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Joint reliability importance (JRI) of components is the effect of a change of their reliability on the system reliability. The authors consider two coherent multi-component systems – a series-in-parallel (series subsystems arranged in parallel) and a parallel-in-series (parallel subsystems arranged in series) system. It is assumed that all the components in the subsystems are independent but not identically distributed. The subsystems do not have any component in common. The paper aims to discuss these issues.

For both the systems, the expressions for the JRI of two or more components are derived. The results are extended to include subsystems where some of the components are replicated.

The findings are illustrated by considering bridge structure as a series-in-parallel system wherein some of the components are repeated in different subsystems. Numerical results have also been provided for a series-in-parallel system with unreplicated components. JRI for various combinations of components for both the illustrations are given through tables or figures.

Chang and Jan (2006) and Gao et al. (2007) found the JRI of two components of series-in-parallel system when the components are identical and independently distributed. The authors derive the JRI of m=2 components for series-in-parallel and parallel-in-series systems when components are independent but need not be identically distributed. Expressions are obtained for the above-mentioned systems with replicated and unreplicated components in different subsystems. These results will be useful in analyzing the joint effect of reliability of several components on the system reliability. This will be of value to design engineers for designing systems that function more effectively and for a longer duration.

The purpose of this paper is to evaluate the reliability and signature reliability of solar panel k-out-of-n-multiplex system with the help of universal generating function.

Energy scarcity and global warming issues have become important concerns for humanity in recent decades. To solve these problems, various nations work for renewable energy sources (RESs), including sun, breeze, geothermal, wave, radioactive and biofuels. Solar energy is absorbed by solar panels, referred to as photovoltaic panels, which then transform it into electricity that can be used to power buildings or residences. Remote places can be supplied with electricity using these panels. Solar energy is often generated using a solar panel that is connected to an inverter for power supply. As a result, a converter reliability evaluation is frequently required. This paper presents a study on the reliability analysis of k-out-of-n systems with heterogeneous components. In this research, the universal generating function methodology is used to identify the reliability function and signature reliability of the solar array components. This method is commonly used to assess the tail signature and Barlow-Proschan index with independent and identically distributed components.

The Barlow-Proschan index, tail signature, signature, expected lifetime, expected cost and minimal signature of independent identically distributed are all computed.

This is the first study of solar panel k-out-of-n-multiplex systems to examine the signature reliability with the help of universal generating function techniques with various measures.

The purpose of this paper is to introduce some basic knowledge of statistical learning theory (SLT) based on random set samples in set‐valued probability space for the first time and generalize the key theorem and bounds on the rate of uniform convergence of learning theory in Vapnik, to the key theorem and bounds on the rate of uniform convergence for random sets in set‐valued probability space. SLT based on random samples formed in probability space is considered, at present, as one of the fundamental theories about small samples statistical learning. It has become a novel and important field of machine learning, along with other concepts and architectures such as neural networks. However, the theory hardly handles statistical learning problems for samples that involve random set samples.

Being motivated by some applications, in this paper a SLT is developed based on random set samples. First, a certain law of large numbers for random sets is proved. Second, the definitions of the distribution function and the expectation of random sets are introduced, and the concepts of the expected risk functional and the empirical risk functional are discussed. A notion of the strict consistency of the principle of empirical risk minimization is presented.

The paper formulates and proves the key theorem and presents the bounds on the rate of uniform convergence of learning theory based on random sets in set‐valued probability space, which become cornerstones of the theoretical fundamentals of the SLT for random set samples.

The paper provides a studied analysis of some theoretical results of learning theory.

Considers trend testing in the context of reliability/survival applications. Suggests that the very common tendency in reliability testing to fit lifetime distributions to reliability/maintenance data might occasionally be invalid. Details the appropriate methods to assess the validity, or otherwise, of such a procedure. More specifically, discusses ROCOF curves and the Laplace test for trend, and demonstrates their use by means of a practical, reliability example.

Bounds on the rate of convergence of learning processes based on random samples and probability are one of the essential components of statistical learning theory (SLT). The constructive distribution‐independent bounds on generalization are the cornerstone of constructing support vector machines. Random sets and set‐valued probability are important extensions of random variables and probability, respectively. The paper aims to address these issues.

