An Efficient Robust Nonparametric Triple EWMA Wilcoxon Signed-Rank Control Chart for Process Location

Abstract

The nonparametric (NP) control charts are famous for detecting a shift in the process parameters (location and/or dispersion) when the underlying process characteristic does not follow the distributional assumptions. Similarly, when the cost of estimations is very high and the ranking of observational is relatively simple, the ranked set sampling (RSS) technique is preferred over the simple random sampling (SRS) technique. On the other hand, the NP triple exponentially weighted moving average (EWMA) control chart based on SRS is superior to the NP EWMA and NP double EWMA (NP DEWMA) based on the SRS technique to detect a shift in the process location. This study designed an advanced form of NP TEWMA Wilcoxon signed-rank based on RSS, denoted as <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:msub> <a:mrow> <a:mtext>TEWMA</a:mtext> <a:mo>−</a:mo> <a:mtext>SR</a:mtext> </a:mrow> <a:mrow> <a:mtext>RSS</a:mtext> </a:mrow> </a:msub> </a:math> control chart to identify a shift in the process location parameter. The Monte Carlo simulation method is used to assess the performance of the proposed <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:msub> <c:mrow> <c:mtext>TEWMA</c:mtext> <c:mo>−</c:mo> <c:mtext>SR</c:mtext> </c:mrow> <c:mrow> <c:mtext>RSS</c:mtext> </c:mrow> </c:msub> </c:math> control chart along with SRS-based NP TEWMA (TEWMA-SR), SRS-based NP TEWMA sign (TEWMA-SN), SRS-based <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M3"> <e:mtext>TEWMA</e:mtext> <e:mo>−</e:mo> <e:mover accent="true"> <e:mi>X</e:mi> <e:mo stretchy="true">¯</e:mo> </e:mover> </e:math> , and RSS-based NP DEWMA-SR <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" id="M4"> <i:mfenced open="(" close=")" separators="|"> <i:mrow> <i:mtext>DEWMA</i:mtext> <i:mo>−</i:mo> <i:msub> <i:mrow> <i:mtext>SR</i:mtext> </i:mrow> <i:mrow> <i:mtext>RSS</i:mtext> </i:mrow> </i:msub> </i:mrow> </i:mfenced> </i:math> control charts. The study shows that the proposed <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" id="M5"> <n:msub> <n:mrow> <n:mtext>TEWMA</n:mtext> <n:mo>−</n:mo> <n:mtext>SR</n:mtext> </n:mrow> <n:mrow> <n:mtext>RSS</n:mtext> </n:mrow> </n:msub> </n:math> control chart is more efficient in identifying shifts (especially in small shifts) in the process location than the existing control charts. Finally, a real-life application is also provided for the practical implementation of the proposed <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" id="M6"> <p:msub> <p:mrow> <p:mtext>TEWMA</p:mtext> <p:mo>−</p:mo> <p:mtext>SR</p:mtext> </p:mrow> <p:mrow> <p:mtext>RSS</p:mtext> </p:mrow> </p:msub> </p:math> control chart.