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This study aimed at establishing fault tree analysis (FTA) using expert opinion to compute the probability of an event. To find the probability of the top event (TE), all probabilities of the basic events (BEs) should be available when the FTA is drawn. In this case, employing expert judgment can be used as an alternative to failure data in an awkward situation. The fuzzy analytical hierarchy process as a standard technique is used to give a specific weight to each expert, and fuzzy set theory is engaged for aggregating expert opinion. In this regard, the probability of BEs will be computed and, consequently, the probability of the TE obtained using Boolean algebra. Additionally, to reduce the probability of the TE in terms of three parameters (safety consequences, cost and benefit), the importance measurement technique and modified TOPSIS was employed. The effectiveness of the proposed approach is demonstrated with a real-life case study.

The inflow of refugees from Syria into Lebanon necessitates a robust and efficient healthcare system in Lebanon to withstand the growing demand for healthcare service. For this purpose, we evaluate the efficiency of healthcare system in Lebanon from 2000 through 2015 by applying a modified data envelopment analysis (DEA) model. We have selected four output variables: life expectancy at birth, maternal mortality ratio, infant mortality rate, and newly infected with HIV and two input variables: total health expenditure (% of GDP) and number of hospital beds. The findings of the paper show improvement in the efficiency of the healthcare system in Lebanon after the widespread of the health system reform in 2005. It also shows that reduction in health expenditure does not necessarily reduce efficiency if operational and technical aspect of the healthcare system is improved. The study infers that the healthcare system in Lebanon is capable of withstanding the increase in health demand provided further resources are made available and the existing technical and operational improvement are maintained.

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The millennium development goals (MDGs) were designed to realign national priorities towards human development of which healthcare is the foundation. An extension of the MDGs, the sustainable development goals (SDGs), has more recently been introduced and has become the core focus for Sub-Saharan Africa (SSA) regardless of her performance vis-à-vis the MDGs. A transition into accomplishing the SDGs without identifying the efficiency and determinants of the shortfall in achieving the MDGs is a flawed approach. This paper seeks to estimate the efficiency of healthcare systems in SSA based on health focused MDGs. We estimate the technical efficiency and total factor productivity of these systems, and rank the annual performance of SSA's healthcare systems from 2010 to 2015 using a robust data envelopment analysis (DEA) approach. Regression analysis is applied to the determinants of healthcare system efficiency. The DEA results show healthcare systems in SSA to be inefficient, with only three countries; Botswana in 2015, Rwanda in 2014 and 2015, and Tanzania in 2015; identified as efficient over the evaluated period. Failure to achieve technological advancements is the identified leading cause of a decrease in productivity. Scale inefficiency is determined to be the primary cause of technical inefficiency. The study also shows that governance measures, i.e., the rule of law and government efficacy, impact healthcare system efficiency more than public expenditure on health, indicating that the volume of resources invested in healthcare systems is not as important as the efficient management of the said resources in SSA countries.Keywords Healthcare system • Efficiency • Total factor productivity • Sub-Saharan Africa • Order-alpha • Data envelopment analysis Supplementary data associated with this article can be found at: https ://data.mende ley.com/datas ets/4ppyt 2bnx5 /draft ?a=28eeb 9dc-7e31-431e-8375-58f55 13b26 a7.