Shewhart type simultaneous univariate control chart based on ranked set sampling scheme

The control charts with the Ranked Set Sampling (RSS) scheme performs better in detecting shifts in mean and variance of the process compared to the control charts with the Simple Random Sampling scheme (SRS). In this article, we develop a Novel Shewhart type simultaneous univariate control chart (Max Chart) based on the RSS scheme. Since the distribution of the statistics <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>M</mml:mi> <mml:mo>(</mml:mo> <mml:msub><mml:mi>n</mml:mi> <mml:mi>i</mml:mi></mml:msub> <mml:mo>)</mml:mo></mml:mrow> </mml:math> based on the RSS scheme is not known, an alternative approach is taken by using an improved bootstrap method in developing a novel Shewhart type simultaneous control chart based on RSS. The results of the Monte Carlo simulation study show that, when compared to the conventional Max chart based on the SRS scheme, the average run length under out-of-control conditions (ARL₁) obtained from that the Improved Bootstrap Max Chart based on the RSS scheme is superior in detecting shifts in mean and variance of the process. A real case example is also given to illustrate the operation and performance of the proposed control chart. Key points:1.A novel Shewhart type simultaneous univariate control chart (Max Chart) based on the RSS scheme is proposed to improve the performance of the of control chart in detecting process shifts.2.The Control limit of Shewhart type simultaneous univariate control chart (Max Chart) based on the RSS scheme was constructed using an Improved Bootstrap method.