Number Of Failed Units Research Articles

Cost analysis of N-policy vacation machine repair problem with optional repair

In this paper, we deal with the N-policy machine repairable system with warm spares and two repairmen under optional repair. The first repairman is always available to serve the failed units in the system while the second repairman leaves for a vacation of random length when the number of failed units is less than N. The second repairmen firstly performs essential repair to all failed units and then may provide second optional repair to some failed units which demand for it. We construct the system state governing equations and the system performance measures under transient condition which are examined by using a numerical approach based on Runge-Kutta method of the fourth order. Further, the sensitivity and cost analysis are facilitated to demonstrate the validity of the model by taking a numerical illustration. The effect of different parameters on system performance indices is demonstrated graphically.

Transient analysis of computing system with reboot and recovery delay

PurposeThe purpose of this paper is to present a sensitivity analysis of fault-tolerant redundant repairable computing systems with imperfect coverage, reboot and recovery process.Design/methodology/approachIn this investigation, the authors consider the computing system having a finite number of identical working units functioning simultaneously with the provision of standby units. Working and standby units are prone to random failure in nature and are administered by unreliable software, which is also likely to unpredictable failure. The redundant repairable computing system is modeled as a Markovian machine interference problem with exponentially distributed failure rates and service rates. To excerpt the failed unit from the computing system, the system either opts randomized reboot process or leads to recovery delay.FindingsTransient-state probabilities have been determined with which the authors develop various reliability measures, namely reliability/availability, mean time to failure, failure frequency, and so on, and queueing characteristics, namely expected number of failed units, the throughput of the system and so on, for the predictive purpose. To spectacle the practicability of the developed model, a numerical simulation, sensitivity analysis and so on for different parameters have also been done, and the results are summarized in the tables and graphs. The transient results are helpful to analyze the developing model of the system before having the stability of the system. The derived measures give direct insights into parametric decision-making.Social implicationsThe conclusion has been drawn, and future scope is remarked. The present research study would help system analyst and system designer to make a better choice/decision in order to have the economical design and strategy based on the desired mean time to failure, reliability/availability of the systems and other queueing characteristics.Originality/valueDifferent from previous investigations, this studied model provides a more accurate assessment of the computing system compared to uncertain environments based on sensitivity analysis.

Factors affecting the results of comprehensive pre-internship exam among medical students of Kermanshah University of Medical Sciences.

PurposeThis study was aimed to evaluate the factors affecting the results of comprehensive pre-internship exam (CPIE) among medicals students of Kermanshah University of Medical Sciences.MethodsIn this descriptive-analytical study, all students (n=240) participating in CPIE over a 3-year period (2012–2014) were selected. Data were gathered by a questionnaire, including the CPIE results and educational and demographic data. Spearman correlation coefficient, Mann-Whitney U-test, and analysis of variance were used to analyze the association of students’ success with study variables. Also, regression analysis was applied to determine the role of independent variables in students’ success.ResultsThe frequency of the failed units in apprenticeship course was one of the most important risk factors associated with failure in CPIE. Average scores of pre-internship course were the most important factors of success in CPIE. The CPIE score had the highest direct relationship with grade point average (GPA) of apprenticeship course, total GPA of all three courses, GPAs of physiopathology and basic sciences courses, and score of comprehensive basic sciences examination, respectively.ConclusionCPIE showed the highest inverse correlation with the number of failed units in apprenticeship course. The most important factors influencing this exam were failure in apprenticeship course and GPA of previous educational stages.

N-policy for a repairable redundant machining system with controlled rates

The present investigation deals with a multi-component machining system operating under N -policy. There is a provision of k type of mixed standbys units and maintenance crew consisting of permanent repairman as well as removable additional repairmen. The life time and repair time of the units are exponentially distributed with interdependent rates. The permanent repairman can start the repair only when N failed units are accumulated in the system. As soon as a unit fails, it is replaced by an available standby unit. In case when all the standby units are exhausted, the machining system starts to function in a degraded mode due to overload. Markov model is developed by constructing the governing transient state equations which are solved by using Runge−Kutta method. Various performance measures viz. queue size distribution, expected number of failed units, cost function, etc. are evaluated. By taking numerical illustration, numerical results are computed and also depicted with the help of graphs and figures.

