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Comparing Acceptance Sampling Standards, Part 2 a
Dean V. Neubauer & Stephen Luko
b
a
Corning Incorporated, Corning, New York
b
United Technologies Aerospace Systems, Terryville, Connecticut
To cite this article: Dean V. Neubauer & Stephen Luko (2013): Comparing Acceptance Sampling Standards, Part 2, Quality Engineering, 25:2, 181-187 To link to this article: http://dx.doi.org/10.1080/08982112.2013.758557
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Quality Engineering, 25:181–187, 2013 Copyright # Taylor & Francis Group, LLC ISSN: 0898-2112 print=1532-4222 online DOI: 10.1080/08982112.2013.758557
Comparing Acceptance Sampling Standards, Part 2 Dean V. Neubauer1, Stephen Luko2
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1
Corning Incorporated, Corning, New York 2 United Technologies Aerospace Systems, Terryville, Connecticut
ABSTRACT In Part 1 of this two-part series, common attribute sampling standards were discussed and compared. Attribute sampling standards date back to the 1930s and the original work of Harold F. Dodge and others at Bell Labs. Today’s attribute standards (ANSI=ASQ Z1.4, ASTM E2234, ISO 2859) find their common heritage in the older Military Standard 105 series. In this article, the discussion will shift to the development of variables sampling standards which find their linkage to a military standard as well— Military Standard 414. Like MIL-STD-105, MIL-STD-414 has derivative standards as well which are in use today. This article will serve to discuss and compare these derivative standards in the manner in which attributes standards were covered in Part 1. Once again we find that sampling schemes are not restricted to attributes. They may be composed of variables plans as well. Thus, it was that Military Standard 414 (MIL-STD-414) was issued on June 11, 1957. It has since become a classic companion standard to MILSTD-105 and has been used throughout the world. The protection afforded by this standard is roughly matched to MIL-STD-105A. However, modifications in the tables incorporated in the MIL-STD-105D version upset the match somewhat. Commander Gascoigne of the British Navy showed how to restore the balance and his simple method has been incorporated into civilian sampling systems. The MIL-STD-414 sampling system will be discussed in depth here as an example of a classic variables system, and its relation to other systems, including MIL-STD-105E, will be indicated. KEYWORDS ASTM E2762-10, ANSI/ASQ Z1.9, ISO 3951, MIL-STD-414, normal distribution, range, sampling system, variability known, variables sampling plans, variability unknown
INTRODUCTION Edited by Stephen N. Luko, United Technologies Aerospace Systems, Windsor Locks, Connecticut. Address correspondence to Dean V. Neubauer, 15 Stoneybrook Road, Horseheads, NY 14845-1168. E-mail:
[email protected]
In Part 1 of this two-part series, common attribute sampling standards were discussed and compared. Attribute sampling standards date back to the 1930s and the original work of Harold F. Dodge and others at Bell Labs. Today’s attribute standards (ANSI=ASQ Z1.4 (2008), ASTM E2234 (2009), ISO 2859 (1974)) find their common heritage in the older Military Standard 105 series. In Part 2, the discussion will shift to the development of variables sampling standards that find their linkage to a military standard as 181
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well—Military Standard 414. Like MIL-STD-105, MIL-STD-414 has derivative standards as well that are in use today. This article will serve to discuss and compare these derivative standards in the manner in which attributes standards were covered in Part 1. Sampling schemes are not restricted to attributes. They may be composed of variable plans as well. Thus it was that Military Standard 414 (MIL-STD414) was issued on June 11, 1957. It has since become a classic companion standard to MIL-STD105 and has been used throughout the world. The protection afforded by this standard is roughly matched to MIL-STD-105A. However, modifications in the tables incorporated in the MIL-STD-105D version upset the match somewhat. Commander Gascoigne of the British Navy showed how to restore the balance, and his simple method has been incorporated into civilian sampling systems. The MIL-STD414 sampling system will be discussed in-depth here as an example of a classic variables system, and its relation to other systems, including MIL-STD-105E, will be indicated.
