The aim of this paper is to explore and evaluate previous work focusing on the relationship and links between Lean manufacturing and industrial work. This study reviews the literature on Lean Manufacturing Assessment (LMA) during the last decade; 2008-2017 and analyses the literature from different perspectives. This paper highlights various key words, scopes, objectives, case study, definitions, methodologies, tools and main results. A total of 126 research papers have been reviewed in this study to help the researchers in the evaluation of lean manufacturing practices to identify and benefit from these studies. This paper provides a quantitative descriptive analysis and qualitative thematic analysis to provide an analysis of impact of lean on performance. Consequently, this paper can be considered as a guide for researchers in LMA. It is expected to be a brief reference for future researchers that reduces effort and time consuming during their studies.

The implementation of lean manufacturing practices (LMP) means a systematic approach of several management procedures and practices, which may impact content, nature and quality of people’s work. This implementation process is often performed after an accurate assessment to ensure the effectiveness and efficient execution of these practices. However, the necessity and logic of different assessments according to the situation required by assessment objective, the logic requires general rules for designing assessment with effective and reliable results. The aim of this research paper is to develop a logical perception to explain the impact of LMP on the actual and overall performance of the company and explains the computational basics and mathematical equations contributing to the assessment design of these practices to ensure efficiency and accuracy in the results. Moreover, this study also concludes a novel mathematical equations that can be used in the effective assessment to increase the effectiveness of evaluation for improvement processes in different sectors.

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Objective - This paper aims to provide a new mathematical model for the construction of assessment tools for Lean Manufacturing Practices (LMP) through the integration process with the set operations. This study also strives to develop key elements to enhance the effectiveness of LMP assessments and their impact through mathematical interrelationship.  Problem - Previous studies have shown a lack of clear mathematical methodology to carry out a rigorous assessment of the LMP effects on the firm’s operational and financial performance. Therefore, this paper tries to address this aspect by developing new equations.  Design - The methodology of this study is based on the conversion of the linguistic description (companies, processes, waste, practices) into numerical measurement model by integrating with set theory.  Finding - The results show a set of relationships and equations that can be applied to be a fundamental basis for ensuring the effectiveness of the assessment. This paper may contribute to the improvement of LMP’s design and development.