In recent years, process capability indices (PCIs) have been widely applied in quality control by most practitioners to assess whether the production process reaches a required level. However, the characteristic variable in many industrial production processes has non-normal distribution. This paper uses the Clements’s method to estimate four non-normal process capability indices for lognormal distribution. A simulation study is done to analyze the influence of skewness and kurtosis on the precision of estimation of process capability indices for the given distribution.