MIL-STD-414 Sampling Procedure and Tables for Inspection by Variables for Percentage Defective Unlike MIL-STD-105E, MIL-STD-414 is a sampling system utilizing variable inspection. It was devised by the military, as a consumer, to be used to assess the percentage defective beyond contractual limits. Because it is a sampling system, it incorporates switching rules to move from normal to tightened or reduced inspection and return to achieve consumer protection. These switching rules must be used if the standard is to be properly applied. The switching rules differ somewhat from those used in MIL-STD-105E. The standard assumes underlying normality of the distribution of the measurements to which it is applied and is intended to be used with a steady stream of lots. MIL-STD-414 allows for the use of three alternative measures of variability: known standard deviation (r), estimated standard deviation (s), or average range of subsamples of five (R). If the variability of the process producing the product is known and stable, it is profitable to use r. The choice between s and R when r is unknown is an economic one. D. V. Neubauer and S. Luko
The range requires larger sample sizes but is easier to compute and understand. Operating characteristic (OC) curves given in the standard are based on the use of s, where the r and R plans have been matched as closely as possible to those using s. The basic statistic to be calculated in applying MIL-STD-414 may be considered to be the standardized distance from the sample mean to the specification limit. For an upper specification limit U, when r is known, the statistic tU ¼ ðU XÞ=r is used. When r is unknown, tU ¼ ðU XÞ=s or tU ¼ ðU XÞ=R is substituted depending on the measure of variability chosen. A comparison of tU to the acceptance constant k will show whether the sample mean is or is not in the region of acceptance. MIL-STD-414 offers an alternate procedure to using the acceptance constant k—the M method. This involves using a statistic similar to those above to estimate proportion defective in the lot and is referred to in the standard as Form 2. The k method, involving a simple comparison of t to k to determine the acceptability, is called Form 1. Form 2 is the preferred procedure because the switching rules cannot be applied unless the fraction defective p^ of each lot is estimated from the sample. MIL-STD-414 is complex. It consists of sections indexed by measure of variability, type of specification (single or double), and form number of the acceptance procedure. Only Form 2 is officially available for the case of double specification limits. The standard’s structure is shown in Figure 1. Application of MIL-STD-414 follows the pattern of MIL-STD-105E. Note that MIL-STD-414 and MIL-STD105E plans are not matched. The classification of defects used in MIL-STD-414 is the same as that used in MIL-STD-105E: critical, major, and minor. Sample sizes are determined from lot size and acceptable quality level (AQL) and, after choosing the measure of variability to be used and the form of acceptance procedure, appropriate acceptance constants are obtained from the standard. MIL-STD-414 has a liberal supply of excellent examples. The reader should refer to the standard for detailed numerical examples of its application. The necessary assumption of a known, stable underlying normal distribution of individual measurements is inherent in the MIL-STD-414 variables plans, and this is a limitation in its application. The use of MIL-STD-414 plans without investigating the 182
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FIGURE 1 Content of MIL-STD-414. Indicates tables for estimating p and criteria for tightened and reduced inspection (Schilling and Neubauer 2009).
true nature of the underlying distribution is not recommended, because the results can be seriously in error. Sensible evaluation of the normality of the underlying distribution and implementation of prudent procedures to insure stability over time does provide sufficient justification for use of MIL-STD414. Because any sampling plan in this standard depends on variability, when using a historical estimate of the standard deviation, or average range, one needs to evaluate whether the estimate holds up over time. This is particularly true for in-process and final inspection at the source where the distribution of the process producing the product is not beyond the control or investigation of those applying the plan. The rewards for painstaking, thorough analysis are great in terms of sample size and worthwhile information on the process involved. A detailed discussion of the operation, selection of plans, and measures of these plans can be found in Schilling and Neubauer (2009, ch. 12). An excellent description of the theory behind MIL-STD-414 has been given by Lieberman and Resnikoff (1955) in the Journal of the American Statistical Association. Much of this material was later presented in a detailed technical report on MIL-STD-414 published by the Assistant Secretary of Defense (United States Department of Defense 1958). These works give a detailed technical description of the background of the standard. A classic review of MIL-STD-414 was undertaken by Kao (1971) and appeared in the 183
Journal of Quality Technology. In a two-part series, Duncan (1975) and Bender (1975) described the history and matching of MIL-STD-414 to other national and international standards including MIL-STD-105D.
