A probabilistic early fault detection model for a feedback machining system with multiple types of spares.

This paper studies corrective and preventive maintenance to provide a quality control policy. The corrective maintenance, depending on the time, of a feedback machining system model with a finite source and standbys is presented. Moreover, the system has a known number of servers to repair the damaged units, and it contains an inspector to ensure the maintenance quality of the repaired units. The exact value of the probability of n units in the system will be obtained by using an efficient algorithm that depends on the Laplace transformation. To promote the concept of preventive maintenance, we use this probability to get the probability of early fault detection as a function of time and in the steady state. The applicability of this model is discussed for different system capacities.

Developing a detection model for a COVID-19 infected person based on a probabilistic dynamical system.

This paper presents a novel model to detect the COVID-19 infected person from a Markovian feedback persons in a limited department capacity. The persons arrive one by one to the department and the balking and the retention of reneged person approaches are considered. There exists one server presents the service to these persons according to first-come, first-served (FCFS) discipline. An efficient and novel algorithm is presented to get the exact value of the probability of n persons in the department at any time interval. This algorithm depends on the Laplace transform to solve a probabilistic dynamical system of differential equations. By considering the exponential detection function and if the probability of the infected person in the department is equal to the probability of each one, then this algorithm is useful to obtain the detection probability of the infected one. Under steady state, the detection probability of the infected person is described. The usefulness of this model is illustrated for different capacities by using a numerical example to describe the behavior of probabilities of the persons in the department, the detection probabilities of the infected person as functions in time, and the mean time to detection.

Detection of an appropriate pharmaceutical company to get a suitable vaccine against COVID-19 with minimum cost under the quality control process.

Some international pharmaceutical companies have succeeded in producing vaccines against COVID-19. Countries all over the world have aimed to obtain these vaccines with minimum cost. We consider a set of K-independent Markovian waiting lists. Each list contains a set of countries, where each one of them has an exponential service time and a Poisson arrival process. These companies differ in some characteristics such as the vaccine production cost and the speed of the required quantity delivery. We present a new detection model that helps in providing an appropriate decision to choose a suitable company. Moreover, the concept of balking and the retention of reneged countries is taken into consideration under the quality control process of each waiting list. Under steady state, we face an interesting and difficult discrete stochastic optimization problem. Its solution gives an optimal distribution of the searching effort, which is bounded by a known probability distribution. A simulation study has been derived to get the minimum value of the paid cost random values. The highest service rate, the total expected profit of each queuing system, and the optimum performance measures, which depend on this cost, have been obtained to show the effectiveness of this model.