Reliability is a primary concern in industrial manufacturing because operational interruptions can reduce production, cause substantial economic losses, and create workplace-safety risks. This study applies the two-parameter Weibull distribution and the regenerative point technique (RPT) to a repairable system comprising two non-identical units: a primary unit operating in parallel with a secondary unit arranged in cold standby. The model incorporates inspection, repair, and replacement activities and is used to derive transition probabilities, mean sojourn times, mean time to system failure (MTSF), steady-state availability, maintenance busy periods, and a profit function. Numerical results show that system profitability decreases as the failure rate and Weibull shape parameter increase, whereas a higher repair rate improves profitability. For the reported parameter set, profit increases from 7325.258 to 8726.043 when the repair rate rises from 0.1 to 1.0 at a=0.01, and from 4879.802 to 6970.602 at a=0.05. The analysis also identifies reported zero-profit thresholds near a=1.45, 1.38, and 1.21 for k=0.8, 1.0, and 2.0, respectively. The framework supports maintenance planning and economic assessment of multi-state repairable systems.

Low back pain (LBP) is a significant health and economic problem among populations in high-resource countries. LBP is one of the prevalent complaints among all age groups. Objective: To assess the frequency of low back pain (LBP) among medical and its impact on their daily activities and life while exploring potential associations with socio-demographic factors, exercise habits, pain-relieving consumption, history of spine trauma, and body mass index (BMI) Methods: A retrospective survey was conducted at Bilawal Medical College (BMC) among first year to final year MBBS students. Data was collected during the period of January 2022 to February 2023 using a questionnaire created on Google Form that included questions regarding the information on socio-demographic characteristics and factors such as exercise, pain-relieving consumption, any history of spine trauma, specific questions pertaining to LBP pain frequency and issues. Results: A total of 62 medical students participated in the study, of which about half were in their fourth year (50.0%), followed by the third year (20.9%) of medical school. The 20–24 age group accounted for most individuals (64.5%), followed by the 25–30-year-old age group (33.9%). Only 25.8% of the participants were overweight, defined as having a BMI of more than 25 kg/m2. Conclusion: It was concluded that low back pain is one of the most frequent health crises among medical students. Students from senior academic years reported more frequent lower back pain, which was highly significant due to increased mental stress and increased physical strain due to clinical learning. Additionally, it was found that there is no potential link between BMI and a history of spine trauma on the frequency of lower back pain or its impact on the medical student's life and their daily activities.

The initiative of this paper is to present the Runge Kutta Type technique for the development of mathematical solutions to the problems concerning to ordinary differential equation of order six of structure v vi = f(u, v, v′ ) denoted as RKSD with initial conditions. The three and four stage Runge-Kutta methods with order conditions up to order seven (RKSD7) have been designed to evaluate global and local truncated errors for the ordinary differential equation of order six. The framework and evaluation of equations with their results are well established to obtain the effectiveness of RK method towards implicit function satisfying the required initial conditions and for obtaining zero-stability of RKSD7 in terms of their accuracy with maximum precision under minimal processing.

The present paper aims at providing an insight to embedded Runge-Kutta sixth order (RKSD) ordinary differential equation method for solving the initial value problem of order six of type vvi(u) = f(u, v, v', v'',v''',viv). The concept of order conditions for the three and four stages up to the eighth and ninth orders, respectively, is designed and evaluated; furthermore, the zero-stability of the proposed method is proved. Comparisons are made between these orders with the help of a mathematical example, and global and local truncated error norms are evaluated.

The present paper presents the numerical conclusion to solve sixth order initial value ordinary differential equation (ODE). The concept of order conditions for three stage eighth order (RKSD8) & four stage ninth order Runge-Kutta methods (RKSD9) has been derived for finding global truncation error of differential equation The global and local truncated errors norms, zero stability of extended Runge-Kutta method (RK) is well defined and demonstrated with the help of an example.

This paper elaborates on the approach towards reliability analysis for the active redundant system with a dual nature of repair strategy according to the kind of failure. The reliability characteristics using regenerative techniques are analyzed stochastically for the system, which includes two parallel units acting in an active redundancy form. A transition model has been designed for the working mechanism discussed in the paper and evaluated with the help of a geometric distribution possessing distinct repair. Regenerative techniques and geometric distribution were used to derive the numerical equations for reliability parameters such as availability, mean time to system failure, and repair mechanisms following down period of the system. A graphical analysis of the repair/failure rate with respect to the profit function has also been presented.

The present paper provides an innovative approach in developing numerical structure with minimal processing and maximum precision for sixth order ordinary differential equation satisfying underlying associated initial conditions. The algebraic order conditions for the three stage eighth order Runge-Kutta methods (RKSD8) been well designed for evaluating local and global truncated errors towards sixth order ordinary differential equation having form vvi = f (u,v,v',v''). The convergence of a numerical method is well explained and proved beneficial in evaluating norms of error and zero stability of RKSD8 with effective values of weights and nodes in the form of Butcher tableau.

