1、_ SAE Technical Standards Board Rules provide that: “This report is published by SAE to advance the state of technical and engineering sciences. The use of this report is entirely voluntary, and its applicability and suitability for any particular use, including any patent infringement arising there
2、from, is the sole responsibility of the user.” SAE reviews each technical report at least every five years at which time it may be revised, reaffirmed, stabilized, or cancelled. SAE invites your written comments and suggestions. Copyright 2014 SAE International All rights reserved. No part of this p
3、ublication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of SAE. TO PLACE A DOCUMENT ORDER: Tel: 877-606-7323 (inside USA and Canada) Tel: +1 724-776-497
4、0 (outside USA) Fax: 724-776-0790 Email: CustomerServicesae.org SAE WEB ADDRESS: http:/www.sae.org SAE values your input. To provide feedback on this Technical Report, please visit http:/www.sae.org/technical/standards/AIR6553 AEROSPACE INFORMATION REPORT AIR6553 Issued 2010-01 Reaffirmed 2014-10 Me
5、asurement Uncertainty and Consumer Risk RATIONALE AIR6553 has been reaffirmed to comply with the SAE five-year review policy. TABLE OF CONTENTS 1. SCOPE 2 2. REFERENCES 2 3. DEFINITIONS . 2 4. DEFINITION EXPANSIONS . 6 APPENDIX A CONFIDENCE LEVEL TRANSFORMATION . 8 APPENDIX B UNCERTAINTY RATION (UR)
6、 . 9 APPENDIX C EXAMPLE MEASUREMENT UNCERTAINTY EVALUATION (UNCERTAINTY RATIO) 10 APPENDIX D ERROR RATIO (ER) . 18 APPENDIX E EXAMPLE MEASUREMENT UNCERTAINTY EVALUATION (ERROR RATIO) - CONSERVATIVE OPTION . 19 APPENDIX F EXAMPLE MEASUREMENT UNCERTAINTY EVALUATION (ERROR RATIO) STANDARD OPTION . 22 A
7、PPENDIX G CONFIDENCE LEVEL ESTIMATION . 29 APPENDIX H HISTORICAL MEASURAND ESTIMATE UNCERTAINTY 35 APPENDIX I COVERAGE FACTOR AND EFFECTIVE DEGREES OF FREEDOM 37 APPENDIX J RISK-BASED ATTRIBUTE GAGE DESIGN AND BUILD. 39 APPENDIX K PRODUCT DISTRIBUTIONS AND CONSUMER RISK . 43 APPENDIX L EXPLANATION O
8、F STATISTICAL QUALITY RISK MANAGEMENT FOR THREAD PITCH DIAMETER . 46 APPENDIX M CALIBRATION UNCERTAINTY . 49 APPENDIX N APPENDICES REFERENCES . 56 1. SCOPE This document addresses measurement uncertainty and consumer risk as they relate to AS8879 thread inspection. It describes the rationale, theory
9、 and methodology used to generate the technical content of the AS5870. The document describes how to calculate measurement consumer risk. It documents all of the calculation methods which industry employs today to calculate what is commonly called measurement uncertainty (Appendices A, B, C, D, E an
10、d F). These, in turn, are used to calculate measurement uncertainty ratios which are required inputs to calculate measurement consumer risk. Users of this document can apply the information described herein for the evaluation of the capability of their measurements based on the measurement consumer
11、risk. It involves the analysis of the measurement (product) distribution and biases of both the product and measurement system distributions. It protects the consumer from the worst case distribution results. 2. REFERENCES 2.1 Applicable Documents: The following publications form a part of this stan
12、dard to the extent specified herein. The latest issue of SAE publications shall apply. The applicable issue of other publications shall be the issue in effect on the date of the purchase order. In the event of conflict between the text of this standard and references cited herein, the text of this s
13、tandard takes precedence. Nothing in this standard, however, supersedes applicable laws and regulations unless a specific exemption has been obtained 2.1.1 SAE Publications Available from SAE, 400 Commonwealth Drive, Warrendale, PA 15096-0001. AS5870 Thread Inspection Practices AS8879 Screw Threads,
14、 UNJ Profile, Inch, Controlled Radius Root With Increased Minor Diameter 2.1.2 ASME Publications Available from the American Society of Mechanical Engineers (ASME) through the web at http:/www.asme.org or in writing at ASME, 22 Law Drive, Box 2900, Fairfield, NJ 07007-2900 ASME B1.2 Gages and Gaging
15、 for Unified Inch Screw Threads ASME B46.1 Surface Texture (Surface Roughness, Waviness and Lay) 2.1.3 FAA Publications Available from Federal Aviation Administration, 800 Independence Avenue, SW. Washington, DC 20591 REPORT NO: FAA-IR-01-02 - AVIATION FASTENER AUDIT FINAL REPORT JUNE 13, 2001 Avail
16、able at: www.faa.gov/library/reports/media/FASTENER_AUDIT_REPORT.pdf 3. DEFINITIONS 3.1 Average Outgoing Quality Limit (AOQL) Maximum Average Outgoing Quality over all possible values of incoming product quality level for a given acceptance sampling plan. SAE INTERNATIONAL AIR6553 2 OF 56 3.2 Averag
17、e Outgoing Quality (AOQ) The average quality of outgoing product after sampling inspection for a given steady value of incoming product quality. 3.3 Calibration Set of operations that establish, under specified conditions, the relationship between values of quantities indicated by a measuring instru
