Variable Parameters <i>t</i> Chart: An Application in Automobile Engine Piston Rings Manufacturing Process

The [Formula: see text] type charts possess a drawback as they may falsely indicate out-of-control (OOC) situations when the process standard deviation is unstable. They are not robust against estimation errors or variations in the process standard deviation. To overcome this setback, the [Formula: see text] type charts were developed. This research introduces the variable parameters (VP) [Formula: see text] chart for effectively monitoring the process mean. This study encompasses the implementation, optimal designs and performance evaluation of the proposed VP [Formula: see text] chart. The average time to signal (ATS), standard deviation of the time to signal (SDTS) and expected average time to signal (EATS) criteria are used to assess and compare the performance of the VP [Formula: see text] chart with existing charts, such as Shewhart (SH) [Formula: see text], synthetic (Syn) [Formula: see text], side-sensitive group runs (SSGR) [Formula: see text], exponentially weighted moving average (EWMA) [Formula: see text] and variable sampling interval (VSI) EWMA [Formula: see text] charts. From extensive analysis, we observe that the VP [Formula: see text] chart outperforms the SH [Formula: see text], Syn [Formula: see text] and SSGR [Formula: see text] charts for all sizes of mean shifts. However, the EWMA [Formula: see text] and VSI EWMA [Formula: see text] charts exhibit better performance for small shifts. Additionally, to demonstrate the implementation and usage of the proposed VP [Formula: see text] chart, we present a real-world manufacturing example.