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Appendix a Shewhart Constants for Control Charts

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Appendix a Shewhart Constants for Control Charts Appendix A Shewhart Constants for Control Charts The main Shewhart constants d2, d3, and c4 can be obtained for any n using R as shown in the following examples: library(SixSigma) ss.cc.getd2(n = 5) ## d2 ## 2.325929 ss.cc.getd3(n = 5) ## d3 ## 0.8640819 ss.cc.getc4(n = 5) ## c4 ## 0.9399856 The rest of Shewhart constants that can be found at any textbook are computed using those three basic constants. A full table of constants can also be generated using R. Table A.1 shows the constants used in this book. There are other constants not covered by this book which could also be computed just using the appropriate formula. A data frame with the constants in Table A.1 can be obtained with the following code: nmax <- 25 n <- 2:nmax d2 <- sapply(2:nmax, ss.cc.getd2) d3 <- sapply(2:nmax, ss.cc.getd3) c4 <- sapply(2:nmax, ss.cc.getc4) A2 <- 3/(d2*sqrt(n)) © Springer International Publishing Switzerland 2015 285 E.L. Cano et al., Quality Control with R, Use R!, DOI 10.1007/978-3-319-24046-6 286 A Shewhart Constants for Control Charts Table A.1 Shewhart constants n d2 d3 c4 A2 D3 D4 B3 B4 2 1.1284 0.8525 0.7979 1.8800 0.0000 3.2665 0.0000 3.2665 3 1.6926 0.8884 0.8862 1.0233 0.0000 2.5746 0.0000 2.5682 4 2.0588 0.8798 0.9213 0.7286 0.0000 2.2821 0.0000 2.2660 5 2.3259 0.8641 0.9400 0.5768 0.0000 2.1145 0.0000 2.0890 6 2.5344 0.8480 0.9515 0.4832 0.0000 2.0038 0.0304 1.9696 7 2.7044 0.8332 0.9594 0.4193 0.0757 1.9243 0.1177 1.8823 8 2.8472 0.8198 0.9650 0.3725 0.1362 1.8638 0.1851 1.8149 9 2.9700 0.8078 0.9693 0.3367 0.1840 1.8160 0.2391 1.7609 10 3.0775 0.7971 0.9727 0.3083 0.2230 1.7770 0.2837 1.7163 11 3.1729 0.7873 0.9754 0.2851 0.2556 1.7444 0.3213 1.6787 12 3.2585 0.7785 0.9776 0.2658 0.2833 1.7167 0.3535 1.6465 13 3.3360 0.7704 0.9794 0.2494 0.3072 1.6928 0.3816 1.6184 14 3.4068 0.7630 0.9810 0.2354 0.3281 1.6719 0.4062 1.5938 15 3.4718 0.7562 0.9823 0.2231 0.3466 1.6534 0.4282 1.5718 16 3.5320 0.7499 0.9835 0.2123 0.3630 1.6370 0.4479 1.5521 17 3.5879 0.7441 0.9845 0.2028 0.3779 1.6221 0.4657 1.5343 18 3.6401 0.7386 0.9854 0.1943 0.3913 1.6087 0.4818 1.5182 19 3.6890 0.7335 0.9862 0.1866 0.4035 1.5965 0.4966 1.5034 20 3.7349 0.7287 0.9869 0.1796 0.4147 1.5853 0.5102 1.4898 21 3.7783 0.7242 0.9876 0.1733 0.4250 1.5750 0.5228 1.4772 22 3.8194 0.7199 0.9882 0.1675 0.4345 1.5655 0.5344 1.4656 23 3.8583 0.7159 0.9887 0.1621 0.4434 1.5566 0.5452 1.4548 24 3.8953 0.7121 0.9892 0.1572 0.4516 1.5484 0.5553 1.4447 25 3.9306 0.7084 0.9896 0.1526 0.4593 1.5407 0.5648 1.4352 D3 <- sapply(1:(nmax-1), function(x){ max(c(0, 1 - 3*(d3[x]/d2[x])))}) D4 <- (1 + 3*(d3/d2)) B3 <- sapply(1:(nmax-1), function(x){ max(0, 1 - 3*(sqrt(1-c4[x]^2)/c4[x]))}) B4 <- 1 + 3*(sqrt(1-c4^2)/c4) constdf <- data.frame(n, d2, d3, c4, A2, D3, D4, B3, B4) The table of constants is also available as a one-page pdf document through one of the SixSigma package vignettes: vignette(topic = "Shewhart Constants", package = "SixSigma") Appendix B ISO Standards Published by the ISO/TC69: Application of Statistical Methods This appendix contains all the international standards and technical reports published by the ISO TC69—Application of Statistical Methods, grouped by subcommittees. Please note that ISO standards are continously evolving. All references to standards in this appendix and throughout the book are specific for a given point in time. In particular, this point in time is end of June 2015. Therefore, some new standards may have appeared when you are reading this book, or even other changes may have happen in ISO. For example, at the time of publishing a subcommittee has changed its denomination! Keep updated in the committee website: http://www.iso.org/iso/home/store/catalogue_tc/catalogue_tc_ browse.htm?commid=49742. TC69/SCS: Secretariat ISO 11453:1996 Statistical interpretation of data—Tests and confidence intervals relating to proportions. ISO 11453:1996/Cor 1:1999 . ISO 16269-4:2010 Statistical interpretation of data—Part 4: Detection and treat- ment of outliers. ISO 16269-6:2014 Statistical interpretation of data—Part 6: Determination of statistical tolerance intervals. ISO 16269-7:2001 Statistical interpretation of data—Part 7: Median— Estimation and confidence intervals. ISO 16269-8:2004 Statistical interpretation of data—Part 8: Determination of prediction intervals. ISO 2602:1980 Statistical interpretation of test results—Estimation of the mean—Confidence interval. ISO 2854:1976 Statistical interpretation of data—Techniques of estimation