<p>Memory-type control charts, such as EWMA charts, excel at detecting small and gradual process shifts, making them essential for manufacturing process monitoring. This study proposes a Realistic Economic-Statistical Design (RESD) framework for non-Shewhart charts that explicitly incorporates multiple independent assignable causes and assumes no new cause occurs after the first until a true alarm. The Burr XII distribution models the occurrence of assignable causes, extending the classical Lorenzen–Vance cost framework for more accurate monitoring cost estimation. Numerical results reveal that classical models underestimate expected costs in multi-cause environments by up to 173.58% (depending on Burr-XII parameters <i>c</i>, <i>s</i>, and NE/UN/HN). The proposed RESD-BurrXII EWMA model significantly mitigates this bias, achieving lower optimal expected costs <i>E</i>(<i>A</i>) than the Shewhart chart (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\lambda =1\)</EquationSource> </InlineEquation>). Moderate smoothing (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\lambda \approx 0.7\)</EquationSource> </InlineEquation>) consistently yields the lowest costs (typically 4–10% reduction versus Shewhart across tested scenarios) by balancing sensitivity and stability, whereas high smoothing (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\lambda =0.2\)</EquationSource> </InlineEquation>) raises costs due to over-sensitivity. The model also effectively detects small shifts (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\delta _i = 0.5\)</EquationSource> </InlineEquation>–1.8), maintaining reasonable costs ($366–476). This framework aids industries in optimizing quality control systems and lays groundwork for future adaptive and multivariate chart designs.</p>

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Optimized realistic economic-statistical design of memory-type control charts with Burr type XII shock model for multiple independent assignable causes

  • Farnoosh Shiravani,
  • M. Bameni Moghaddam,
  • Reza Pourtaheri

摘要

Memory-type control charts, such as EWMA charts, excel at detecting small and gradual process shifts, making them essential for manufacturing process monitoring. This study proposes a Realistic Economic-Statistical Design (RESD) framework for non-Shewhart charts that explicitly incorporates multiple independent assignable causes and assumes no new cause occurs after the first until a true alarm. The Burr XII distribution models the occurrence of assignable causes, extending the classical Lorenzen–Vance cost framework for more accurate monitoring cost estimation. Numerical results reveal that classical models underestimate expected costs in multi-cause environments by up to 173.58% (depending on Burr-XII parameters c, s, and NE/UN/HN). The proposed RESD-BurrXII EWMA model significantly mitigates this bias, achieving lower optimal expected costs E(A) than the Shewhart chart ( \(\lambda =1\) ). Moderate smoothing ( \(\lambda \approx 0.7\) ) consistently yields the lowest costs (typically 4–10% reduction versus Shewhart across tested scenarios) by balancing sensitivity and stability, whereas high smoothing ( \(\lambda =0.2\) ) raises costs due to over-sensitivity. The model also effectively detects small shifts ( \(\delta _i = 0.5\) –1.8), maintaining reasonable costs ($366–476). This framework aids industries in optimizing quality control systems and lays groundwork for future adaptive and multivariate chart designs.