Control Charts, Synthetic

Abstract

It is well known that the Shewhart control charts are not very sensitive for detecting small and moderate shifts in the process parameters. A synthetic chart, which is a combination of a Shewhart control chart and a conforming run‐length (CRL) chart, has been proposed and studied as a viable alternative for that purpose. The advantage of a synthetic chart is its ease of design, operation, and interpretation. In this contribution, we discuss the most common types of synthetic charts, along with some illustrations of their practical implementation. Both parametric and nonparametric synthetic charts are considered.

An expanded case against synthetic‐type control charts

“…Therefore, it is not too restrictive to apply the conditional steady-state ARL 𝒟 1 relying on 𝝍 1 and the related CED 𝐷 𝜏 for the rest of the paper. Note that neither Rakitzis et al 7 nor Chakraborti and Rakitzis 26 touched on these subtle complications in their discussion of the steady-state ARL.…”

“…24 The remaining values are given in Shongwe and Graham. 10 Before continuing with the competitor EWMA, we want to mention that the recent Chakraborti and Rakitzis 26 labeled the synthetic-type charts differently. Their 𝑆 1 and 𝑆 3 correspond to WS (our 𝑆 1 ) and DW (our 𝑆 2 ), respectively.…”

“…Their S 1 and S 3 correspond to WS (our S 1 ) and DW (our S 2 ), respectively. The remaining two in Chakraborti and Rakitzis, 26 S 2 and S 4 , are just the latter combined with a Shewhart alarm rule.…”

“…Note that neither Rakitzis et al 7 . nor Chakraborti and Rakitzis 26 touched on these subtle complications in their discussion of the steady‐state ARL.…”