Abstract
A proper monitoring of stochastic systems is the control charts of statistical process control and drift in characteristics of output may be due to one or several assignable causes. Although many research works have been done on the economic design of control charts with single assignable cause, the economic statistical design of T^2 control chart under Weibull shock model with multiple assignable causes and considering multivariate Taguchi loss function has not been presented yet. Using Taguchi loss function in the concept of quality control charts with economic and economic statistical design leads to better decisions in the industry. Based on the optimization of the average cost per unit of time and taking into account the different combination values of Weibull distribution parameters, optimal design values ??of sample size, sampling interval and control limit coefficient were derived and calculated. Then the cost models under non-uniform and uniform sampling scheme were compared. The results revealed that the model under multiple assignable causes with Taguchi loss function has a lower cost than single assignable cause model and integrated model with non-uniform sampling has a lower cost than that with uniform sampling.
Highlights
The control charts technique for monitoring the process behavior is one of the basic tools of statistical process control (SPC)
Designing a control chart means to find the optimal values for three design parameters, namely, sample size, sampling interval and control limit coefficient which is done under three types of statistical, economic, and economic statistical designs
In most of the research works such as Heikes, Montgomery, and Yeung (1974), Yang and Rahim (2006), Chen, Hsieh, and Chang (2007), Seif, Moghadam, Faraz, and Heuchenne (2011), Bahiraee and Raissi (2014), Faraz, Heuchenne, Saniga, and Costa (2014)the economic design of T 2 control chart is presented with single assignable cause Jolayemi and Berrettoni (1989) generalized Duncan (1971) cost model, and produce economic design of T 2 control chart with multiple assignable causes
Summary
The control charts technique for monitoring the process behavior is one of the basic tools of statistical process control (SPC). Banerjee and Rahim (1988) Extended Duncan (1956) by using the more flexible Weibull distribution for single assignable cause model and non-uniform sampling interval by considering the fact that using uniform sampling interval is not logical for the process with increasing failure rate. In most of the research works such as Heikes, Montgomery, and Yeung (1974), Yang and Rahim (2006), Chen, Hsieh, and Chang (2007), Seif, Moghadam, Faraz, and Heuchenne (2011), Bahiraee and Raissi (2014), Faraz, Heuchenne, Saniga, and Costa (2014)the economic design of T 2 control chart is presented with single assignable cause Jolayemi and Berrettoni (1989) generalized Duncan (1971) cost model, and produce economic design of T 2 control chart with multiple assignable causes. Papers Duncan (1956) Duncan (1971) Montgomery and Klatt (1972) Lorenzen and Vance (1986) Banerjee and Rahim (1988) Jolayemi and Berrettoni (1989) Rahim and Banerjee (1993) Elsayed and Chen (1994) Alexander, Dillman, Usher, and Damodaran (1995) Zhang and Berardi (1997) Chen and Yang (2002) Chou et al (2001) Ben-Daya and Duffuaa (2003) Al-Oraini and Rahim (2002) Yang and Rahim (2006) Yu and Chen (2009) Kraleti and Kambagowni (2010) Yu, Tsou, Huang, and Wu (2010) Safaei et al (2012) Heydari et al (2016) Moghadam et al (2016)
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