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The purpose of this paper is to study likelihood ratio order for mixture and its components via their Glaser’s functions for weighted distributions. So, some theoretical examples using exponential family and their mixtures are presented.

First, Glaser’s functions of mixture and its components for weighted distributions in different scenarios are computed. Then by them the likelihood ratio order is investigated between mixture and its components.

The authors find conditions for weight functions under which the mixture random variable is between of its components in likelihood ratio order.

Results are obtained for weight function in general. It is well known that the some special weights are order statistics, up and down records, hazard rate, reversed hazard rate, moment generating function, etc. So, the results are valid for all of them.

IT has been said that the trouble with a mathematical solution to an industrial problem is that it is, only too often, an exact solution to another problem. This state of affairs has arisen because of the number of simplifying assumptions that arc usually necessary before such a mathematical solution may be attempted. However, the writer holds the view that a mathematical solution tends to throw light upon the problem of design and hence, even when a number of assumptions are made, the results may serve as a guide to the designer where otherwise guess‐work, inspired by experience, would be the only course.

The purpose of this study is to propose and model an integrated production‐maintenance strategy for unreliable production systems producing conforming and non‐conforming items.

The proposed integrated policy is defined and modeled mathematically.

The paper focuses on finding simultaneously the optimal values of the lot size Q and the age T at which preventive maintenance must be performed. These values minimize the total average cost per time unit over an infinite horizon.

The paper attempts to integrate in a single model the three main aspects of any manufacturing system: production, maintenance, and quality. It deals with the lot‐sizing problem for a production system which may randomly shift to an out‐of‐control state and produce non‐conforming units. The system is submitted to an age‐based preventive maintenance policy. The effect of performing preventive maintenance on quality‐ and inventory‐related costs is shown through a numerical example.

The paper proposes an integrated model that links EMQ, quality and an age‐based preventive maintenance policy. It is shown that performing preventive maintenance yields reduction in inventory‐ and quality‐related costs.

The amount of scientific and technical information published annually in the form of journal articles, conference papers, reports, theses, patents, and books now greatly exceeds, in every field of interest, the amount which may be scanned by a scientist wishing to keep himself completely up to date in his own subject. For a scientist wishing to inform himself of new developments in neighbouring subject‐fields the problem is even greater. Consequently, either the scientist reconciles himself to the knowledge that he is not aware of all relevant information in his field or he places increasingly more reliance on such bibliographic tools as are available to guide him towards the relevant literature.

The salvation of human life is the goal of work for all rescue units. At the same time, a significant part of rescue operations is carried out in buildings or premises, which themselves are often in a state of destruction or are emergency ones. This paper aims to find how it is possible to carry out rescue operations in the face of the threat of constant collapse of the building.

To study the collapse hazard of the building, the information systems are used that display the process of rescue measures in case of a threat of deformation of the building in which there is a risk of burnback or destruction.

The findings show that the analysis of destruction parameters online allows using infrared sensors to form a picture of the allocation of places where people can be and thus saves lives while reducing the risk for the fire and rescue unit. To implement the presented format, it is proposed to use infrared sensors.

The use of infrared sensors allows online interaction with foci of dangerous situations and identifies the main aspects of the stratification of the preparation of the fire and rescue unit’s activities in conditions of increased danger.

This chapter aims at providing an understanding of the research and devlopment (R&D) process in the pharmaceutical industry, by exploring the methodological challenges and approaches in the assessment of the determinants of innovation in the pharmaceutical industry. It (i) discusses possible methodological approaches to model occurrence of events; (ii) describes in detail competing risks duration models as the best methodological option in light of the nature of pharmaceutical R&D processes and data; (iii) concludes with an estimation strategy and overview of potential covariates that have been found to correlate with the likelihood of failure of R&D pharmaceutical projects.

The purpose of this paper is to investigate the stochastic comparisons of the parallel system with independent heterogeneous Gumbel components and series and parallel systems with independent heterogeneous truncated Gumbel components in terms of various stochastic orderings.

The obtained results in this paper are obtained by using the vector majorization methods and results. First, the components of series and parallel systems are heterogeneous and having Gumbel or truncated Gumbel distributions. Second, multiple-outlier truncated Gumbel models are discussed for these systems. Then, the relationship between the systems having Gumbel components and Weibull components are considered. Finally, Monte Carlo simulations are performed to illustrate some obtained results.

The reversed hazard rate and likelihood ratio orderings are obtained for the parallel system of Gumbel components. Using these results, similar new results are derived for the series system of Weibull components. Stochastic comparisons for the series and parallel systems having truncated Gumbel components are established in terms of hazard rate, likelihood ratio and reversed hazard rate orderings. Some new results are also derived for the series and parallel systems of upper-truncated Weibull components.

To the best of our knowledge thus far, stochastic comparisons of series and parallel systems with Gumbel or truncated Gumble components have not been considered in the literature. Moreover, new results for Weibull and upper-truncated Weibull components are presented based on Gumbel case results.