Effects of quality characteristic distributions on the integrated model of Taguchi’s loss function and economic statistical design of \(\bar{X}\)-control charts by modifying the Banerjee and Rahim economic model.

*(English)*Zbl 1392.62348Summary: Although the normality is a usual assumption for quality measurements, it may be erroneous and misleading in many industrial applications of quality control online models. In addition, incorporating Taguchi’s loss function to these inspection activities leads the management to better decisions. In this paper, the integrated model of Taguchi’s loss function and the economic statistical design of \(\bar{X}\)-control charts are investigated under both normal and non normal quality data. This purpose has been achieved by modifying the cost model of P. K. Banerjee and M. A. Rahim [Technometrics 30, No. 4, 407–414 (1988; Zbl 0721.62101)] in which a non uniform sampling scheme is utilized for systems with increasing failure rate and Weibull shock model. For the same values of time and cost quantities and Weibull distribution parameters, the effects of three most popular quality characteristic distributions (Normal, Burr, and Johnson) that are fitted on a case study data in [M. A. Rahim, “Economic design of control charts assuming Weibull distribution in-control times”, J. Quality Tech. 25, No. 4, 296–305 (1993; doi:10.1080/00224065.1993.11979475)] are studied and compared. The optimal parameters of both economic and economic statistical designs reveal that there is an insignificant difference between Normal and Burr distributions, whereas a relative difference can be observed in the case of Johnson distribution.

##### MSC:

62P30 | Applications of statistics in engineering and industry; control charts |

##### Keywords:

optimal design; Taguchi’s loss function; quality characteristic distribution; process failure mechanism; non uniform sampling scheme; integrated hazard over sampling intervals##### Software:

AS 99
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\textit{M. A. Pasha} et al., Commun. Stat., Theory Methods 47, No. 8, 1842--1855 (2018; Zbl 1392.62348)

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##### References:

[1] | Alexander, S. M., M. A. Dillman, J. S. Usher, and B. Damodaran. 1995. Economic design of control charts using the Taguchi loss function. Computers & Industrial Engineering 28:671-679. |

[2] | Amiri, F., K. Noghondarian, and R. Noorossana. 2014. Economic-statistical design of adaptive X-bar control chart: a Taguchi loss function approach. Scientica Iranica 21:1096-1104. |

[3] | Banerjee, P. K., and M. A. Rahim. 1988. Economic design of ##img####img##-Control charts under Weibull shock models. Technometrics 30:407-414. · Zbl 0721.62101 |

[4] | Ben-Daya, M., and S. O. Duffuaa. 2003. Integration of Taguchi’s loss function approach in the economic design of ##img####img##-chart. International Journal of Quality & Reliability Management 20:607-619. |

[5] | Burr, I. W.1942. Cumulative frequency functions. Annals of Mathematical Statistics 13:215-232. · Zbl 0060.29602 |

[6] | Chen, H., and Y. Cheng. 2007. Non-normality effects on the economic-statistical design of ##img####img## charts with Weibull in-control time. European Journal of Operational Research 176:986-998. · Zbl 1140.62356 |

[7] | Chen, F. L., and C. H. Yeh. 2009. Economic statistical design of non-uniform sampling scheme Xbar control charts under non-normality and gamma shock model using genetic algorithm. Expert Systems with Applications 36:9488-9497. |

[8] | Chen, F. L., and C. H. Yeh. 2011. Economic statistical design for x-bar control charts under non-normal distributed data with Weibull in-control time. Journal of the Operational Research Society 62:750-759. |

[9] | Deming, W. E.1986. Out of crisis. Cambridge, MA: Massachusetts Institute of Technology, Center for Advanced Engineering Study. |

[10] | Duncan, J.1956. The economic design of ##img####img##-Charts used to maintain current control of a process. Journal of American Statistical Association 51:228-242. · Zbl 0071.13703 |

[11] | Hill, I. D., R. Hill, and R. L. Holder. 1976. Algorithm AS 99. Fitting Johnson curves by moments. Applied Statistics 25:180-189. |

[12] | Johnson, N. L.1949. Systems of frequency curves generated by methods of translation. Biometrika 36:149-176. · Zbl 0033.07204 |

[13] | Lorenzen, T. J., and L. C. Vance. 1986. The economic design of control charts: A unified approach. Technometrics 28:3-10. · Zbl 0597.62106 |

[14] | Rahim, M. A.1993. Economic design of ##img####img## control charts assuming Weibull distribution in-control times. Journal of Quality Technology 25:296-305. |

[15] | Ross, S. M.1970. Applied probability models with optimization applications. San Francisco, CA: Holden-Day. · Zbl 0213.19101 |

[16] | Safaei, A. S., R. B. Kazemzadeh, and S. T. A. Niaki. 2012. Multi-objective economic-statistical design of X-bar control chart considering Taguchi loss function. The International Journal of Advanced Manufacturing Technology 59:1091-1101. |

[17] | Saniga, E. M.1989. Economic statistical control chart designs with an application to ##img####img## and R charts. Technometrics 31:313-320. |

[18] | Seif, A., A. Faraz, and E. Saniga. 2015. Economic statistical design of the VP control charts for monitoring a process under non-normality. International Journal of Production Research 53:4218-4230. |

[19] | Taguchi, G.1986. Introduction to quality engineering: designing quality into products and processes. White Plains, NY: Kraus. |

[20] | Taguchi, G., and Y. Wu. 1979. Introduction to off-line quality control. Tokyo: Central Japan Quality Control Association. |

[21] | Taguchi, G., E. A. Elsayed, and T. Hsiang. 1989. Quality engineering in production systems. New York, NY: McGraw-Hill. |

[22] | Yeong, W. C., M. B. C. Khoo, M. H. Lee, and M. A. Rahim. 2013. Economic and economic statistical designs of the synthetic ##img####img## Chart using loss functions. European Journal of Operational Research 228:571-581. · Zbl 1317.91059 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.