# Lean Manufacturing Soft Sensors for Automotive Industries
## 2 Methodology  
### Data Collection from Companies and Initial Analyses  
The present study was based on the lean manufacturing and manufacturing flexibilities' data collected and analysed by [PERSON] and [PERSON] [30]. The authors surveyed forty-six automotive parts manufacturing firms spread across the Pune region of Maharashra State, India. The authors floated expert-curated questionnaires (provided in the supplementary material) to directly and indirectly gauge the levels of lean manufacturing and manufacturing flexibilities in these participating firms. The alpha test was employed to ensure the statistical validity of the designed questionnaires. The exhaustive survey questionnaires sought feedback on up to fifty different parameters related to various flexibilities mentioned in the previous section, viz. MF, VF, PF, RF, LF, and MH. Another section of the questionnaire probed nine parameters related to lean manufacturing attainments. In terms of ownerships, 4 of the surveyed companies were owned publicly, whereas 42 companies were privately owned. The product-wise categories of these companies comprised 23 auto component manufacturers, 19 assembling units, and 4 sub-assembly production units. A total of 14 companies produced goods at large scale, followed by 14, 12, and 6 medium, small, and micro-scale industries, respectively. As far as the respective labour strengths are concerned, 16 companies employed more than 250 staff, 13 firms had employee strengths between 50 and 250 followed by less than 50 workers in the remaining 17 units.  
The exhaustive survey data were checked for sampling adequacy and significance using the KMO and the Bartlett's sphericity tests. The resultant KMO value of 0.675 confirmed the sampling adequacy of the collected data. On the other hand, the sphericity test at a confidence level of 95% resulted in a \(p\) value of 0.000, confirming the significance of the statistical relationships between the various flexibilities and lean manufacturing levels of the surveyed firms. The levels of flexibilities and lean manufacturing for all firms were quantified by the authors following an analytical hierarchical process that involved experts from industry as well as from academia to assign suitable weights to different performance parameters. The resultant levels of the six manufacturing flexibilities and the corresponding lean manufacturing attainments of all 46 companies are depicted in Table 1. Finally, the authors used structural equation modeling to derive direct and indirect effects of flexibilities on lean manufacturing levels. In a subsequent study [31], the authors carried forward this study and implemented machine learning-assisted control theory to determine the exact levels of flexibilities needed by the surveyed firms to attain the desired lean manufacturing levels in their operations.  
The present work aimed to take this study to its next level: implementing a plethora of machine learning-based models to explore the best performing lean manufacturing soft sensor. This soft sensor would be able to classify the lean manufacturing level of an auto component manufacturing enterprise as high, medium or low based on its existing levels of manufacturing flexibilities (Figure 1). Experimental/survey data-based predictive modeling, machine learning-based soft sensors, and system identification/control architectures have been proved to be quite effective in estimating critical system performance outcomes based on the operating conditions/parameters [54; 55; 56; 57; 58; 59; 60]. The next subsection gives details of the machine learning-based soft sensor modeling of lean manufacturing followed in the present work.