A Distribution-Free THWMA Control Chart under Ranked Set Sampling

Abstract

The basic assumption of the parametric control charts is that the underlying process follows the specific distribution. The appropriateness of parametric control charts is questionable when different industrial applications do not support this desired assumption. Recently, nonparametric control charts have been introduced to overcome this deficiency of parametric control charts. Nonparametric control charts have the same in-control run-length characteristics for all continuous distributions and are in-control robust. On the other hand, the ranked set sampling technique is preferred over the simple random sampling technique with control charts because it reduces variability and improves the control chart’s performance. So, this study aims to propose a nonparametric triple homogenously weighted moving average control chart under Wilcoxon signed-rank test with a ranked set sampling technique (regarded as <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:msub> <a:mrow> <a:mtext>NPTHWMA</a:mtext> </a:mrow> <a:mrow> <a:mtext>RSS</a:mtext> </a:mrow> </a:msub> </a:math> ) to further enhance the process location monitoring. Monte Carlo simulations are used for computational purposes. The proposed control chart’s run-length performance is compared with competing control charts, like TEWMA-SR, TEWMA- <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:mover accent="true"> <c:mi>X</c:mi> <c:mo>¯</c:mo> </c:mover> </c:math> , TEWMA-SN, TEWMA- <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" id="M3"> <f:msub> <f:mrow> <f:mtext>SR</f:mtext> </f:mrow> <f:mrow> <f:mtext>RSS</f:mtext> </f:mrow> </f:msub> </f:math> , and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" id="M4"> <h:msub> <h:mrow> <h:mtext>NPDHWMA</h:mtext> </h:mrow> <h:mrow> <h:mtext>RSS</h:mtext> </h:mrow> </h:msub> </h:math> control charts. The comparison revealed that the proposed <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" id="M5"> <j:msub> <j:mrow> <j:mtext>NPTHWMA</j:mtext> </j:mrow> <j:mrow> <j:mtext>RSS</j:mtext> </j:mrow> </j:msub> </j:math> control chart outperformed the other competing control charts, particularly for small to moderate shifts in process location. Finally, a real-life application is presented for quality practitioners to illustrate the effectiveness of the proposed control chart.