| Summary: | The Shewhart <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover><mi>X</mi><mo>¯</mo></mover></semantics></math></inline-formula>- and <i>S</i>-charts are most commonly used for monitoring the process mean and variability based on the assumption of normality. However, many process distributions may follow a positively skewed distribution, such as the lognormal distribution. In this study, we discuss the construction of three combined <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover><mi>X</mi><mo>¯</mo></mover></semantics></math></inline-formula>- and <i>S</i>-charts for jointly monitoring the lognormal mean and the standard deviation. The simulation results show that the combined lognormal <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover><mi>X</mi><mo>¯</mo></mover></semantics></math></inline-formula>- and <i>S</i>-charts are more effective when the lognormal distribution is more skewed. A real example is used to demonstrate how the combined lognormal <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover><mi>X</mi><mo>¯</mo></mover></semantics></math></inline-formula>- and <i>S</i>-charts can be applied in practice.
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