Comparative analysis between FAR and ARL based control charts with runs rules
In this study, we have conducted comparative analysis between false alarm rate (FAR) and average run length (ARL) based control charts with runs rules. In this regard, we have considered various univariate and multivariate control charts which include mean, standard deviation, variance, Hotelling, and generalized variance. For evaluation purpose, we have used actual false alarm rate, power, in-control actual average run length, and out-of-control average run length as performance indicators. Furthermore, the performance indicators are calculated through Monte Carlo simulation procedures. Results revealed that performance order of runs rules with FAR based control charts are persistent whereas, performance order of runs rules with ARL based control charts are dependent on the circumstances, that is, sample size, size of shift, type of control chart, and side of control limit (upper-sided and lower-sided). Besides, we have provided a real life example using the data on electrical resistance of insulation. In this approach, we have determined that behavior of FAR and ARL based control charts using the real data is recorded similar to the behavior using the statistical performance indicators.
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- [1] L.C. Alwan, Statistical Process Analysis, McGraw-Hill International Editions, Singapore,
2000.
- [2] S. Chakraborti and S. Eryilmaz, A nonparametric Shewhart-type signed-rank control
chart based on runs, Comm. Statist. Simulation Comput. 36 (2), 335–356, 2007.
- [3] C.W. Champ and W.H. Woodall, Exact results for Shewhart control charts with supplementary
runs rules, Technometrics 29 (4), 393–399, 1987.
- [4] M.B. Khoo, Design of runs rules schemes, Qual. Eng. 16 (1), 27–43, 2003.
- [5] M. Klein, Two alternatives to the shewhart x control chart, J. Qual. Technol. 32 (4),
427–431, 2000.
- [6] J.C. Malela-Majika, S.C. Shongwe and P. Castagliola, One-sided precedence monitoring
schemes for unknown shift sizes using generalized 2-of-(h+1) and w-of-w improved
runs-rules, Comm. Statist. Theory Methods, 1–35, 2020.
- [7] R. Mehmood, M.H. Lee, M. Riaz, B. Zaman and I. Ali, Hotelling T2 control chart
based on bivariate ranked set schemes, Comm. Statist. Simulation Comput., 1–28,
2019.
- [8] R. Mehmood, M.S. Qazi and M. Riaz, On the performance of $\bar{X}$ control chart for
known and unknown parameters supplemented with runs rules under different probability
distributions, J. Stat. Comput. Simul. 88 (4), 675–711, 2018.
- [9] R. Mehmood, M. Riaz and R.J.M.M. Does, Control charts for location based on
different sampling schemes, J. Appl. Stat. 40 (3), 483–494, 2013.
- [10] R. Mehmood, M. Riaz and R.J.M.M. Does, Efficient power computation for r out of
m runs rules schemes, Comput. Statist. 28 (2), 667–681, 2013.
- [11] R. Mehmood, M. Riaz and R.J.M.M. Does, Quality quandaries: on the application of
different ranked set sampling schemes, Qual. Eng. 26 (3), 370–378, 2014.
- [12] R. Mehmood, M. Riaz, T. Mahmood, S.A. Abbasi and N. Abbas, On the extended
use of auxiliary information under skewness correction for process monitoring, Trans.
Inst. Meas. Control. 39 (6), 883–897, 2017.
- [13] D.C. Montgomery, Introduction to Statistical Quality Control, John Wiley Sons, New
York, 2009.
- [14] Jr, J.J. Pignatiello and G.C. Runger, Comparisons of multivariate cusum charts, J.
Qual. Technol. 22 (3), 173–186, 1990.
- [15] M. Riaz, R. Mehmood and R.J.M.M. Does, On the performance of different control
charting rules, Qual. Reliab. Eng. 27 (8), 1059–1067, 2011.
- [16] D.K. Shepherd, S.E. Rigdon and C.W. Champ, Using runs rules to monitor an attribute
chart for a markov process, QTQM 9 (4), 383–406, 2012.
- [17] W.A. Shewhart, Economic Control of Quality of Manufactured Product, ASQ Quality
Press, 1931.
- [18] S.C. Shongwe, On the design of nonparametric runs-rules schemes using the markov
chain approach, Qual. Reliab. Eng. 36 (5), 1604–1621, 2020.
- [19] S.C. Shongwe, J.C. Malela-Majika and T. Molahloe, One-sided runs rules schemes to
monitor autocorrelated time series data using a first-order autoregressive model with
skip sampling strategies, Qual. Reliab. Eng. 35 (6), 1973–1997, 2019.
- [20] S. Shongwe, J.C. Malela-Majika and E. Rapoo, One-sided and two-sided w-of-w runsrules
schemes: An overall performance perspective and the unified run-length derivations,
J. Probab. Stat., 1–20, 2019.
- [21] E.C. Western, Statistical Quality Control Handbook, Western Electric Company, Indianapolis,
1956.
- [22] B. Zaman, M. Riaz and S.A. Abbasi, On the efficiency of runs rules schemes for
process monitoring, Qual. Reliab. Eng. 32 (2), 663–671, 2016.