Proposed Control Charts For Monitoring Cumulative Counts Of Conforming Items And Ratio Of Two Variables - Salihu, Abubakar Sani (2021)
This research provides a derivation of the analytical formulae to compute the average time to signal (ATS) value of the exponentially weighted moving average (EWMA) cumulative count of conforming (CCC) chart using the Markov chain technique. In the current literature, this chart is evaluated using simulation. Additionally, the variable sampling interval (VSI) EWMA CCC chart is also proposed to increase the sensitivity of the basic EWMA CCC chart in detecting process shifts. The optimal designs of the VSI EWMA CCC chart are obtained based on the Markov chain procedure by minimizing the expected delay time in detecting a process shift. The optimal parameters that minimize the average time to signal (ATS) criterion are provided and can be directly used in practice. Four charts, i.e. the basic CCC, VSI CCC, EWMA CCC and VSI EWMA CCC charts are considered in the numerical comparison using the ATS criterion. The VSI EWMA CCC chart has an impressive performance in comparison to the basic CCC, VSI CCC and EWMA CCC charts. An illustrative example via real data from an injection moulding process producing an array of micro-prism of an optical element is given to demonstrate the implementation of the VSI EWMA CCC chart in practice. In addition, this research proposes a two-sided run sum ratio chart to monitor the ratio of two normal variables. A Markov chain procedure is applied to evaluate the statistical performance of the chart based on the average run length (ARL) and expected average run length (EARL) criteria. Numerical comparisons with the Shewhart ratio and synthetic ratio charts based on the zero state analysis reveal that the run sum ratio chart has a better sensitivity in most cases.