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Estimated parameters of 6 x 6 Latin square design consisting of two missing values
(2019-01-01)
Sirikasemsuk, Kittiwat
;
Thachongthumla, Kanokwan
A design of experiment is a computational technique which is used to select the significant independent variables. The well-designed experiments should reduce the experiment error. We referred to the blocking technique to prevent the error from other variables. This paper focused on the incomplete latin square design (ILSD) based on the blocking technique. The missing values from experiments caused the unbalance design in which the instant formulae were not provided for the analysis of the variance (ANOVA). By means of the exact approach, this paper considered the incomplete latin square design of order 6 x 6 with the two missing values to develop the mathematical formulae for the estimated parameters for full effect model. Finally, it is easy to make the ANOVA. It is noted that the mathematical formulae in this paper can be used to solve all indexes.
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Full-model regression sum of squares of randomized complete block design having one unrecorded observation
(2019-01-01)
Sirikasemsuk, Kittiwat
;
Leerojanaprapa, Kanogkan
;
Sirikasemsuk, Sirisak
In the classical design of experiment, a randomized complete block design (RCBD) is a helpful experimental design because this design uses a small number of experimental units. The randomized complete block design is comprised of two factors, i.e., a nuisance factor and a potential factor. In many real experiments, some data might be missing or unrecorded. The instant formulae were not provided for an analysis of variance in this case. This paper took into account the randomized complete block design (RCBD) with a treatments and b blocks. In this contribution, the RCBD with an unrecorded value was analyzed by means of the exact scheme with the model comparison approach. The advantages of the exact scheme are that the unrecorded value for the unfilled cell is not estimated and the treatment sum of squares is unbiased. It is important to note that there is no ready-made formula for RCBD in the past. Hence, this research paper provided the mathematical formulae for the fitted parameters and the overall regression sum of squares (ORSS) for the full model of experimental data. It is also noted that the ORSS is imperative for the analysis of the variance by means of the exact scheme.
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Warpage reduction through optimized process parameters and annealed process of injection-molded plastic parts
(2018-10-01)
Sudsawat, Supattarachai
;
Sriseubsai, Wipoo
The objective of this paper is to achieve the minimization of warpage for an injection molded part. The techniques that were implemented to minimize the warpage are the design of experiment (DOE), response surface methodology (RSM), firefly algorithm (FA), and annealing treatment. The packing time, cooling time, and melt temperature were shown to be significant parameters and FA was employed to seek these suitable values by experimental tests based on simulation software Moldex3D and injection machine. Analysis of variance (ANOVA) was used to validate experiments. Annealing treatment process was then applied to reduce more warpage phenomenon; the results showed that warpage phenomenon decreased dramatically compared with popular optimized parameter methodology. Moreover, the residual stress which was obtained by using photoelasticity showed that it has a direct relationship with warpage reduction. Therefore, the best solution of warpage mitigation can be solved by popular optimum process parameters and also annealing treatment.
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Analysis of two-missing-observation 4 × 4 latin squares using the exact approach
(2018-01-01)
Sirikasemsuk, Kittiwat
;
Leerojanaprapa, Kanogkan
This research deals with the analysis of incomplete Latin square designs using the exact approach. Specifically, the study investigated the 4 × 4 Latin square designs with two missing observations without replication. In the research, the general regression significance test (i.e. the exact approach) was used to derive the estimation formulae of fitted parameters for the full and reduced linear statistical models, thereby simplifying the calculation process. In addition, the proposed exact approach-based formulae facilitate the determination of the treatment sum of squares and the error sum of squares, both of which are subsequently employed in the analysis of variance (ANOVA).
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Measure of overall regression sum of squares of symmetric randomized complete block design with a lost observation
(2018-01-01)
Sirikasemsuk, Kittiwat
A randomized complete block design (RCBD) is useful for analyzing a treatment variable and one block variable under the condition where experimental units are limited. The RCBD is assumed that there is no interaction between the treatment variable and the block variable. This paper considered the symmetric randomized complete block design (SRCBD) with t treatments and t blocks, when a lost value occurs in the experiments. For the analysis of variance for the unbalanced data, the ready-made formulae were not provided in the past. The SRCBD with a lost value was analyzed by means of the fundamental underlying linear regression model in order to det ermine the reliable mathematical formulae for the fitted parameters and the overall regression sum of squares of e xperimental data. It is noted that all possible parameters are considered in the overall regression sum of squares which will be helpful for the analysis o f variance through the exact approach (the model comparison approach) at a later stage.

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