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Optimal tariff strategies, with and without optimal responses, are derived, based on a linear partial equilibrium trade model, A, and a nonlinear general equilibrium trade model with two nations, B. Under free trade, models A and B are applied to prove that it is always profitable for one nation, N1, to introduce a strictly positive tariff on imports, T1, if other nations do not introduce tariffs. With model B, it is proved that it is rational also for nation N2, to introduce a tariff, T2, if N1, introduces a tariff, T1. The Nash equilibrium tariff combination is unique and stable. The economic results, in both nations, are however higher with free trade, than in the Nash equilibrium tariff solution. If both nations know that the other nations will respond to increasing tariffs, and select the optimal tariff, then it is not rational for any nation to leave free trade and introduce tariffs. Free trade agreements are rational for the participants. It is also shown that it may be rational for a dictator, to introduce a tariff, even if this is not rational for the consumers in the same nation. The dictator may keep the tariff revenues and use these for other purposes. In such a case, the tariff reduces the consumer surpluses in both nations.

Keywords: Optimal tariffs, international trade, Nash equilibrium, Free trade, Dynamic non- zero-sum game theory.

In this paper, various foldover designs are constructed from 16-run two-level fractional factorial designs developed by Li and Lin (2003). They state that for any core foldover plan there exist 2?????????equivalent foldover plans. These equivalent foldover plans yield designs that are identical in terms of minimum aberration optimality criterion. Minimum aberration criterion alone does not necessarily guarantee comparable performance under practical considerations. Therefore, these equivalent plans obtained from 16 run foldover designs are further compared based on additional criteria of clear factor interaction, trend resistance and number of level changes. The objective of the research is to find optimal foldover designs using four criteria namely minimum aberration, clear factor interactions, minimum number of level changes and trend resistance.

Keywords: Fractional factorial design, Foldover plans, Equivalent designs, Number of level changes, trend free designs.
Subject Classification Code: 62K05.

Pneumonia continues to be the foremost infectious contributor to global mortality across all age groups, with a particularly heavy burden of deaths occurring among children younger than five years worldwide. Beyond its direct health consequences, the disease imposes profound social and economic burdens on affected individuals, families, communities, and the broader society. In response to this public health challenge, the State government has committed considerable financial resources to the health sector through the Ministry of Health. These efforts are particularly focused on the provision of free healthcare services for vulnerable populations, including children, older adults, and pregnant women, with the overarching goal of preventing avoidable deaths from preventable diseases. This study aims to evaluate the impact of government interventions on the prevalence of childhood pneumonia by employing an appropriate time-series analytical approach. The findings indicate that before the implementation of the intervention, 2,609 cases of pneumonia were recorded among children, whereas 596 cases were documented during the post-intervention period. The study identified 3,243 pneumonia cases among children aged 0 to 14 years. A value of 19.5285 for the impact parameter shows that the intervention failed because the number of admissions increased after the intervention. The postintervention admissions fluctuated between a minimum of 10 and a maximum of 34, which is wider than the fluctuation recorded before the intervention. The estimated onset effect of the intervention, valued at 20, is equivalent to its long-term impact. This equivalence further substantiates that the intervention produced an instantaneous and abrupt effect.

Keywords: Paediatric Pneumonia, Impact analysis, Government's intervention.
AMS Classification: 62M10, 62P10.

For a univariate / multivariate production process, an ‘Improved Control Chart with Two Levels of inspection’ to detect changes in the target value (ICCTL) is proposed. For univariate processes, target value may be the processes mean, process fraction defective etc. For multivariate processes, target value may be a mean vector. Like in MIL-STD-105-E sampling plan, two levels of inspections namely ‘Reduced’ and ‘Tightened’ are used to develop ICCTL. Corresponding expressions for ‘Average Run Length’ (ARL) and ‘Average Time to Signal’ (ATS) of ICCTL are obtained. It is numerically illustrated that ICCTL performs significantly better as compared to the related control charts.

Key Words: Control Limits, Average Run Length, Average Time to Signal, Synthetic control chart, GR control chart.
MSC 2020 subject classification: 62P30.