designated in this publication are applicable, but not limited, to inspection of the following: (1) end items, (2) components and raw materials, (3) operations or services, (4) materials in process, (5) supplies in storage, (6) maintenance operations, (7) data or records, and (8) administrative procedures.
1.2.1 These plans are intended primarily to be used for a continuing series of lots or batches. The plans may also be used for the inspection of isolated lots or batches, but, in this latter case, the user is cautioned to consult the operating characteristic curves and Table VI or Table VII to find a plan which will yield the desired protection (see 4.11).
1.2.2 This practice should be used to guide the user in the development of an inspection strategy that provides a cost effective approach to attaining confidence in product compliance with contractual technical requirements. The user is warned of the assumed risks relative to the chosen sample size and AQL.
1.2.3 This practice provides the sampling plans of MIL-STD-105E in ASTM format for use by ASTM committees and others. It recognizes the continuing usage of MIL-STD-105 in industries supported by ASTM. The practiceprovides the fundamental basis for many existing sampling procedures currently in effect in laboratories and other facilities. As such, it provides a primary source for other AQL standards and for specifically engineered sampling plans developed by other standards bodies and individual facilities and appearing in various forms on the shelves of countless laboratories and operations. It replaces the AQL scheme previously incorporated in the Related Materials Section of Volume 14.02 of the Annual Book of ASTM Standards.