(m, M) Machining system with two unreliable servers, mixed spares and common-cause failure

This paper deals with multi-component machine repair model having provision of warm standby units and repair facility consisting of two heterogeneous servers (primary and secondary) to provide repair to the failed units. The failure of operating and standby units may occur individually or due to some common cause. The primary server may fail partially following full failure whereas secondary server faces complete failure only. The life times of servers and operating/standby units and their repair times follow exponential distribution. The successive over relaxation (SOR) technique has been used to obtain the steady state queue size distribution of the number of failed units in the system. To explore the system characteristics, various performance indices such as expected number of failed units in the queue, throughput, etc. have been obtained. Numerical results have been provided to illustrate the computational tractability of the proposed SOR technique. To examine the effect of system descriptors on the performance indices, the sensitivity analysis is also performed.

Performance prediction of machine repair problem with spares and two modes of failure

This investigation is concerned with the transient analysis of machine repair problem with M operating units and multi types of warm spares. In case when all spares are being used, the failure of units occurs in degraded fashion. Each unit is assumed to fail in two modes. When all permanent repairmen are busy, the caretaker who brings the failed units for repair departs from the system after waiting for sometime in the queue due to impatience. For transient state, Chapman–Kolmogorov equations governing the model are constructed. Various performance measures such as expected number of failed units in each mode, average number of operating units in the system, average number of idle and busy repairmen in the system, operative utilisation factor, etc., are obtained. The cost minimisation problem to determine the optimum number of spares in terms of various cost elements has been formulated. We used Runge–Kutta technique to find the numerical solution for the transient model. The sensitivity analysis is performed to observe the effect of different parameters on various performance indices.

Reliability analysis of a repairable system with geometric reneging and threshold-based recovery policy

This article attempts to investigate the reliability measures of a repairable system with [Formula: see text] identical operating units, [Formula: see text] standby units, and a repairman. The repairman is subject to breakdowns and operates threshold-based recovery policy. As soon as the repairman breaks down, the repair does not start immediately until the number of failed units in the system reaches a specified threshold value [Formula: see text]. When the repairman is working or broken down, failed units arriving for maintenance may renege and decide sequentially whether to leave the queue or not. The failed times of operating and standby units, maintenance times and reneging time of failed units, and breakdown and repair times of the repairman are all assumed to be exponential distributions. We develop the system reliability and mean time to system failure. Through numerical results, sensitivity analysis is carried out to assess the impact of various system parameters on the system reliability and mean time to system failure. Finally, an application example is given to evaluate the reliability measures of an electric power system.

Bi-level control of degraded machining system with two unreliable servers, multiple standbys, startup and vacation

This investigation deals with bi-level (N, L) switch over policy for multi-component machine repair system with two unreliable repairmen and multiple types of standbys. The repairman (R1) turns on when N-failed units are accumulated in the system and starts repair of failed units by taking a startup rate. As soon as there is no failed unit in the system, the repairmen (R1) goes for a vacation and returns back when he finds the number of failed units in the system greater than or equal to the threshold value N. The second repairman (R2) turns on when there are L (>N) failed units in the system and leaves for a vacation if the number of failed units are less than L. The repairmen can also breakdown while repairing the failed units. The life time and repair time of operating/standbys units, unreliable servers, and startup time of the servers are assumed to be exponentially distributed. The transient state probabilities of the system states are obtained by using Runge-Kutta's method. Expressions for various performance indices viz. throughput, average number of failed units in the system and reliability of the system etc. are established. In order to examine the effects of various parameters, the sensitivity analysis is carried out by taking numerical illustration.

