Applied Mathematics

The purpose of this article is to compute the reliability measures of an automobile assembly plant. An automobile assembly plant consists of five sub-systems working in series as: Vendor (supply steel metal and body parts), Weld shop, Paint shop, Assembly shop and Quality department. Weld shop and Assembly shop has the configuration 2-out-of -3: G and 1-out-of-3: F. Considered system can completely fail due to failure of any of the subsystems. It is also assumed that the system can fail due to machine failures. Machine failures can be major or minor. All failures follow exponential time distribution whereas all repairs follow general time distribution. Preventive maintenance policy has been applied to reduce the failure in the system. Risk analysis has been made which may occur due to the mistake of quality department in quality checks. Various reliability characteristics such as transition state probabilities, steady state behaviour, reliability, availability, M.T.T.F, sensitivity analysis and the cost analysis have been obtained using supplementary variable technique and Gumbel-Hougaard copula methodology. We also perform a parametric investigation which provides numerical results to show the effects of different system parameters to the reliability and MTTF which may be helpful to managerial staff of the industry in the decision making.

Rotation and radiation effects on MHD flow through porous media past an impulsively started vertical plate with variable temperature is studied here. The fluid considered is gray, absorbing-emitting radiation but a non- scattering medium. The governing equations involved in the present analysis are solved by the Laplace transform technique. The velocity, temperature and skin friction are studied for different parameters like Thermal Grashof number, Prandtl number, magnetic field parameter, rotation parameter, radiation parameter, permeability of porous media and time.

A subgroup is said to be weakly -normal in a group if there exists a subnormal subgroup such that and is -quasinormally embedded in . We give some conditions for supersolvability of finite groups .

In this article, we deal with the Holy Quran Miracles from the view point of Numbers. The research is a library one and has focused on the number 19. The Holy Book's depth of meaning and mysteries is something far well-known and has been interpreted and studied from different tenets. This research emphasis on the mathematically numerical relationship between different parts of the Chapters and verses of the wholly Book is novelty and purpose of this research.

This work reports the numerical study of MHD free convection boundary layer flow of Casson fluid brought by vertically inclined porous surface in presence of thermal radiation and chemical reaction effects. Darcian viscous flow model for the porous medium is employed and the Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. The homogeneous chemical reaction of first order is accounted in mass diffusion equation. The arising mathematically modelled non-linear partial differential equations of Casson fluid flow are successfully converted into linear coupled partial differential equations with the source of suitable transformation. The numerical solutions are computed through the application of finite difference method. The effect logs of an interesting physical parameters namely, Grashof number for heat and mass transfer, Magnetic field parameter, Permeability parameter, Prandtl number, Schmidt number, Thermal radiation parameter, Heat sink parameter, Chemical reaction parameter, Casson fluid parameter and Angle of inclination parameter number are discussed graphically. Further, the variations of skin-friction coefficient, heat and mass transfer rates are identified by way of tables. Comparison with the previous published literature is presented and an excellent agreement is reported.

In present paper an attempt is made to study the effect of radiative heat transfer term on the propagation of a weak shock in a two dimensional steady supersonic flow of non ideal gas along a curved wall. The flow phenomenon in characteristic plane is investigated and its behavior at the first frozen Mach wave is discussed .The position and condition of breakdown of the solution and condition necessary for no shock formation on the first frozen Mach line is also obtained and discussed. Using perturbation technique governing equation up to second order of approximation are obtained and from there it is concluded that for a set of boundary conditions at the shock waves homogeneous parts are same for first and second order approximation.

This investigation deals with the reliability of utensils processing unit. Utensils processing unit consists of six subsystems, viz., hot rolling machine, cold rolling machine, cutting machine, pressing machine, polishing machine and packaging machine, connected in 1-out-of-6: F arrangement system. Mathematical formulation of the model is carried out by employing Boolean Function Technique. Various measures of system effectiveness such as reliability and mean time to failure are obtained. Numerical results are also presented to demonstrate the validity of analyzed results. The failure rate is exponentially distributed.

In this Paper, the Fuzzy Transportation Problem is investigated with the aid of Triangular Fuzzy Numbers. A new relevant numerical example is included.

This investigation deals with finite population loss and delay multi server queue with no passing, discouragement and additional servers. The concept of no passing has its own consideration as the customers are permitted to leave the system in the same chronological order in which they join the system. Due to no-passing restrictions, the customers can be categorized into two types (i) those who do not need service even waiting in the queue and (ii) the customers having exponentially distributed service time. Also customer is assumed to be discouraged on seeing long queue at the service station. This discouraging behaviour of the customer puts the system to loss and the customer decides not to join the queue. To overcome such situations the system organigers may facilitate the additional removable server to provide faster service. Keeping this in view the above-mentioned factors have been included in this study. By using birth death rate and product type solution, queue size distribution is established, which is further employed to derive various performance indices namely expected waiting time, average number of customers in the system and the difference between the expected waiting time of both types of customers in the system.

This paper introduces the notion of the Generalization of Cartesian Product on Intuitionistic L-fuzzy H-ideals of BF-algebra and deals some simple but interesting results.