Effect of Measurement Error on Joint Monitoring of Process Mean and Variability under Ranked Set Sampling

In this paper first we apply ranked set sampling (RSS) procedure in joint monitoring of both process mean and variance. Then, we study the effect of measurement error on joint monitoring of process mean and variance when simple random sampling (SRS) as well as RSS procedure is used. The results prove that the measurement error can seriously deteriorate the ability of the control chart in detecting all out‐of‐control scenarios. The results also represent that using RSS procedure can improve the ability of the monitoring scheme in detecting mean shifts, variance shifts as well as joint shifts either measurement error exists or not. In other words, RSS procedure can reduce the adverse effect of measurement error on detecting ability of joint monitoring scheme. After that, we utilize multiple measurements at each sample point when both SRS and RSS procedures are used. We investigate the effect of parameters in the covariate model thorough a sensitivity analysis. Finally, the applicability of the proposed control charts is illustrated using a real case of the piston rings in an automotive engine manufactured by a forging process.