Run sum ratio chart when measurement errors are present

As far as literature of quality control is concerned, this is the first article that advocates the run sum ratio scheme with measurement errors, called the RS-RZ ME chart. The linear covariate error model is employed in designing the RS-RZ ME chart in detecting increases and decreases in the ratio of two variables from the normal distribution. The average run length and expected average run length values of the RS-RZ ME chart are obtained using the Markov chain model. A comparison of the RS-RZ ME scheme with two measurement errors based charts in the literature, namely, the Shewhart ratio and standard run sum ratio charts is conducted. The results indicate the superiority of the RS-RZ ME chart over the aforesaid existing charts for most of the shift sizes and shift intervals considered. The findings reveal that as the values of the parameters controlling the accuracy error of the measurement system, (theta X,theta Y)$({{\theta _X},{\theta _Y}} )$ increase, the RS-RZ ME scheme's efficiency increases. In the same vein, as the values of the parameters controlling the precision of the measurement system, (eta X,eta Y)$( {{\eta _X},{\eta _Y}} )$ decrease, the RS-RZ ME scheme' efficiency increases. Furthermore, as the value of the correlation coefficient between variables X and Y increases, the RS-RZ ME chart's efficiency increases. The application of the RS-RZ ME scheme is illustrated using data from a food industry.