Match Between MIL-STD-414 and MIL-STD-105E In 1976, the American National Standards Institute (ANSI) Committee Z-1 on Quality Assurance recommended that a revision of the ANSI version of MIL-STD-414 be made incorporating some of the suggestions made by Gascoigne (1976) resulting from his work on British Defense Standard (05-30= 1) and with the International Organization for Standardization (ISO). Principal among these was a method for adjusting the code letter of the ANSI version of MIL-STD-414 to make its OC curves roughly match those of the ANSI version of MIL-STD105D (ANSI Z1.4) at the adjusted code letter and AQL. Revision of the ANSI version of MIL-STD-414 (ANSI Z1.9) was accomplished by the American Society for Quality Control Standards Group and it now appears as ANSI Z1.9 (2008). Table 1 shows the match between the revised ANSI Z1.9 (2008) code letter, the MIL-STD-414 code letter, and the corresponding code letter of MIL-STD-105D. (A comparison with MIL-STD-105E would be identical.) Plans with these code letters are roughly matched and will allow switching between variables and Comparing Acceptance Sampling Standards, Part 2
TABLE 1 Matching the Lettersa
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MIL-STD-105D (ANSI=ASQ Z1.4 (2008)) code letter
MIL-STD-414 (1957) code letter
ANSI=ASQ Z1.9 (2008) code letter
B C D E F G H I K M N O P Q
B C D E F G H I J K L M N P
B C D E F G H H J K L M N P a
Delete MIL-STD-414 AQLs: 0.04, 0.065, 15.00.
attribute plans within the code letters shown at a given AQL. To preserve the match, MIL-STD-414 AQLs 0.04, 0.065, and 15.00 should not be used and were dropped from ANSI Z1.9. For example, MIL-STD-105D, Code J, 1.5 AQL is roughly matched to MIL-STD-414, Code K, 1.5 AQL, which matches ANSI Z1.9, Code J, 1.5 AQL. Other changes in ANSI Z1.9 (2008) from the earlier version identical to MIL-STD-414 included an update of terminology and changes in the switching rules, inspection levels, and other features to match MILSTD-105E (1989). Standards Z1.4 and Z1.9 may be obtained from the American Society for Quality (ASQ). Schilling and Sheesley (1984) have addressed scheme properties of the variables standard ANSI=ASQ Z1.9. MIL-STD-414 was issued on June 11, 1957, and has not undergone any major changes since. However, this classic standard was the precursor of several derivative standards, most notably ASTM E2762 (2010), ANSI=ASQ Z1.9 (2008), and ISO 3951-1, which will be discussed in the following sections.
provide a source for use in conjunction with ASTM and other standards that directly reference MIL-STD414. It is best used in a testing or laboratory environment and with methodology in support of other standards.
ANSI/ASQ Z1.9 Sampling Procedures and Tables for Inspection by Variables for Percentage Nonconforming A United States national standard, ANSI=ASQ Z1.9 (2008) represents an effort to unify variables and attributes sampling systems by providing a reasonable match between a modified MIL-STD-414 and MILSTD-105. This was done using the Gascoigne technique. Other changes included making the inspection levels coincide between the two standards and adopting the switching rules and lot size ranges of MIL-STD105. Other editorial changes were made as appropriate. ANSI=ASQ Z1.9 (2008), then, is a companion standard to the ANSI=ASQ Z1.4 (2008) attributes standard. Given the lot size and AQL, it is possible to move between the two standards with the same code letter and AQL. The procedures and structure of ANSI=ASQ Z1.9 are essentially the same as for MIL-STD-414. The excellent set of examples in MIL-STD-414 has been retained and will lead the user through application of the Z1.9 standard. The ANSI=ASQ Z1.9 standard is an excellent vehicle for in-house use and stands as the national standard to be employed internally to the United States.
