Dairy Wastewater Treatment with Organic Coagulants: A Comparison of Factorial Designs

Optimization of coagulant dosage and pH to reduce the turbidity and chemical oxygen demand (COD) of synthetic dairy wastewater (SDW) was investigated using a full factorial design (FFD) and full factorial design with center point (FFDCP). Two organic coagulants, polyacrylamide (PAM) and Tanfloc were used. The optimal values of coagulant dosage and pH were determined using a multiple response optimization tool and desirability function. The results obtained revealed that the optimum condition for removing turbidity and COD were at pH 5.0 using 50 mg L−1 of coagulant. The same optimum point was obtained in both experimental designs, indicating a good agreement between them. In optimum conditions, the expected removal of turbidity was above 98% with PAM and above 95% with Tanfloc. The estimated COD removal was above 72% with PAM and above 65% with Tanfloc. The addition of center points with replicates in the factorial design allowed to obtain the estimate of the experimental error with a smaller number of runs, allowing to save time and cost of the experimental tests. Moreover, the addition of center points did not affect the estimates of the factorial effects and it was possible to verify the effect of curvature, allowing obtaining information about the factors at intermediate levels.

Comparative Analysis of Mono-Factorial Effects on Compressive Strength of Sandcrete Block Produced at Various Curing Age in the Warm Humid Climate of Nigeria

Quality of a composite material like sandcrete block is basically a function of the basic properties of the constituent ingredients, mix ratio relationship and its production characteristics. This study, investigate the effects of change in quantities of the constituent ingredient on compressive strength of sandcrete blocks produced at various curing ages in Owerri Metropolis. Field survey was conducted in the area to determine the production characteristics of the blocks marketed in the area. Based on the prevalent nominal mix ratio of the block, mix design on the constituent ingredients of the block based on box-wilson symmetric composite plan B3was adopted. Results of the strength from each experimental set of the design were used to formpolynomial regression models of blocks cured at various ages. Findings show that the average compressive strengths of the 7-day, 14-day, and 28-day old cured blocks are 1.578 N/mm2, 1.604 N/mm2, and 1.975 N/mm2.Mono-factorial analysis shows that at its respective age of curing, cement and water factors have stronger effect on the strength of the block than sand factor. The nature of their influences is positive, and more linear than quadratic and mutual interaction relationships. The relationship of mutual interaction between the cement and water factors is seen only in the models of the 7-day and 28-day curing ages in the study. Since the strength of the block increases with increase in the age of curing, it therefore confirms the standard practice of 28-day curing age for improved quality of sandcrete block in the industry; as well as recommending mono-factorial analyses on the effects of the independent factors of the mix designed blocks cured age 28-day age, towards optimum composition of the sandcrete mix ingredients for the desired quality of the blocks produced in the study area.

Sharpening randomization-based causal inference for 22 factorial designs with binary outcomes

In medical research, a scenario often entertained is randomized controlled 22 factorial design with a binary outcome. By utilizing the concept of potential outcomes, Dasgupta et al. proposed a randomization-based causal inference framework, allowing flexible and simultaneous estimations and inferences of the factorial effects. However, a fundamental challenge that Dasgupta et al.’s proposed methodology faces is that the sampling variance of the randomization-based factorial effect estimator is unidentifiable, rendering the corresponding classic “Neymanian” variance estimator suffering from over-estimation. To address this issue, for randomized controlled 22 factorial designs with binary outcomes, we derive the sharp lower bound of the sampling variance of the factorial effect estimator, which leads to a new variance estimator that sharpens the finite-population Neymanian causal inference. We demonstrate the advantages of the new variance estimator through a series of simulation studies, and apply our newly proposed methodology to two real-life datasets from randomized clinical trials, where we gain new insights.

On the Existence Conditions for Balanced Fractional $2^{m}$ Factorial Designs of Resolution $\mathrm{R}^{\ast}(\{1\}|\mathrm{\Omega}_{\ell})$ with $N<\nu_{\ell}(m)$

We consider a fractional $2^{m}$ factorial design derived from a simple array (SA) such that the $(\ell+1)$-factor and higher-order interactions are assumed to be negligible, where $2\ell\le m$. Under these situations, if at least the main effect is estimable, then a design is said to be of resolution $\mathrm{R}^{\ast}(\{1\}|\mathrm{\Omega}_{\ell})$. In this paper, we give a necessary and sufficient condition for an SA to be a balanced fractional $2^{m}$ factorial design of resolution $\mathrm{R}^{\ast}(\{1\}|\mathrm{\Omega}_{\ell})$ for $\ell=2,3$, where the number of assemblies is less than the number of non-negligible factorial effects. Such a design is concretely characterized by the suffixes of the indices of an SA.