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The purpose of this paper is to evaluate the reliability and structure function of refrigeration complex system consisted of four components in complex manner.

Although, a variety of methodologies have been used to assess the refrigeration system's reliability function that has proven to be effective, the universal generating function approach is the basis of this research study, which is used in the calculation of a domestic refrigeration system with four separate components that are related in series and parallel with a corresponding sample to form a complex machine.

In this paper, signature reliability of the refrigeration system has been evaluated with the universal generating function technique. There are four components present in the proposed system in complex (series and parallel) manner. The tail signature, signature, Barlow–Proschan index, expected lifetime and expected cost of independent identically distributed are all computed.

This is the first study of domestic refrigeration system to examine the signature reliability with the help of universal generating function techniques with various measures. Refrigeration systems are an essential process in industries and home applications as they perform cooling or the maintain temperature at the desired value. A cycle of refrigeration consists of four main components such as, heat exchange, compression and expansion with a refrigerant flowing through the units within the cycle.

This paper aims to find the best tools to influence the improvement of sustainability in food supply chains (FSCs) by conducting a systematic review of articles. The reader will learn how the different industry 4.0 tools (I4.0T) benefit the FSC and the limitations of each tool.

A review of 436 articles published during the period 2019 to 2022 referenced in the Scopus and Web of Science databases was performed. The review was limited to articles published in English and directly related to Industry 4.0, circular economy and sustainability in the food supply chain.

The results show different contributions of I4.0, with some being more influential than others in improving sustainability in FSCs; for example, Internet of Things and Blockchain have been shown to contribute more toward transparency, traceability, process optimization and waste reduction.

The paper's contribution consisted of ranking according to their importance and the I4.0T that affect sustainability in FSCs by classifying the aspects of each tool and the sustainability factors through a categorization by the Analysis Hierarchy Process.