This paper chronicles the evolution of load-sharing parameter estimation methodologies, with a particular focus on the significant contributions made by Kim and Kvam (2004) and Park (2012). Kim and Kvam's pioneering work underscored the inherent challenges in deriving closed-form solutions for load-share parameters, which necessitated the use of sophisticated numerical optimization techniques. Park's research, on the other hand, provided groundbreaking closed-form solutions and extended the theoretical framework to accommodate more general distributions of component lifetimes. This was achieved by incorporating EM-type methods for maximum likelihood estimation, which represented a significant advancement in the field. Unlike previous efforts, this paper zeroes in on the specific characteristics and advantages of closed-form solutions for load-share parameters within reliability systems. Much like the basic Economic Order Quantity (EOQ) model enhances the understanding of real-life inventory systems dynamics, our analysis aims to thoroughly explore the conditions under which these closed-form solutions are valid. We investigate their stability, robustness, and applicability to various types of systems. Through this comprehensive study, we aspire to provide a deep understanding of the practical implications and potential benefits of these solutions. Building on previous advancements, our research further examines the robustness of these solutions in diverse reliability contexts, aiming to shed light on their practical relevance and utility in real-world applications.

The planetary gearing system is compact and lightweight. The performance of planetary gearing system which uses floating intermediate rings have been found to be very good for practical systems. To apply this system for the reduction of rotation of an engine, in designing stage, the quantitative estimate of the load sharing factors is required for understanding the performance. The method widely used for this purpose is to make use of elastic deformation of components of the structure or to utilize hydrodynamic oil film. This paper shows the way how to analyze the static load sharing factors by using the coefficient ''. This method can be applied for non-linear systems such as oil film bearing. The influences of various factors on '' of oil film spring are also shown. Furthermore, It is established in this study that the use of floating intermediate ring in designing the planetary gearing system has a very high reliability.