Revised triple sampling X control charts for the mean with known and estimated process parameters

Abstract

The primary aim of this research is to propose a revised triple sampling (TS) X¯ chart, where the derivations of new formulae for computing the average run length of the triple sampling (TS) X¯ chart correctly are provided. The secondary aim is to develop the revised TS X¯ chart with estimated process parameters. The revised TS X¯ charts are compared with the double sampling (DS) X¯, two stage adaptive sample size (AS2) X¯ and three stage adaptive sample size (AS3) X¯ charts when process parameters are known and estimated using the average run length (ARL), average number of observations to signal (ANOS), average of the average run lengths (AARL), standard deviation of the average run lengths (SDARL), average of the average number of observations to signal (AANOS) and standard deviation of the average number of observations to signal (SDANOS) criteria, where the revised TS X¯ charts are found to be superior. Additionally, a table giving the minimum number of Phase-I samples for estimating the process mean so that the revised TS X¯ chart with estimated process parameters has the desired in-control AARL and AANOS performances is provided.

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