and tests relating to means and variances. © Springer International Publishing Switzerland 2015 287 E.L. Cano et al., Quality Control with R, Use R!, DOI 10.1007/978-3-319-24046-6 288 B ISO Standards Published by the ISO/TC69: Application of Statistical Methods ISO 28640:2010 Random variate generation methods. ISO 3301:1975 Statistical interpretation of data—Comparison of two means in the case of paired observations. ISO 3494:1976 Statistical interpretation of data—Power of tests relating to means and variances. ISO 5479:1997 Statistical interpretation of data—Tests for departure from the normal distribution. ISO/TR 13519:2012 Guidance on the development and use of ISO statistical publications supported by software. ISO/TR 18532:2009 Guidance on the application of statistical methods to quality and to industrial standardization. TC69/SC1: Terminology and Symbols Statistics ISO 3534-1:2006 —Vocabulary and symbols—Part 1: General statistical terms and terms used in probability. ISO 3534-2:2006 Statistics—Vocabulary and symbols—Part 2: Applied statistics. ISO 3534-3:2013 Statistics—Vocabulary and symbols—Part 3: Design of experiments. ISO 3534-4:2014 Statistics—Vocabulary and symbols—Part 4: Survey sampling. TC69/SC4: Applications of Statistical Methods in Process Management ISO 11462-1:2001 Guidelines for implementation of statistical process control (SPC)—Part 1: Elements of SPC. ISO 11462-2:2010 Guidelines for implementation of statistical process control (SPC)—Part 2: Catalogue of tools and techniques. ISO 22514-1:2014 Statistical methods in process management—Capability and performance—Part 1: General principles and concepts. ISO 22514-2:2013 Statistical methods in process management—Capability and performance—Part 2: Process capability and performance of time-dependent process models. ISO 22514-3:2008 Statistical methods in process management—Capability and performance—Part 3: Machine performance studies for measured data on dis- crete parts. B ISO Standards Published by the ISO/TC69: Application of Statistical Methods 289 ISO 22514-6:2013 Statistical methods in process management—Capability and performance—Part 6: Process capability statistics for characteristics following a multivariate normal distribution. ISO 22514-7:2012 Statistical methods in process management—Capability and performance—Part 7: Capability of measurement processes. ISO 22514-8:2014 Statistical methods in process management—Capability and performance—Part 8: Machine performance of a multi-state production process. ISO 7870-1:2014 Control charts—Part 1: General guidelines. ISO 7870-2:2013 Control charts—Part 2: Shewhart control charts. ISO 7870-3:2012 Control charts—Part 3: Acceptance control charts. ISO 7870-4:2011 Control charts—Part 4: Cumulative sum charts. ISO 7870-5:2014 Control charts—Part 5: Specialized control charts. ISO/TR 22514-4:2007 Statistical methods in process management—Capability and performance—Part 4: Process capability estimates and performance mea- sures. TC69/SC5: Acceptance Sampling ISO 13448-1:2005 Acceptance sampling procedures based on the allocation of priorities principle (APP)—Part 1: Guidelines for the APP approach. ISO 13448-2:2004 Acceptance sampling procedures based on the allocation of priorities principle (APP)—Part 2: Coordinated single sampling plans for acceptance sampling by attributes. ISO 14560:2004 Acceptance sampling procedures by attributes—Specified quality levels in nonconforming items per million. ISO 18414:2006 Acceptance sampling procedures by attributes—Accept-zero sampling system based on credit principle for controlling outgoing quality. ISO 21247:2005 Combined accept-zero sampling systems and process control procedures for product acceptance. ISO 24153:2009 Random sampling and randomization procedures. ISO 2859-10:2006 Sampling procedures for inspection by attributes—Part 10: Introduction to the ISO 2859 series of standards for sampling for inspection by attributes. ISO 2859-1:1999 Sampling procedures for inspection by attributes—Part 1: Sampling schemes indexed by acceptance quality limit (AQL) for lot-by-lot inspection. ISO 2859-1:1999/Amd 1:2011 . ISO 2859-3:2005 Sampling procedures for inspection by attributes—Part 3: Skip-lot sampling procedures. ISO 2859-4:2002 Sampling procedures for inspection by attributes—Part 4: Procedures for assessment of declared quality levels. 290 B ISO Standards Published by the ISO/TC69: Application of Statistical Methods ISO 2859-5:2005 Sampling procedures for inspection by attributes—Part 5: System of sequential sampling plans indexed by acceptance quality limit (AQL) for lot-by-lot inspection.
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