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This research formulates, and numerically quantifies the optimal response that can be discovered in a design space characterized by main effects, and two-way and three-way interactions. In an experimental design setup, this can be conceptualized as the response of the best treatment combination of a $$2^k$$ 2 k full factorial design. Using Gaussian and Uniform priors for the strength of main effects and interaction effects, this study enables a practitioner to make estimates of the maximum possible improvement that is possible through design space exploration. For basic designs up to two factors, we construct the full distribution of the optimal treatment. Whereas, for values of $$k\ge 3$$ k ≥ 3 , we analytically formulate two indicators of a greedy heuristic of the expected value of the optimal treatment. We present results for these formulations up to $$k=7$$ k = 7 factors and validate these through simulations. Finally, we also present an illustrative case study of the power loss in disengaged wet clutches, which confirms our findings and serves as an implementation guide for practitioners.

This paper seeks to evaluate the impact of the removal of restrictions (partial and complete) imposed during COVID-19-induced lockdowns on property offences such as robbery, burglary, and theft during the milder wave one and the more severe wave two of the pandemic in 2020 and 2021, respectively. Using 10-year data of the daily counts of crimes, the authors adopt an auto-regressive neural networks method to make counterfactual predictions of crimes, representing a scenario without the pandemic-induced lockdowns. The difference between the actual and forecast is the causal impact of the lockdown in all phases. Further, the research uses Google Mobility Community Reports to measure mobility. The analysis has been done at two levels: first, for the state of Tamil Nadu, which has a sizeable rural landscape, and second for Chennai, the largest metropolitan city with an urban populace. During the pandemic-induced lockdown in wave one, there was a steep decline in the incidence of property offences. On removing restrictions, the cases soared above the counterfactual predicted counts. In wave two, despite the higher severity and fatality in the COVID-19 pandemic, a similar trend of fall and rise in property cases was observed. However, the drop in mobility was less substantial, and the increase in the magnitude of property offences was more significant in wave two than in wave one. The overall trend of fluctuations is related to mobility during various phases of restrictions in the pandemic. When most curbs were removed, there was a surge in robberies in Tamil Nadu and Chennai after adjusting for mobility. This trend highlights the effective increase in crime due to pandemic-related economic and social consequences. Further, the research enables law enforcement to strengthen preventive crime work in similar situations, when most curbs are removed after a pandemic or other unanticipated scenarios.

The use of Association Rule Mining techniques in diverse contexts and domains has resulted in the creation of numerous interestingness measures. This, in turn, has motivated researchers to come up with various classification schemes for these measures. One popular approach to classify the objective measures is to assess the set of mathematical properties they satisfy in order to help practitioners select the right measure for a given problem. In this research, we discuss the insufficiency of the existing properties in literature to capture certain behaviors of interestingness measures. This motivates us to present a novel approach to analyze and classify measures. We refer to this as a rate of change analysis (RCA). In this analysis a measure is described by how it varies if there is a unit change in the frequency count $(f_{11},f_{10},f_{01},f_{00})$, for different pre-existing states of the frequency counts. More formally, we look at the first partial derivative of the measure with respect to the various frequency count variables. We then use this analysis to define two new properties, Unit-Null Asymptotic Invariance (UNAI) and Unit-Null Zero Rate (UNZR). UNAI looks at the asymptotic effect of adding frequency patterns, while UNZR looks at the initial effect of adding frequency patterns when they do not pre-exist in the dataset. We present a comprehensive analysis of 50 interestingness measures and classify them in accordance with the two properties. We also present empirical studies, involving both synthetic and real-world datasets, which are used to cluster various measures according to the rule ranking patterns of the measures. The study concludes with the observation that classification of measures using the empirical clusters share significant similarities to the classification of measures done through the properties presented in this research.

This paper explores the use of designed experiments in an online environment. Motivated by real-world examples, we model a scenario where the practitioner is given a finite set of units and needs to select a subset of these which are expended toward a one-shot, multi-factor designed experiment. Following this phase, the designer is left with the remaining set of unused units to implement any learnings from the experiments. With this setting, we answer the key design question of how much to experiment, which translates to choosing the number of replicates for a given design. We construct a Bayesian framework that captures the expected cumulative gain across the entire set of units. We derive theoretical results for the optimal number of replicates for all two-level, full and fractional factorial designs with seven factors or fewer. We conduct simulations that serve as validation of the theoretical results, as well as enabling us to explore scenarios and techniques of analysis that are not captured in the theoretical studies. Our overall results indicate that the optimal allocation of units for experimentation varies from 1 to $$20\%$$ 20 % of the total units available, which is mainly governed by the experimental environment and the total number of units. We conclude that experimenting with the optimal number of replicates recommended by our study can lead to a cumulative improvement which is 80–95% greater than the expected cumulative improvement gained when a practitioner chooses the number of replicates randomly.