## 1 Introduction  
Coal is the primary fuel of power plants in Korea, and coal-fired power plants have produced around 40% of the country's total electricity in recent years. In a coal-fired power plant, measuring the calorific value is important for the plant's efficiency and its environmental impact, since information on the coal components can be valuable for supplying the appropriate amount of excess combustion air. For given operating conditions, the supply of coal for a known calorific value is important for estimating the power plant's efficiency. Therefore, the development of a real-time measurement technique to analyze the calorific value of coal is required. Laser-induced breakdown spectroscopy (LIBS) is an in situ measurement that detects the elemental composition from the specific wavelengths of each element [1; 2; 3; 4]. LIBS can be used for analyzing solid [5], liquid [6], and gas [7] samples within the detection limits of specific ppm levels. Conventionally, the loss on ignition method and a CHN (carbon, hydrogen, and nitrogen) analyzer have been used for determining the coal components. In the aforementioned methods, the coal samples must be pre-treated and the analysis takes more than 10 h. On the contrary, LIBS needs little or no sample preparation compared to the conventional loss on ignition method and less time to analyze the result. In LIBS,the intensity of the signal depends on the concentration of the elemental components. The signal intensity shows a transient evolution behavior after laser pulse irradiation. To increase the measurement accuracy, the appropriate detection time, which is controlled by a delay time, should be determined [8; 9; 10]. To increase the accuracy of component analyses for various types of samples, studies on the effects of variation in the experimental parameters have been carried out [11; 12]. [PERSON] et al. [13] investigated the variables that affect the precision of LIBS measurements for pelletized coal samples. The experimental parameters, including the relative standard deviation, the pressure to pelletize the coal sample, deviations from the focal point of the sample, the number of laser shots, and various ambient gases, were investigated. [PERSON] et al. [14] experimentally and numerically presented the effect of the packing density of pellets on the fluctuation of emission lines in C and Fe. A numerical model based on the two-dimensional random close packing of disks in a confined geometry showed a good agreement with the experimental results. The results showed that finer particles in a binary sample provided a higher homogeneity in the laser-target interaction region, which yielded smaller fluctuations in the LIBS emission lines. Besides improving sample preparation, statistical approaches have been applied to data processing to improve the estimation accuracy. [PERSON] et al. [15] derived the coefficients of determination, \(R^{2}\), based on a partial least squares regression analysis and presented a method for determining the concentration of coal by using a function with the correction factor of a simple regression analysis. In their work, a total of 40 laser spectra were used to increase the accuracy of measurements of the carbon and hydrogen contained in bituminous coal. Using the partial least squares method, they derived the coefficient of determination (\(R^{2}\) = 0.880). Using the root mean square error of prediction (RMSEP) in a simple regression analysis, the error was reduced to a range from 4.47 to 5.52%. [PERSON] et al. [16] investigated the influences of different spectral preprocessing methods such as smoothing, standard normal variate transformation, multiplicative scatter correction, mean centering, and derivation by convolution (the Savitzky-Golay method) on a quantitative model for the calorific value analysis of coal. [PERSON] et al. [12] and [PERSON] et al. [17] used the signal-to-noise ratio (SNR) for the selection of the delay time. By measuring a total of 25 points, the impact of laser energy on the SNR was analyzed.