Recently, there has been explosive growth in the development of the digital industry concept. One of the most important elements of this concept is the application of mathematical modeling methods and data mining to create models of production processes and final products, with the aim of making decisions under stochastic uncertainty. In this paper, a method of diversifying the investment portfolio in the formation of a digital twin is proposed, which is aimed at reducing the total risk by distributing existing assets (resources, investments, etc.) between the analog and digital enterprises. Three types of scenario are proposed: pessimistic - when an enterprise - a pessimist - does not show risk exposure under this scenario when forming a digital counterpart; neutral - when an enterprise shows a neutral attitude to risk (indifference); optimistic - enterprise - optimist is exposed to risk, in particular the risk of untapped opportunities. The result is a set of optimal portfolios, each reflecting a particular position of the enterprise on the risks of untapped opportunities and a certain scenario of forming a portfolio structure, taking into account the relationship between the individual components of the risks of untapped opportunities. Highlighted the advantages of technology "digital twins" for business. Digital counterparts use the data obtained from sensors installed on production lines or on the basis of the final product to predict equipment malfunctions, optimize product quality and reduce the negative impact of production processes on the environment.

The purpose of this paper is to discuss the state of the art on models and methods for reliability optimization problems (ROPs) including reliability allocation, redundancy allocation and reliability-redundancy allocation. There are literally few surveys for reviewing the literature of the ROPs. Tillman et al. (1980) classified the related papers by system structure, problem type, and solution methods, separately. In another work, Tzafestas (1980) reviewed system reliability optimization models and the optimization techniques. Yearout (1986) reviewed the literature related to standby redundancy. Kuo (2000) studied the system reliability optimization based on system structure and solution methods. Kuo and Prasad (2004) overviewed system reliability optimization methods. Later, Kuo (2007) reviewed recent advances in optimal reliability allocation problems. The present study adds to the previous literature surveys and focuses mainly on papers after year 2000 but with a quick review on the previous works so that the readers become familiar with the existing approaches. This research investigates the literature from system structure, system performance, uncertainty state and solution approach standpoints, simultaneously.