In this study, the bounds on the rate of convergence of learning processes based on random sets and set‐valued probability are discussed. First, the Hoeffding inequality is enhanced based on random sets, and then making use of the key theorem the non‐constructive distribution‐dependent bounds of learning machines based on random sets in set‐valued probability space are revisited. Second, some properties of random sets and set‐valued probability are discussed.

In the sequel, the concepts of the annealed entropy, the growth function, and VC dimension of a set of random sets are presented. Finally, the paper establishes the VC dimension theory of SLT based on random sets and set‐valued probability, and then develops the constructive distribution‐independent bounds on the rate of uniform convergence of learning processes. It shows that such bounds are important to the analysis of the generalization abilities of learning machines.

SLT is considered at present as one of the fundamental theories about small statistical learning.

Definitions of pooling effects in insurance companies may convey the impression that the achieved risk reduction effect will be beneficial for policyholders, since typically lower premiums are paid for the same safety level with an increasing number of insureds, or a higher safety level is achieved for a given premium level for all pool members. However, this view is misleading and the purpose of this paper is to reexamine this apparent merit of pooling from the policyholder's perspective.

This is achieved by comparing several valuation approaches for the policyholders' claims using different assumptions of the individual policyholder's ability to replicate the contract's cash flows and claims.

The paper shows that the two considered definitions of risk pooling do not offer insight into the question of whether pooling is actually beneficial for policyholders.

The paper contributes to the literature by extending and combining previous work, focusing on the merits of pooling claims (using the two definitions above) from the policyholder's perspective using different valuation approaches.

The purpose of this paper is to investigate how queueing theory has been applied to derive results for a Sparre Andersen risk process for which the claim inter‐arrival distribution is hyper Erlang.

The paper exploits the duality results between the queueing theory and risk processes to derive explicit expressions for the ultimate ruin probability and moments of time to ruin in this renewal risk model.

This paper derives explicit expressions for the Laplace transforms of the idle/waiting time distribution in GI/HE_r(k_i,λ_i)/1 and its dual HE_r(k_i,λ_i)/G/1. As a consequence, an expression for the ultimate ruin probability is obtained in this model. The relationship between the time of ruin and busy period in M/G/1 queuing system is used to derive the expected time of ruin.

The study of renewal risk process is mostly concentrated on Erlang distributed inter‐claim times. But the Erlang distributions are not dense in the space of all probability distributions and therefore, the paper cannot approximate an arbitrary distribution function by an Erlang one. To overcome this difficulty, the paper uses the hyper Erlang distributions, which can be used to approximate the distribution of any non‐negative random variable.

The demand of cement in India is expected to increase rapidly as the government has been giving immense boost to various housing facilities, infrastructure projects, road networks and railway corridors. One of the ways to meet this rise in the demand of cement is to increase the capacity utilization of the existing cement plants by improving their availability. The availability of a cement plant can be improved by avoiding failures and reducing maintenance time through reliability, availability and maintainability (RAM) analysis of its subsystems. The paper aims to discuss this issue.

The data related to time between failure (TBF) and time to repair (TTR) of all the critical subsystems of a cement plant were collected over a period of two years for carrying out RAM analysis. Trend test and serial correlation test were performed on TBF and TTR data to verify whether these data are independent and identically distributed or not. Afterwards, the authors use EasyFit 5.6 professional software to find best-fit distribution of TBF and TTR data and their parameters. The effectiveness of a preventive maintenance policy was evaluated by simulating the real and proposed systems.

The results of the analysis show that the raw mill and the coal mill are critical subsystems of a cement plant from a reliability point of view, whereas the kiln is a critical subsystem from an availability point of view. The analysis shows that the repair time of the cement mill should be reduced for improving the availability of the cement plant. The RAM analysis showed that the capacity of the case study company is 17 percent underutilized due to maintenance-related problems and 15 percent underutilized because of management-related problems.

The study exhibits the usage of RAM analysis in deciding preventive maintenance programs of several cement plant subsystems. Thus, it would serve as a reference for reliability and maintenance managers in deciding maintenance strategies of cement plants as well as in improving their capacity utilization.

The study exhibits the usage of RAM analysis in deciding preventive maintenance programs of several cement plant subsystems. Even more, using a simulation study, the authors show that preventive maintenance of the cement plant beyond a certain level can be disadvantageous as it leads to an increase in downtime and decrease in availability.