Number Of Spare Units Research Articles

Joint optimisation on maintenance policy and resources for multi-unit parallel production system

Multi-unit parallel production systems (MuPPSs) widely exist in many industry areas. A general requirement for the MuPPS is that each production system should continuously run and its downtime should be as short as feasible. For such systems, optimising preventive maintenance (PM) policy is crucial so that resources such as the number of spare units and that of repairmen can be optimally used. On this basis, this paper develops an optimal model jointly optimising the PM policy and the number of repairmen and spare units, for which the genetic algorithm is used to determine the optimal displacement sequence of spare units. According to the developed model, a real case study of a train working line is presented to demonstrate its necessity. Finally, the sensitivity analysis is conducted to assess the influence of some parameters on the optimal results.

Spare Assessment of Distribution Power Transformers Considering the Issues of Redundancy and MUS Capability

Probabilistic methods based on Markov models were developed in the last few years to determine the optimal number of spare transformers (regular spare units and mobile substation units) for a group of similar distribution power transformers. These methods accounted for a number of factors that affected the number of spare transformers. The two issues that would have an impact on the number of spare units are transformer redundancy and whether or not the station has a mobile unit substation capability. These two issues were not fully investigated in the earlier spare assessment work and need to be studied in more detail. This paper describes the recent reliability study performed at Hydro One to address the two issues. The study includes a review of three spare assessment methods, two existing and one new, and a detailed analysis of how each method handles the two issues. Examples are provided to illustrate and compare the various assessment methods and to draw some recommendations with regard to the use of these methods.

Maintenance Model of Digital Avionics

The cost of avionics maintenance is extremely high for modern aircraft. It can be as high as 30% of the aircraft maintenance cost. A great impact on the cost of avionics maintenance is provided by a high level of No Fault Found events (NFF). Intermittent faults are the leading cause of the NFF appearance in avionics. The NFF rate for avionics systems is between 20% and 50%. The practice of avionics operation and maintenance confirms the relevance of assessing the impact of intermittent faults on the maintenance cost and the choice of such option of the maintenance management, in which the negative impact of the intermittent faults is minimized. In this paper, a new mathematical model of digital avionics maintenance is developed. Key maintenance effectiveness indicators are selected. General mathematical expressions are obtained for the average availability, mean time between unscheduled removals (MTBUR), and expected maintenance cost of single unit and redundant avionics systems, which are subject to permanent failures and intermittent faults. The dependence of the maintenance effectiveness indicators on the rate of permanent failures and intermittent faults is investigated for the case of exponential distribution of time to failures and faults. The dependence of average availability on the number of spare units in the airline’s warehouse is also analyzed. On the base of the proposed maintenance model, different options of avionics maintenance management are considered. Numerical examples illustrate how to reduce the expected maintenance cost of avionics systems.

Assessment of Spare Breaker Requirements for High Voltage Transmission Stations

This paper describes a probabilistic method based on a total risk index (probability times consequences) for assessing the number of spare breakers required for a group of similar high voltage breakers used in switching and transformer stations. The proposed method uses a Markov model for assessing the probability of failures and a bulk power system reliability program for evaluating failure consequences. The method considers a number of factors such as the group size, unit failure rate, unit repair time, transmission station layout, and other power system parameters that may impact the number of spare breakers. A cost/benefit analysis approach is used in determining the required number of spare breakers. The number of spare units is determined when the total cost (sum of spare unit costs, system operating costs and system outage costs due to breaker failures) is minimum. An example is given to illustrate the proposed method of assessment.

