Variable Sampling Interval X-bar Control charts with Runs Rules

Abstract

This paper proposes two variable sampling interval schemes in (X) over bar control charts with runs rules. One determines the next sampling interval based on the number of consecutive sample means falling in the regions specified by the runs rules for signaling, and the other based on the number of consecutive sample means belonging to the regions complementary to the ones used in the first scheme. These two schemes can easily be applied to the situations where typical runs rules have been used in practice. An illustrative example of the proposed charts is given and a Markov chain approach is used to derive the formulas for evaluating the performances of the proposed schemes. The proposed charts are compared with the fixed sampling interval and existing variable sampling interval (X) over bar control charts with runs rules. Significance: Few works have been done on variable sampling interval (X) over bar control charts with runs rules. In this paper, we propose two variable sampling interval schemes for situations where typical runs rules are added to the (X) over bar control charts.