Transient analysis of a machine repair system with standby, two modes of failure, discouragement and switching failure

The present study is concerned with a machine repair problem with mixed standbys, permanent and additional repairmen. To deal with the realistic situation, the concepts of balking and reneging are also included. The operating units as well as standby units are assumed to fail in two modes. The units have exponential life time and repair time distributions. It is also assumed that there is a probability of a switching failure of the standby units to the operating state. The transient state probabilities are obtained by Runge-Kutta method. Some performance indices such as expected number of failed units, expected number of standby units, machine availability, etc., are obtained. To determine the expected total cost per unit time, a cost function has been facilitated. The numerical experiment is carried out to validate the analytical results of the developed model. The sensitivity analysis is also performed to explore the effect of different parameters on the performance indices.

N-policy for a multi-component machining system with imperfect coverage, reboot and unreliable server

This investigation aims at predicting the transient performance measures of a machining system comprising of M operating units and multi types of warm standbys under the care of a single unreliable server. To deal with more realistic situations, the concepts of imperfect recovery and reboot delay are also incorporated. The queue size distribution is obtained by using the matrix method. The explicit expressions for various performance measures such as reliability, throughput, expected number of failed units in the system, failure frequency of the server, etc. are obtained. A numerical illustration is presented to demonstrate the practical application of the proposed model in the flexible manufacturing systems.

Cost analysis of a machine repair problem with standby, working vacation and server breakdown

This paper investigates a machine repair model with standbys, working vacation and server breakdown. As soon as an operating unit fails, it is immediately replaced by a standby unit for the smooth running of the production. When there is no failed unit in the system, the server goes on vacation; meanwhile, the server performs some works and is said to be on working vacation. The life time and the repair time of the units are assumed to be exponentially distributed. The matrix recursive method is used to evaluate various performances measures such as the expected number of failed units in the system, the expected number of operating units in the system, machine availability, operating utilisation, etc. The cost function is established to maximise the gain. The sensitivity analysis is also carried out to examine the effect of different parameters on various system characteristics.

M/M/R+r machining system with reneging, spares and interdependent controlled rates

The present investigation deals with the multi component machine repair problem by including the concepts of reneging and interdependent controlled rates. We consider a machining system consisting of M operating units, S 1 and S 2 warm spares of two kinds and a repair facility having R permanent repairmen and r additional removable repairmen. When all the spares are used and the operating units fail, the system works in degraded mode. By using interdependent controlled arrival and service rates and reneging parameters along with time-sharing concept, the queueing model is developed for more versatile situations encountered in production/ manufacturing industries. The solution is obtained by using recursive technique. The expressions for the queue size distribution and expected queue length are established. Some more performance indices such as expected number of failed units waiting for the service, expected number of busy repairmen, expected number of both types of spare parts functioning as standbys, etc., are obtained with the help of recursive technique. By taking numerical illustrations, the sensitivity analysis is provided to validate the analytical results.

Threshold N-policy for (M, m) degraded machining system with K-heterogeneous servers, standby switching failure and multiple vacations

This paper is concerned with multi-component machining system having online or operating units along with K-type of standby units under the facility of K-heterogeneous servers. The servers switch on one by one when the number of failed units in the system reaches to a predefined threshold policy (Ni for ith server: i = 1, 2, …, K). Once server returns from a vacation, he can leave the system and go for another vacation only if no failed unit available in the system for repair. Whenever any unit fails, it is immediately replaced by an available standby unit. In case when all standbys are used, the system works in degraded mode. The standby units have switching failure probability q. The governing equations are constructed by using appropriate birth-death rates. A cost function has also been constructed to calculate the optimal number of standby units for providing the desired efficiency to the system. The SOR method is employed to find the steady state probabilities, mean number of failed units in the system, reliability and throughput. Numerical results obtained by successive over relaxation (SOR) method are matched by the results evaluated using soft computing approach based on adaptive neuro-fuzzy inference system (ANFIS).