The present paper had analyzed the reliability of a real-life working mechanism having two units arranged in parallel form and following the cold standby redundancy technique. The repair mechanism includes inspection/repair policy for normal and major repair service according to the nature of failure. Initially One unit is in operative mode, while the other is in passive mode. The new notion of having a repairman has two aspects: checking small failures and being able to repair routine failures. Furthermore, inspecting the repaired equipment to determine if it was effectively fixed or not would reduce the likelihood of any repair deficiencies, as well as improve customer satisfaction and product reliability. Mathematical modelling and all reliability measures evaluated using stochastic process, regenerative techniques and geometric distribution been proved beneficial for analyzing system profit function including mean time to system failure, availability of the system in operative form, down period of the system.

Background: The automobile industry has traditionally been paper-intensive. Such a glut of paperwork presents an organizational challenge for both the financial institution and the customer. Deciding how to store and organize such paperwork presents a further challenge since much of the information contained therein is of a confidential nature. In today's highly electronic world, the array of disparate technologies available for interacting with customers is expanding rapidly. Vehicles and commercial vehicles must be maintained relatively often and therefore, documents appertaining to each maintenance must be locatable. The frequency with which the documents are produced increases the burden of keeping track of the necessary documents. Objective: The objective of developing a new innovative electronic management device system is an attempt to ease the burden of keeping track of and making available the necessary documents for maintaining one or more vehicles. Methods: The present paper relates to an electronic document management device, system, and method for storing, requesting, and accessing all vehicle-related documents. The designed electronic device includes a non-transitory medium with a computer-readable program code embodied therein. The computer-readable program code, on execution by one or more processors, configures the electronic device to receive the first one or more set(s) of trigger input(s). The device accesses one or more remote database comprising of non-personalised as well as personalised electronic documents, after detecting the receipt of the first set of trigger inputs and stores information relevant to the set of trigger inputs from the non-personalised and personalised electronic documents in the database of the electronic device. Results: The results consist of an electronic device that can receive one or more first sets of trigger inputs and can access one or more remote databases comprising a non-personalized electronic document and a personalized electronic document and store information at least partially relevant to the one or more first set of trigger inputs. Conclusion: The designed machine been proved to be efficient by involving innovative ideas, design consisting of a device manufactured for the transparency and user friendly for saving the vehicle documents, such as RC, pollution, insurance, service, driving license, vehicle specification etc. by linking the concerned department with user.

The present paper is an initiative towards analyzing the maintenance process of an industrial model using regenerative techniques. With an increase in demands to analyze the reliability of any industrial models following continuous or discrete distribution, the major concern to be considered inspect the possibility and level of failure and proceeding the failed unit for further repairing process. The system consists of two parallel units following the passive standby redundancy and with different failure mechanism. The proposed analytical methodology in the paper made it possible to assess the reliability of the whole system in the event of failure of its components. The stochastic analysis of reliability characteristics of the considered system to the types of repair time distributions was also studied using geometric distribution. The numerical equations and results being calculated for reliability parameters like mean time to system failure, availability of system in operative form, down period of the system following repair mechanism, using regenerative techniques, and geometric distribution. Graphical and analytical analysis were presented.

The purpose of this article is to discuss the availability of a three unit framework (A, As, B) existing in the paper industry with the provision of inspection of one unit and that can be replaced after inspection. Here in this work we have considered that failure and repair time of every unit is correlated with each other and by using the regenerating point technique (RPT) we find the optimal system reliability and availability. With the help of experimental results we have found the optimal values of reliability characteristics like availability and busy period of the repair person. We have also discussed the impact of these characteristics on profit .This work would be of great interest of industrial managers and engineers.

The present paper is an initiative taken by emerging reliability model to a automobile repair industries for its products by dividing repair policy into two categories as (a) regular/normal service and (b) strategy for accidental or additional failure. The concept of inspection process has been introduced for proper verification of failure and also to its repairing strategy with time and cost. The maintenance cost for regular services are fixed but for the case of additional failures the additional cost will be decided upon the level of damage. The stochastic analysis for system been numerically and graphically analyzed by calculating reliability variables like MTSF, availability, inspection and maintenance analysis of the system with the concept of geometric distribution, Markov process and regenerative technique. The results been proved beneficial for fulfilling the objective of calculating profit function that increases with increasing repair and decreasing failure rate.

