Controlling over-adjusted process means and variances using VSI cause selecting control charts

Abstract

Process adjusted unnecessarily is a common problem in statistical process control. Incorrect adjustment of a process may result in shifts in process mean, process variance, or both, ultimately affecting the quality of products. The article considers the variable process control scheme for two dependent process steps with incorrect adjustment. We construct the variable sampling interval (VSI) Z X ¯ - Z S 2 and Z e ¯ - Z S e 2 control charts in order to effectively monitor the quality variable produced by the first process step with incorrect adjustment and the quality variable produced by the second process step with incorrect adjustment, respectively. The performance of the proposed VSI control charts is measured by the adjusted average time to signal (AATS) derived using a Markov chain approach. An example of process control for automobile braking system shows the application and performance of the proposed joint VSI Z X ¯ - Z S 2 and Z e ¯ - Z S e 2 control charts in detecting small and median shifts in mean and variance for the two dependent process steps with incorrect adjustment. The performance of the VSI Z X ¯ - Z S 2 and Z e ¯ - Z S e 2 control charts and the fixed sampling interval (FSI) Z X ¯ - Z S 2 and Z e ¯ - Z S e 2 control charts are compared via the numerical analysis results. These demonstrate that the former is much faster in detecting shifts in mean and variance. Whenever quality engineers cannot specify the values of variable sampling intervals, the optimal VSI Z X ¯ - Z S 2 and Z e ¯ - Z S e 2 control charts are suggested. Furthermore, the impacts of misusing Z Y ¯ - Z S y 2 charts to monitoring the process mean and variance in the second step are also investigated.