## Efficient power computation for $$r$$ out of $$m$$ runs rules schemes.(English)Zbl 1305.65063

Summary: In this article we develop a power computation code in the $$R$$ language which provides an easy to use tool to researchers in designing Shewhart control charts. It enables researchers to use different existing and newly introduced sensitizing rules and runs rules schemes designed for Shewhart-type control charts for location and spread. The code provides researchers to compute the power for different options of $$r$$ out of $$m$$ rules/schemes. The code is flexible to apply for any sample size, false alarm rate, type of control limits (one- or two-sided), amount of shift in the process parameters and a variety of popular distributions for commonly used Shewhart-type control charts (i.e.$$\bar{{X}}$$, $$R$$, $$S$$ and $$S^{2}$$ charts). These mentioned benefits of the developed functional code are only partially found in features of the existing software packages and these programs may be enhanced by adding the features of the developed code as a function in their libraries dealing with quality control charting.

### MSC:

 62-08 Computational methods for problems pertaining to statistics

### Software:

truncdist; CircStat; R; qcc; JavaStat; Surveillance; RWeka; codetools
Full Text:

### References:

 [1] Abbasi SA, Miller A (2011) On proper choice of variability control chart for normal and non-normal processes. Qual Reliab Eng Int. doi:10.1002/qre.1244 [2] Albers W, Kallenberg WCM (2006) Self-adapting control charts. Statistica Neerlandica 60: 292-308 · Zbl 1109.62121 [3] Alwan LC (2000) Statistical process analysis. McGraw-Hill International Editions, Singapore [4] Antzoulakos DL, Rakitzis AC (2008) The modified r out of m control chart. Commun Stat Simul Comput 37: 396-408 · Zbl 1132.62103 [5] Berens P (2009) CircStat: a MATLAB toolbox for circular statistics. J Stat Softw 31(10): 1-21 [6] Croux, C.; Rousseeuw, PJ; Dodge, Y. (ed.); Whittaker, J. (ed.), Time efficient algorithms for two highly robust estimators of scale., 411-428 (1992), Heidelberg [7] Harner EJ, Luo D, Tan J (2009) JavaStat: a Java/R-based statistical computing environment. Comput Stat 24: 295-302 · Zbl 1232.62006 [8] Höhle M (2007) Surveillance: an R package for the monitoring of infectious diseases. Comput Stat 22: 571-582 · Zbl 1186.62004 [9] Hornik K, Buchta C, Zeileis A (2009) Open-source machine learning: R meets Weka. Comput Stat 24: 225-232 · Zbl 1232.62007 [10] Khoo MBC (2004) Design of runs rules schemes. Qual Eng 16: 27-43 [11] Klein M (2000) Two alternatives to the Shewhart X control chart. J Qual Technol 32: 427-431 [12] Koutras MV, Bersimis S, Maravelakis PE (2007) Statistical process control using Shewhart control chart with supplementary runs rules. Methodol Comput Appl Probab 9: 207-224 · Zbl 1171.62366 [13] Mahoney M, Magel R (1996) Estimation of the power of the Kruskal-Wallis test. Biometrical J 38: 613-630 · Zbl 1077.62516 [14] Montgomery DC (2009) Introduction to statistical quality control, 6th edn. Wiley, New York [15] Nadarajah S, Kotz S (2007) Programs in R for computing truncated t distributions. Qual Reliab Eng Int 23: 273-278 [16] Riaz M (2008) Improved and robust monitoring in statistical process control. PhD thesis, University of Amsterdam [17] Riaz M, Mehmood R, Does RJMM (2011) On the performance of different control charting rules. Qual Reliab Eng Int 27(8): 1059-1067 [18] Schoonhoven M, Does RJMM (2010) The ${\bar{{X}}}$ control chart under non-normality. Qual Reliab Eng Int 26: 167-176 [19] Scrucca L (2004) qcc: an R package for quality control charting and statistical process control. R News 4/1: 11-17 [20] Spiring F (2010) Exploring process capability with Mathematica. Qual Reliab Eng Int. Available online with doi:10.1002/qre.1112 [21] Tierney L (2009) Code analysis and parallelizing vector operations in R. Comput Stat 24: 217-223 · Zbl 1232.62011
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