Background: The increased rate of global obesity is presenting a major public health spate to people of every age group belonging to any region. Obesity increases health risks, such as cardiovascular disease, cancer, diabetes, osteoarthritis, and chronic kidney diseases. Nowadays, we have all seen the damage that has been done to humanity through COVID-19. All past researches and traditional weight machines were found to be either plate loaded or weight-stack loaded. The plate-loaded machine requires the location of various load plates and manual adjustment of the load. Machines based on such techniques always have chances for user injury Objective: The objective of developing a new and innovative gym machine provides a load lifting apparatus which does not require weight stacks or weight plates for the user to exercise and can be adapted to adjust user of various height, and weight, requiring lower maintenance cost, being safe to use, and it also has an easy handling nature that offers cost-effective alternative to existing devices. Methods: The present paper provide an innovative approach in developing multi exercise self-weight gym machine. The machine includes a unique design with new features for holding the handle during load lifting exercise, an input shaft having one or more first pulleys coupled to the handle for rotating the input shaft. An intermediate shaft having the first set of gears are configured for selective engagement with the input shaft. The output shaft includes a second set of gears which are configured for selective engagement with the intermediate shaft and one or more second pulleys coupled for lifting one or more loads. A weight-based exercise machine depending on user weight will add to its independence of adding or withdrawing weights; this will make the machine cost-effective . Addition of parallelogram linkages in its design benefitted in providing a non-swing motion. The concept of maintaining proper resistance has also been an important factor during the design of the machine. Patents: The paper presents the idea of designing multi self-weight exercise machine as an innovation, involving gear change mechanism for the users, having different weights and heights. Results: The results concerning the gear ratio for the first and second lever are computed for the respective machine. Effective gear ratio and standardized load values had been obtained towards weight lifted for 78 Kilogram to achieve load less or more than weight of the user. Conclusion: The designed machine has been proved to be efficient by involving innovative ideas and design consisting of engagement configuration of the input shaft and intermediate shaft that further provide different gear ratios between the input, output & intermediate shaft. The concept of movable chairs in the change of weight through gear mechanism and the use of this machine in different exercises has proved it to be effective and beneficial for users and the manufacturer because of its easy handling nature.

Introduction: Face Detection is used in many different steams like video conferencing, human-computer interface, face detection, and in the database management of image. Therefore, the aim of our paper is to apply Red Green Blue (RGB) and Hue Saturation Value (HSV) color models in detecting the single, including multiple images of any face. Each color model HSV, Ycbcr and TSL are individually performed with the RGB color model to detect from the single and multiple images, the region of the face. Methods: The morphological operations are performed in the face region to a number of pixels as the proposed parameter to check either an input image contains face region or not. Canny edge detection is also used to show the boundaries of a candidate face region, in the end, the face can be shown detected by using bounding box around the face. Results: The reliability model has also been proposed for detecting the faces in single and multiple images. The results of the experiments reflect that the algorithm been proposed performs very well in each model for detecting the faces in single and multiple images and the reliability model provides the best fit by analyzing the precision and accuracy. Moreover Discussion: The calculated results show that HSV model works best for single faced images whereas YCbCr and TSL models work best for multiple faced images. Also, the evaluated results by this paper provides the better testing strategies that helps to develop new techniques which leads to an increase in research effectiveness. Conclusion: The calculated value of all parameters is helpful for proving that the proposed algorithm has been performed very well in each model for detecting the face by using a bounding box around the face in single as well as multiple images. The precision and accuracy of all three models are analyzed through the reliability model. The comparison calculated in this paper reflects that HSV model works best for single faced images whereas YCbCr and TSL models work best for multiple faced images.

АннотацияНадежность увеличивает свою ценность в развитии механического и промышленного мира за счет включения механизма ремонта, доступности и возможности изготовления машин с различной рабочей мощностью в любых условиях.Настоящая статья представляет собой инициативу, предпринятую с механической системой, работающей с единым сервером ремонта для различного характера отказов и услуг.Стратегия пассивной резервной машины используется для поддержания надежности системы на удовлетворительном уровне.Процесс проверки включен для фильтрации машин в зависимости от их неисправности или уровня ремонтных услуг.Вычисленные числовые и графические данные оказались полезными для выяснения поведения прибыли и надежности при увеличении / уменьшении скорости механизма ремонта и интенсивности отказов

Diesel engine's complexity is a primary cause of breakdown or inability. Engine failure impacts device performance and thus efficiency. It often increases the cost of maintenance as the system goes down again and again. The main aim of this analysis is therefore to concentrate on aspects of the reliability and availability of diesel locomotive engines. For this reason, a large collection of observations is explored to evaluate the availability output of electrical assembly components. Weibull distribution is then used to analyse the reliability of the system and the rate of failure information that can be used in the rail industry to minimize unforeseen failures and to increase the reliability as well as the availability of diesel locomotives. A comparative study of Weibull distribution with the other distribution has been carried out to show the benefits of the Weibull distribution.