"Explore the concept of Total Quality Management $($TQM$)$ as a comprehensive approach to improving organizational performance. Define the core principles and elements that constitute TQM and elucidate how these principles contribute to enhancing quality, productivity, and customer satisfaction within an organization. Discuss the significance of leadership commitment and employee involvement in successfully implementing TQM initiatives. Evaluate the potential challenges that companies might encounter when adopting TQM and propose effective strategies to overcome these hurdles. Additionally, analyze the correlation between TQM and organizational culture, emphasizing its role in fostering a culture of continuous improvement and innovation. Provide real$-$world examples or case studies to support your arguments and illustrate the impact of TQM on business success."