Conversion of MIL-STD-414 to ANSI/ ASQ Z1.9 (Gascoigne Technique) By following the method of Commander Gascoigne, the tables of MIL-STD-414 are easily converted into the tables of ANSI=ASQ Z1.9. The procedure is as follows:
ASTM E2762-10: Standard Practice for Sampling a Stream of Product by Variables Indexed by AQL
1. Eliminate the MIL-STD-414 rows corresponding to Codes J and K and reletter the remaining code letters so that MIL-STD-414 code letters K, M, N, O, P, and Q become J, K, L, M, N, and P. 2. Eliminate the columns corresponding to AQLs 0.04, 0.065, and 15.00. 3. Use the resulting table with the ANSI=ASQ Z1.4 switching rules.
An ASTM standard that maintains the MIL-STD414 content as closely as possible was created by the ASTM E11 Committee in 2009. It is intended to
This is the original procedure used to produce the ANSI=ASQ Z1.9 tables in 1980. It should be noted
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TABLE 2 Conversion of Table B-1 in MIL-STD-414 to Create the Corresponding Table in ANSI/ASQ Z1.9 (2008) Acceptable quality levels (normal inspection)
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Sample size code letter Sample size B C D E F G H I J J L K L M N P
3 4 5 7 10 15 20 25 30 35 40 50 75 100 150 200
0.04 k
0.065 k
0.10 k
+ + + + + 2.64 2.69 2.72 2.73 2.77 2.77 2.83 2.90 2.92 2.96 2.97 0.065
+ + + + + 2.53 2.58 2.61 2.61 2.65 2.66 2.71 2.77 2.80 2.84 2.85 0.10
+ + + + + 2.42 2.47 2.50 2.51 2.54 2.55 2.60 2.66 2.69 2.73 2.73 0.15
0.15 k
0.25 K
0.40 k
+ + + + + + + + + + 2.00 1.88 2.24 2.11 1.98 2.32 2.20 2.06 2.36 2.24 2.11 2.40 2.26 2.14 2.41 2.28 2.15 2.45 2.31 2.18 2.44 2.31 2.18 2.50 2.35 2.22 2.55 2.41 2.27 2.58 2.43 2.29 2.61 2.47 2.33 2.62 2.47 2.33 0.25 0.40 0.65 Acceptable quality
0.65 k + + 1.65 1.75 1.84 1.91 1.96 1.98 2.00 2.03 2.03 2.08 2.12 2.14 2.18 2.18 1.00 levels
1.00 k
1.50 k
2.50 k
4.00 k
6.50 k
10.00 k
15.00 k
+ + 1.12 0.958 0.765 0.566 1.45 1.34 1.17 1.01 0.814 0.617 1.53 1.40 1.24 1.07 0.874 0.675 1.62 1.50 1.33 1.15 0.955 0.755 1.72 1.58 1.41 1.23 1.03 0.828 1.79 1.65 1.47 1.30 1.09 0.886 1.82 1.69 1.51 1.33 1.12 0.917 1.85 1.72 1.53 1.35 1.14 0.936 1.86 1.73 1.55 1.36 1.15 0.946 1.89 1.76 1.57 1.39 1.18 0.969 1.89 1.76 1.58 1.39 1.18 0.971 1.93 1.80 1.61 1.42 1.21 1.00 1.98 1.84 1.65 1.46 1.24 1.03 2.00 1.86 1.67 1.48 1.26 1.05 2.03 1.89 1.70 1.51 1.29 1.07 2.04 1.89 1.70 1.51 1.29 1.07 1.50 2.50 4.00 6.50 10.00 15.00 (tightened inspection)
0.341 0.393 0.455 0.536 0.611 0.664 0.695 0.712 0.723 0.745 0.746 0.774 0.804 0.819 0.841 0.845
All AQL and table values are in percentage defective. + Use first sampling plan below arrow; that is, both sample size as well as k value. When sample size equals or exceeds lot size, every item in the lot must be inspected.
that a few of the values are slightly off as the result of recomputation over the years, but they are so slight as to be of little consequence in practical application. The match with MIL-STD-105E is quite good, as can be seen in the tables of differences contained in Section E of the ANSI=ASQ Z1.9 tables. Table 2 demonstrates this change.