18、ment or measuring system, or values represented by material measure or a reference material, and the corresponding values realized by standards. VIM, 6.11 3.4 Certification The act of designating that M if the full specification limit, the measurand estimate can be accepted only for a measured value
19、 equal to the certified value. Guardband limit, as defined here, is risk-based and is therefore consistent with the general basis of this document. E3.15 Historical Measurand Estimate Uncertainty This definition facilitates the accurate calculation of consumer and producer risks. As such, it avoids
20、confusion, albeit at the addition of a new definition. The confidence level of the estimate of the measurand refers to the percentage of the area under the probability density function model representing the historical measurand estimate values, for a specific confidence interval, i.e., for either a
21、 biased or unbiased measurand estimate Gaussian density function, for a confidence interval of 2 sigma, the confidence level is 95.45%. For the less accurate option, i.e., Error Ratio, Conservative Option, it is assumed that the maximum allowable error, as represented by the specification limits, ha
22、s an associated normal product distribution centered between the specification limits. In the absence of a required confidence interval, the product distribution confidence interval is defined to be equivalent to the intended (calibration certified performance specification) value. In the absence of
23、 distribution biases, the associated statistics are conservative. In the presence of biases, they can be liberal or conservative. SAE INTERNATIONAL AIR6553 6 OF 56 E3.21 M It is a matter of determining whether it has been achieved. See Appendix F for confidence level estimation guidance. In this exa
24、mple, a statistical analysis reveals that a 90.07% CL has been achieved, and therefore, the desired CL has been achieved. M. Evaluate the Need to Guardband Error Ratio The ER can now be calculated. The ER is =1202.56 : 146.94Historical Quality Level The historical quality level (HQL) is calculated t
25、o be 90%. Guardbanding Based on a desired consumer risk of 0.80%, and HQL of 90%, and an ER of 2.56:1, guardbanding is required since the ER is less than 9.20:1. Linearly interpolating10between the guardband limits (GBL) for uncertainty ratios (URs)11of 2:1 and 3:1 from the appropriate table, reprod
26、uced below, the required GBL is 0.812. HQL UR GBL CR(%) GBL CR(%) 90% 9.20:1 1.0000 0.8006 1.0000 0.8006 (1.6449) 4:1 1.0000 1.6000 0.9210 0.8006 3:1 1.0000 1.9709 0.8656 0.8006 2:1 1.0000 2.5462 0.7451 0.8006 1:1 1.0000 3.5019 0.3726 0.8006 Note: Guardbanding is not required for any consumer risk o
27、f 0.8006% or less, i.e., for uncertainty ratios of 9.20:1 or greater. N. Report the error The thread plug gage can be certified to 120” at a 90.07% CL provided the measured pitch diameter is within 97” (0.812 X 120”) of the nominal pitch diameter. Additional helpful information might include: a. Con
28、ditions of use that can significantly effect the value of total error. b. Error types and values. 10Linear interpolation is slightly conservative compared to the actual curve of the GBL versus UR since the curve is concave downward. 11A Type 2 conservative process assumes the ER and UR are equivalen
29、t. =Maximum Allowable Error MAEERMeasurement System Total Error MSTESAE INTERNATIONAL AIR6553 28 OF 56 APPENDIX G CONFIDENCE LEVEL ESTIMATION Rationale The calculation of Tolerance Ratio, Error Ratio and Uncertainty Ratio all req uire the same confidence level for the numerator and denominator for a
30、 valid calculation. This Appendix enables the valid calculation of those ratios. General In the field of Metrology, it is often necessary to evaluate measurement uncertainty in the presence of significant uncorrected systematic effects. This typically occurs with multifunction and/or multipoint meas
31、urement systems, such as digital multimeters and electronic balances, to name two. It is generally impractical to assign corrections for the many functions and ranges. As a result, these types of systems are usually evaluated with respect to a nominal value and assigned a bilateral confidence interv
32、al. In the strictest sense, evaluations of that sort are not in harmony with the Guide to the Expression of Uncertainty in Measurement (hereafter referred to as the “GUM”, reference Appendix N 1) in the event of remaining uncorrected systematic effects of a significant magnitude relative to the perf
33、ormance specification assigned to the system. According to the GUM, those residual systematic effects must be corrected, in order to legitimately consider the remaining combined random effects as a standard or expanded uncertainty. A deeper look into the philosophy and intent of the GUM, however, re
