Feature extraction in control chart patterns with missing data

Abstract

Data preprocessing and feature extraction are critical steps in control chart pattern (CCP) recognition for reducing dimensionality and irrelevant information. To ensure good quality of input representation, it is important to handle missing values on control charts before feature extraction. Excluding missing values and imputing them with plausible values are two common missing data handling approaches in the literature. In this paper imputation capability of exponentially weighted moving average (EWMA) was investigated. Incomplete process data for three missingness mechanisms namely, missing completely at random (MCAR), missing at random (MAR) and missing not at random (MNAR) were investigated using computer simulation. Missing data at severity levels i.e. 0, 5, 10, 15, 20, 25 and 50 % were evaluated. The investigation covers feature mean, standard deviation, skewness, kurtosis and quartiles extracted from imputed patterns. The imputation performance was measured by comparing the deviation between full patterns and patterns with missing values in term of mean square error (MSE). The results show that EWMA imputation was highly reliable to recover missing values as evident form low feature deviations, MSE values; 0.04 (random), 0.04 (trend-up), 0.3 (shift-up) and 0.5 (cycle) respectively. The results suggest that EWMA imputation technique is superior than the mean and median imputations.