ISO 3951-1 Sampling Procedures for Inspection by Variables—Part 1: Specification for Single Sampling Plans Indexed by Acceptance Quality Limit (AQL) for Lot-By-lot Inspection for a Single Quality Characteristic and a Single AQL Part 1 of a set of five variables standards, ISO 3951-1 is the international version of MIL-STD-414. Early versions were close to ANSI=ASQ Z1.9 (2008). In 2005, the standard underwent a major revision, including adjustment of the tables to produce plans more closely matched to the plans of ISO 2859-1. At that time, the range method was eliminated from 185
the standard. This standard is unique in its approach to variable plans in that it includes graphical acceptance curves. The axes of the curves are converted to (X, s) and the inspector simply plots X and s on the curve to determine whether it is in the region of acceptance or rejection. Given point a on the x axis and point b on the y axis, the transformations are s ¼ a(U L) and X ¼ bðU LÞ þ L A comparison of the procedure for ANSI=ASQ Z1.9 with ISO 3951-1 is shown in Table 3. Note that ISO 3951-1 does not carry the M method used in ANSI=ASQ Z1.9 and uses the k method essentially for single specification limits and the graphical technique for double specification limits. ISO 3951-1 is best used in international trade. ISO has also developed a series of schemes in support of the AQL system in ISO 3951-1 and patterned after the ISO 2859 series. These include the following: .
ISO 3951-1 Specification for single sampling plans indexed by acceptance quality limit (AQL) for lot-by-lot inspection of a single quality characteristic and a single AQL. This is the ISO version of MIL-STD-414 and ANSI=ASQ Z1.9 and provides Comparing Acceptance Sampling Standards, Part 2
D. V. Neubauer and S. Luko
186
Form 1
Form 2
Single specification Double specification Accept if pU þ pL < M Accept if zU > k and zL > k and s k pL < M
U X zU ¼ R Section C (R) X L zL ¼ U R X zU ¼ r Section D (r) X L zL ¼ r — —
—
Obtain M and n from Obtain k and n from appropriate appropriate tables tables U X U X QU ¼ zU ¼ s s Section B (s) X L X L zL ¼ QL ¼ s s
Section
c ¼ scale factor. pffiffiffiffiffiffiffi n v ¼ n1 . Not official procedure. Special procedure is used for sample size 3 or 4.
Action
Estimation
Determine criteria
Preparatory
Step
ANSI=ASQ Z1.9 (MIL-STD-414)
TABLE 3 Procedure and Application of ANSI/ASQ Z1.9 and ISO 3951-1
Double specification
Single specification
—
Section 16
—
Section 15
Section 14
Section
Separate AQLs
ISO 3951-1 Combined AQL
Accept only if QU > k Separate AQLs: or QL > k Accept only if XL X XU
Accept if X XU or X XL Accept if QU > k or QL > k
—
Compare X to XU ¼ U kU r XL ¼ L þ kL r —
—
Plot s; X and compare XU ¼ U kU s to XL ¼ L þ kL s
U X r X L QL ¼ r — QU ¼
QU ¼
U X s X L QL ¼ s
—
Accept if point plotted is inside diagram
—
—
Use separate AQL procedure
diagram
Reject if s>MSD¼f(U L) Otherwise, plot s XL UL ; UL on
Obtain k and n from Obtain k and n from Obtain appropriate appropriate tables appropriate tables acceptance curve
Single specification
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.
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the basic tables and subsidiary matter for the sampling system. ISO 3951-2 General specification for single sampling plans indexed by acceptance quality limit (AQL) for lot-by-lot inspection of independent quality characteristics. This is a complex standard containing univariate and multivariate procedures addressing circumstances not covered by ISO 3951-1 for both the variability known and unknown. The multivariate methods presented are for independent quality characteristics. ISO 3951-3 Double sampling schemes indexed by acceptance quality limit (AQL) for lot-by-lot inspection. This standard is complementary to the double sampling plans of ISO 2859-1 and addresses circumstances not covered there. It is quite complicated and includes both univariate and multivariate methods for independent quality characteristics. ISO 3951-4 Procedures for assessment of declared quality levels. The plans presented in this standard have been matched to those of ISO 2859-4. It is the variables analog of that standard. Note that this is a single test and does not involve a sampling system as do the other parts of ISO 3951. ISO 3951-5 Sequential sampling plans indexed by acceptance quality limit (AQL) for inspection by variables (known standard deviation). This standard presents variable sequential sampling plans matched to the attributes sequential plans of the ISO 2859-5 standard. It takes full advantage of the economics of sequential variables plans in terms of minimal sample size.
