An integration of Taguchi’s loss function in Banerjee-Rahim model for the economic and economic statistical design of \(\overline X\)-control charts under multiple assignable causes and Weibull shock model.

*(English)*Zbl 1384.62329Summary: Incorporating Taguchi’s social loss of quality concept to online monitoring activities such as economic and economic statistical design of control charts presents the underlying process better in managerial language and thus leads to better decisions. In industrial processes, however, the occurrence of multiple assignable causes is more natural than only one assignable cause. Applying the cost model of P. K. Banerjee and M. A. Rahim [Technometrics 30, No. 4, 407–414 (1988; Zbl 0721.62101)] with constant integrated hazard rate over each sampling interval and by incorporating the multiplicity-cause economic model of Y.-S. Chen and Y.-M. Yang [“Economic design of \(\bar{x}\)-control charts with Weibull in-control times when there are multiple assignable causes”, Int. J. Prod. Econ. 77, No. 1, 17–23 (2002; doi:10.1016/S0925-5273(01)00196-7)] with a loss function, we use the advantages of the integrated model to enhance quality. Moreover, as the sample data do not always follow a normal distribution, the study of the integrated model under more general situations becomes a necessity. Thus, three most popular distributions as quality characteristic distribution (Normal, Burr, and Johnson) that are fitted to a specific case study data based on M. A. Rahim [“Economic design of \(\bar{x}\) control charts assuming Weibull in-control times”, J. Qual. Technol. 25, No. 4, 296–305 (1993; doi:10.1080/00224065.1993.11979475)] are applied to cover these situations. The results reveal that the choice of quality characteristic distribution significantly effects on optimal design parameters and hence selecting an improper distribution may be misleading and erroneous. For more illustrations, comparisons between an integrated multiplicity-cause model and the single-cause one are performed with considering some combinations of the parameters of Weibull in-control time.

##### MSC:

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

62P20 | Applications of statistics to economics |

62N05 | Reliability and life testing |

##### Keywords:

constant integrated hazard rate; multiplicity-cause economic model; process failure mechanism; quality characteristic distribution; Taguchi’s loss function##### Software:

AS 99
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\textit{M. A. Pasha} et al., Commun. Stat., Theory Methods 46, No. 24, 12113--12129 (2017; Zbl 1384.62329)

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