Research Article
Identification of the Out-of-Control Variable on a Multivariate Control Chart Signals in Iron Sheet Production Process
Issue:
Volume 8, Issue 1, December 2024
Pages:
1-7
Received:
24 July 2024
Accepted:
15 August 2024
Published:
11 September 2024
Abstract: Monitoring and diagnosis of an out of control signals in manufacturing processes has become more challenging when it involves two or more correlated variables. In any production process and in the manufacturing industry, regardless of how well designed or carefully maintained it is, a certain amount of inherent or natural variability will always exist. The natural variability is the cumulative effect of many small, essentially unavoidable causes. A process that is operating with only chance causes of variation present is said to be in statistical control. In this paper we propose a method for approaching this problem based on principal components analysis. The principal component analysis method based on the ratios form was used to investigate which of the variable(s) were responsible for the out-of-control signal. A display of matrix of scatter plots was applied to investigate the correlation between the process variables and ellipses were used an approximate control limits. The principal component scores were used as an empirical reference distribution to establish a control region for the process to detect the variables causing the out-of-control signal. These insights derived from the principal component analysis offered valuable cues for identifying potential signals of an out-of-control process. The study findings indicated distinctive patterns of variance within the data, shedding light on potential signals for an out-of-control process.
Abstract: Monitoring and diagnosis of an out of control signals in manufacturing processes has become more challenging when it involves two or more correlated variables. In any production process and in the manufacturing industry, regardless of how well designed or carefully maintained it is, a certain amount of inherent or natural variability will always ex...
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Research Article
Suborbital Graphs Involving the Action of the Direct Product of Alternating and Cyclic Groups on the Cartesian Product of Two Sets
Issue:
Volume 8, Issue 1, December 2024
Pages:
8-17
Received:
17 September 2024
Accepted:
6 October 2024
Published:
31 October 2024
Abstract: The combinatorial properties and invariants which includes transitivity, primitivity, ranks and subdegrees of direct product of Alternating group and Cyclic group acting on Cartesian product of two set have been extensively studied. However, the construction of suborbital graphs for this group action remains largely unexplored. As a result, this research paper addresses this gap by constructing suborbital graphs involving direct product of the Alternating group and Cyclic group acting on the Cartesian product of two sets where their respective properties such as connectivity, self-pairedness, girth and vertex degree are analyzed in detail. First, the result shows that all suborbits are self − paired implies that the vertex sets are undirected to each other. Secondly, the constructed suborbital graphs are classified into three parts for any value of n ≥ 3. In part A, it is proven that the constructed suborbital graphs Γ1, Γ2, Γ3,..., Γ(n−1) are undirected, regular of degree (n−1), disconnected with n−connected components and has a girth of 3. In part B, the constructed suborbital graph Γ(n−1)+1 is found to be undirected, regular of degree (n − 1), disconnected with n − connected components and has a girth of 3. Lastly in part C, the graphs Γ(n−1)+2, Γ(n−1)+3, Γ(n−1)+4,..., Γ(n−1)+n are found to be undirected, regular of degree (n − 1)2, disconnected with n2− connected components and has a girth of 3.
Abstract: The combinatorial properties and invariants which includes transitivity, primitivity, ranks and subdegrees of direct product of Alternating group and Cyclic group acting on Cartesian product of two set have been extensively studied. However, the construction of suborbital graphs for this group action remains largely unexplored. As a result, this re...
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Hellen Wanjiru Waititu