As in the attributes plans, with the exception of ISO 3951-4, the ISO 3951 series is primarily intended to be used with a continuing series of lots, utilizing the switching rules as prescribed. The assumptions of variable sampling should be carefully considered in any application of variables plans.
ABOUT THE AUTHORS Dean Neubauer is an engineering fellow with Corning Incorporated in Corning, New York, and is currently the chair of ASTM Committee E11 on
187
Quality and Statistics. He is a fellow of ASTM International, a fellow of the Royal Statistical Society, and a fellow of the American Society for Quality (ASQ). Stephen Luko is an industrial statistician with United Technologies Aerospace Systems in Windsor Locks, Connecticut, and is a past chair of Committee E11. He is a fellow of ASTM International and a senior member of ASQ. He is the editor of this column.
REFERENCES ANSI=ASQ Z1.4. (2008). Sampling Procedures and Tables for Inspection by Attributes. Milwaukee, WI: American Society for Quality (ASQ). ANSI=ASQ Z1.9. (2008). Sampling Procedures and Tables for Inspection by Variables for Percent Nonconforming. Milwaukee, WI: American Society for Quality. Bender, A. (1975). Sampling by variables to control the fraction defective: Part II. Journal of Quality Technology, 7(3):139–143. Duncan, A. J. (1975). Sampling by variables to control the fraction defective: Part I. Journal of Quality Technology, 7(1):34–42. E2234-09. (2009). Standard Practice for Sampling a Stream of Product by Attributes Indexed by AQL. West Conshohocken, PA: American Society for Testing of Materials (ASTM). E2762-10. (2010). Standard Practice for Sampling a Stream of Product by Variables Indexed by AQL. West Conshohocken, PA: American Society for Testing and Materials, ASTM E11 Committee on Quality and Statistics. Gascoigne, J. C. (1976). Future International Standards on Sampling by Variables. American Society for Quality Control Technical Conference Transactions, Toronto, ON, Milwaukee, WI: American Society for Quality (ASQ). ISO 2859-1. (1974). Sampling Procedures for Inspection by Attributes– Part 1: Sampling Schemes Indexed by Acceptance Quality Limit (AQL) for Lot-by-Lot Inspection. Geneva, Switzerland: International Organization for Standardization (ISO). ISO 3951-1. (2011). Sampling Procedures for Inspection by Variables— Part 1: Specification for Single Sampling Plans Indexed by Acceptance Quality Limit (AQL) for Lot-by-Lot Inspection for a Single Quality Characteristic and a Single AQL. Geneva, Switzerland: International Organization for Standardization. Kao, J. H. K. (1971). MIL-STD-414 sampling procedures and tables for inspection by variables for percent defective. Journal of Quality Technology, 3(1):28–37. Lieberman, G. J., Resnikoff, G. J. (1955). Sampling plans for inspection by variables. Journal of the American Statistical Association, 50:457–516. Military Standard 105E. (1989). Sampling Procedures and Tables for Inspection by Attributes. Washington, DC: United States Department of Defense, U.S. Government Printing Office. Military Standard 414. (1957). Sampling Procedures and Tables for Inspection by Variables for Percent Defective. Washington, DC: United States Department of Defense, U.S. Government Printing Office. Schilling, E. G., Neubauer, D. V. (2009). Acceptance Sampling in Quality Control, 2nd ed. New York: CRC Press. Schilling, E. G., Sheesley, J. H. (1984). The performance of ANSI=ASQ Z1.9–1980 under the switching rules. Journal of Quality Technology, 16(2):101–120. United States Department of Defense. (1958). Mathematical and Statistical Principles Underlying MIL-STD-414. Washington, DC: United States Department of Defense, Office of the Assistant Secretary of Defense (Supply and Logistics).
Comparing Acceptance Sampling Standards, Part 2