34、veals a methodology for combining significant uncorrected systematic effects with random effects and still legitimately consider the combination as a standard or expanded uncertainty, provided certain qualifications are made. This document describes that GUM-consistent methodology, the necessary qua
35、lifications, and provides examples of application. 1.1 Introduction The GUM assumes that all significant systematic effects have been corrected, thereby making the evaluated combined standard uncertainty a combination of random effects only. That convention permits the application of standard statis
36、tical treatment methods. For example, if a measurement system has two linearly related, uncorrelated Gaussian random input quantities ()12,xx , the combined standard variance of the output quantity estimate ()y is exactly represented by: () () ( )22212+cuy=ux ux If, however, one of the input quantit
37、ies contains an uncorrected significant systematic effect, the combined standard variance is not equal to the sum of the input quantity variances. In fact, the combined standard variance has not been defined for such a combination of effects. The proper treatment of this relationship requires an unc
38、onventional approach. One such approach is offered here. Other approaches are very limited in number. For one relatively recent such approach, the interested reader is referred to Appendix N 2. 1.2 GUM The general objective of the GUM is the estimation of the quantitative indication of the quality o
39、f the result of a measurement. Contrary to popular belief, that objective can be realized without requiring that all effects be random in nature and that all systematic effects be corrected. More specifically, the fundamentally important objective of a measurement uncertainty evaluation is to quanti
40、fy a “confidence interval” and “confidence level” (or “interval about the measurement result that may be expected to encompass a large fraction of the distribution of values that could reasonably be attributed to the measurand”) of an estimate of a measurand. For measurement systems not containing s
41、ignificant systematic effects, a confidence interval and confidence level can be determined in a straightforward manner by applying the law of propagation of uncertainty to the measurement process mathematical model to obtain the combined standard uncertainty and multiplying by a coverage factor. Th
42、e GUM does not deal with cases involving uncorrected systematic effects. Even paragraph F.2.4.5 of the GUM requires a correction to be made. Since in the practical world of measurement, many measurements contain uncorrected significant systematic effects, it should be recognized that the need exists
43、 for a methodology for treating those cases. The thrust of this DOCUMENT is to achieve the same objective in the presence of uncorrected significant systematic effects. SAE INTERNATIONAL AIR6553 29 OF 56 1.3 The Approach General One metrological definition is as follows: Confidence Level The probabi
44、lity that a measurement result, made at the time of its evaluation by the measurement and test equipment being evaluated, is within the associated confidence interval. It should be noted that non-repeatable conditions and measurement capability variability must be avoided for a measurement result to
45、 have a confidence interval correctly matched to its confidence level. If the sum of systematic effects was to change, the area under the probability density function within the confidence interval would also change. The result would be similar if the expanded uncertainty would change. If both would
46、 change, a similar effect would be likely. It is, therefore, important to emphasize that a confidence level must be limited to the time of evaluation, thereby guaranteeing repeatability conditions and capability constancy. Figure 1 is a graphical illustration of one possible bilateral 97.68% confide
47、nce level. It is reasonable to expect that for many measurement systems the distribution representing the bilateral probability of possible outcomes under repeatability conditions could be modeled by a symmetrical Gaussian distribution, and also that the distribution would be biased by some amount f
48、rom the specification nominal as is shown in Figure 1. FIGURE 1 - GENERAL CONFIDENCE LEVEL. The hatched area under the curve in Figure 1 represents the probability that a measurement result is within its associated confidence interval. For measurement results made by the item being evaluated for Gau
49、ssian measurement outcomes, if the distribution has a +1% (or 1%) systematic error, a standard deviation of 1.50%, and a confidence interval of 4%, the confidence level would be 97.68%. That is to say that 97.68% of the area under the Gaussian probability density function would be contained between the lower and upper specification limits. It would be consistent with the intent of the GUM to consider the 4% confiden