Performance analysis and optimization of a machine repair problem with warm spares and two heterogeneous repairmen

In this paper, we study a machine repair problem with warm spares and two heterogeneous repairmen from the view points of both queueing and reliability. In this system, the first repairman is always available for serving the failed units, while the second repairman leaves for a vacation of random length when the number of failed units is less than N. We obtain expressions for the steady-state probabilities of the system by solving the steady-state probability equations iteratively. Then, we obtain some performance measures for the system. We also obtain some performance measures of reliability for the system such as the steady-state availability, the steady-state failure frequency and the mean time between the system failures. Moreover, we present derivations of the mean time taken until the first failure of the system. A cost model is developed to determine the optimum value N while the system availability is maintained at a certain level. A sensitivity analysis is also performed.

Threshold N-Policy for Degraded Machining System with Multiple Type Spares and Multiple Vacations

This paper deals with a multi-component machining system consisting of M operating units along with k types of spare machines. The repair facility comprises of R heterogeneous repairmen who get switched on one-by-one when the number of failed units reaches a certain pre-determined level (Ni for ith repairman; i = 1, 2,..., R). The repairman can leave for a vacation of random length during its idle time. The ith (i = 2, 3, …, R) repairman would leave for vacation if the number of failed units drops below N. The first repair facility, however would leave for vacation only when the system is empty. Once all the spares are utilized, the system starts working in degraded mode due to load sharing. The repairmen may breakdown individually or due to common cause according to the Poisson process. The mean failure and repair rates of the machines depend on the status of the system. The matrix recursive method is used to find the steady-state probabilities of the number of failed machines in the system as well as other performance measures. The model under consideration is computationally tractable which is illustrated by means of numerical experiments. We also approximate the performance measures by using a special class of neuro-fuzzy systems, i. e. Adaptive Network-based Fuzzy Interference Systems (ANFIS) which can identify parameters by using supervised learning methods. Some special cases have also been deduced to tally our results in particular cases with the existing results.

M/M/R Machine Interference Model with Balking, Reneging, Spares and Two Modes of Failure

This paper is concerned with M/M/R machine interference model consisting of M operating and S spare units. The units are assumed to fail in two modes. The life times and repair times of units are assumed to follow a negative exponential distribution. The both failure modes have equal probability of repairing. The both types of failed units are served by a pool of R repairmen according to FIFO discipline. We obtain queue size distribution at equilibrium in explicit form. The expressions for various performance measures such as the average number of failed units, the average number of idle repairmen etc. have been obtained. The expected total cost per unit time has also been derived. Numerical results are given for various performance measures to validate the analytical results. Optimal allocation of repairmen and spares based on heuristic approach is done in order to minimize the expected total cost under the constraint of availability.

Reliability analysis of repairable and non-repairable systems with common-cause failures

This paper presents a reliability analysis of repairable and non-repairable systems with N active redundant units, r repair facilities and common-cause failures. The system is in a failed state when all N active units have failed or by a common-cause failure. The rate of common-cause failure is dependent on the number of failed units. Laplace transforms of state probabilities and mean time to failure of the system are derived.

Stochastic model of multiple unit system

Stochastic model of a multiple unit, warm standby system is considered. The failure rate of a unit while online is λj when the number of failed units at the commencement of operation is j, while the p d f of the repair time is arbitrarily distributed. Identifying suitable regeneration points, the operating characteristics of the system like Reliability and the Availability are derived and a particular case is also obtained.

A stochastic domino model for a sequential failure process

This paper presents a domino model for a failure process which can occur in the units of an insulator string. It extends the standard independent failure reliability assessment to the case of sequential failures, where failure of one unit increases the risk that its neighbours will also fail. The statistical properties of the resulting distribution of number of failed units per string are derived, and procedures given for estimating the model parameters from observed failure data. Examples of the use of the model are given and its results are compared with those of an alternative model based on a negative binomial distribution.

Reliability and availability of 1-out-of-n:G cold standby systems with arbitrary failure rate and constant repair rate

This paper deals with the availability and reliability of 1-out-of-n: G systems with repair. Initially, one unit is switched on and the other units are kept as cold standbys. Failure rate is arbitrary. Repair rate is constant and depends only on the number of failed units. Suitable regenerative points are identified to obtain the results.