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They used the AFT model in their research that can be applied in multistage processes.
Besides, Du et al. (2015a, b) investigated the cascade effects in multistage processes.
In multistage processes, some functional equations arise in a natural way (cf. Bellman [26] and Bellman and Lee [27]).
In another work, Khedmati and Niaki (2015b) considered Phase-I profile monitoring of general linear profiles in multistage processes.
Recently, Kalaei et al. (2016) proposed a methodology to first remove the effect of the cascade property in multistage processes.
Then, to remove or reduce the cascade property, a method using the U transformation was developed for Phase-I monitoring of linear profiles in multistage processes.
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Ghahyazi et al. (2014) examined the effects of cascade property in multistage process in monitoring simple linear profile in Phase II.
While in the multistage processes, the process in each stage is affected by the processes in the previous stages.
In the multistage processes, the process capability indices in each stage are affected by the capability of the processes in the previous stages.
In such multistage processes, cascade property is a principal feature in which the outgoing quality characteristic is affected by the changes in the incoming variables (Yang 1999; Tsung et al. 2008).
In the multistage processes, the process capability indices are calculated when the process is in control.
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