Improved Nonparametric Control Chart Based on Ranked Set Sampling with Application of Chemical Data Modelling

Abstract

The statistical performance of parametric control charts is questionable when the underlying process does not follow any specified probability distribution. Nonparametric control charts are the best substitute for this situation. On the other hand, the ranked set sampling technique is preferred over the simple random sampling technique because it reduces the variability of process parameters and improves the control chart’s performance. This study aims to offer a nonparametric double homogeneously weighted moving average control chart under Wilcoxon signed-rank test considering the 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>NPDHWMA</a:mtext> </a:mrow> <a:mrow> <a:mtext>RSS</a:mtext> </a:mrow> </a:msub> </a:math> ), to further enhance the process location monitoring. The proposed chart’s run-length performance is compared with competing control charts, such as DEWMA- <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> , NPDEWMA-SR, NPRDEWMA-SR, DHWMA, and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" id="M3"> <f:msub> <f:mrow> <f:mtext>NPHWMA</f:mtext> </f:mrow> <f:mrow> <f:mtext>RSS</f:mtext> </f:mrow> </f:msub> </f:math> control charts. The comparison revealed that the proposed <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 chart outperformed the other competing control charts, particularly for small to moderate shifts in process location. Finally, a real-life application is also offered for quality practitioners to show the strength of the proposed control chart.