The quality of goods and services can be improved if data sets are collected to determine the causes of variation. In this consideration, the data sets will enable the analyst to evaluate the stability of the manufacturing process. However, the purpose of applying any control chart is to identify the occurrence of special causes of variation that emanate from external source of the normal process. Although, the vital aspect of variations is that it reveals the strength and weakness of the process thereby providing means of improving the system. This also provides opportunity to repair and adjust the system due to special causes, though if such exist. In this discussion, the x bar chart and the T2 chart are applied to investigate the quality of ash content in flour production. The analysis is based on the data set obtained revealed that the two procedures showed that the ash content used in producing the flour is stable otherwise the process is in control.
This paper is coined to investigate the performance of students based on two semesters’ examination scores. The objective of this discussion is to determine whether the performance of students is based on each examination taken or performance is based on each semester. Being a variable data, we applied the and control charts to determine the performance of each student. The and control charts are practicable to determine students’ performance. The analysis revealed that an observation exceeding the upper control limit indicates that the student is an exceptional student in terms of the average. The contrary is also true for a student with an average below the lower control limit. In this case, a student whose average is below the lower control limit should be invited by the level adviser or the institutions counseling unit for counseling and possibly inquiry on his/her predicament, this will enable the analyst to proffer advise that will assist the student to overcome his/her academic challenges and possibly improve. In general, the analysis based on the control charts revealed that students’ performance fluctuates from semester to semester.
An interactive approach is proposed to find the optimal fuzzy solution of fully fuzzy multi-level linear programming (FFMLLP) problem. Firstly, convert the problem under consideration into non-fuzzy multi-level multi-objective linear programming (MLMOLP) problem by using the bound and decomposition method. Secondly, simplify the MLMOLP problem by transforming it into separate multi-objective decision-making problems with hierarchical structure, and solving it by using ε-constraint method. The main results obtained in this paper will be explained by an illustrative numerical example. Finally, compare the proposed approach for solving FFMLLP with The result found in O. Emam et al.  to show its effectiveness.
Let 0 < p ≤ 1 and w in the Muckenhoupt class Ap,ν . In this paper, we will characterize the weighted Hardy spaces in the setting of the Laplace-Bessel differential operators by means of the high order Riesz-Bessel transforms generated by generalized shift operator. We give the elemantary result that for certain weight functions w. We also obtain the boundedness of high order Riesz-Bessel transform within the bounds of some necessary conditions through the atomic-molecular characterization.