Use of Markov Models in Assessing Spare Transformer Requirements for Distribution Stations

This paper describes a probabilistic method based on Markov models for assessing the number of spare transformers, regular units and mobile units, required for a group of distribution transformers. The proposed method uses two criteria in determining the required number of spare transformers. The first criterion assumes that a pre-determined level of the group availability is given and the number of spare units is determined when the calculated group availability exceeds the pre-determined level of the group availability. The second criterion uses a cost/benefit analysis method in calculating the number of the spare units. In the second criterion, the number of spare units (optimal number) is determined when the total cost (spare unit capital costs and unit outage costs) is minimum. The proposed method is also used to evaluate the impacts of multi-transformer stations (stations with transformer redundancy) and station capabilities for use of mobile unit transformers on the number of spare units. Two distribution transformer groups of the Hydro One's distribution system are used to illustrate the proposed method of assessment and to compare the results obtained using the two criteria.

State probabilities of a float system

PurposeThe purpose of this paper is to determine the state probabilities for a float system when overhauls are performed periodically.Design/methodology/approachFirst, a model is developed to express the relationship between the rate of occurrence of failure and time interval between overhauls. Then, a methodology is defined to develop differential equations for each system state in order to calculate corresponding system state probabilities.FindingsSince it is considered that units requiring an overhaul stay in operation until replacement, the possibility of failure of those units has to be included. Then, the determination of system state probabilities has to be done iteratively.Practical implicationsThe methodology proposed in this paper enables comparison of different designs for a float system submitted to periodic overhauls through some different performance measures. System state probabilities can also be used to determine the idle time of units, which is essential to obtain the cost of production loss and, therefore, the system maintenance cost.Originality/valueThis paper considers simultaneously three different factors that influence maintenance float system performance: the number of spare units and the number of maintenance crews (which mean minimising the downtime effect) and the overhaul frequency (which means decreasing the number of failures).

Processing Times Modeled by Reliability Systems with a Random Number of Spare Units

SUMMARY A processing job with high reliability of final results is requested. It is performed as a multi-stage process. The facility at each stage may work correctly or malfunction. To enter any subsequent stage a secure result from the previous stage is required. This leads to the necessity of duplication of jobs at each stage many (random number of) times to provide two coinciding results, and a successful and reliable end. Then the total processing time, the quality of total processing of the job and related characteristics are modeled like those in a reliability system with random redundancy. Some analogies with the conventional results in reliability theory apply. Optimization problems are formulated and examples from information traffic are shown.

A fast algorithm for repair-depot reliability-evaluation

The repair-depot (where failed items are replaced with spares and scheduled for repair) system-reliability (RDSR) is the probability that spares are immediately available to replace failed units during the time period of interest, and it is calculated in terms of the constant failure rate for parts under consideration, the number of spare units on-hand (s), and projected repair completion dates for (n-1) units in the repair process, n/spl ges/2. Linton et al. (1995) show an expression for RDSR in terms of n nested sums, where the upper limit of each sum is a function of s. This paper derives a restructured expression (LKYH algorithm) for computing RDSR, and shows that the nested-sum form for RDSR uses O(s/sup n/) mathematical operations, while LKYH requires only O(s) mathematical operations. Numerical examples illustrate the increase in efficiency of LKYH; e.g., when n=s=10, the execution time for computing RDSR on a 486/66-computer is reduced from 198 seconds for the multiple-sum form to less than 1 second for LKYH.

Optimal design of hybrid fault-tolerant computer systems

In many critical applications of digital systems, fault tolerance has been an essential architectural attribute for achieving high reliability. We address the problem of designing an optimal hybrid fault-tolerant computer system. The designer of a system is always confronted with the problem of trading off reliability vs. cost. On the one hand, it is essential to provide for each vital module of the system as many spare units as possible in order to ensure high reliability. On the other hand, it is essential not to have an excessively costly, heavy or bulky system. In this paper, we determine the optimal number of spare units which minimizes the average total system cost. A numerical example is provided to illustrate the methods.

Optimal cost effective design of hybrid hardware redundant systems

In many critical applications of digital systems, fault tolerance has been an essential architectural attribute for achieving high reliability. We address the problem of designing an optimal hybrid hardware redundant system. The designer of a system is always confronted with the problem of trading off reliability against cost. On the one hand, it is essential to provide for each vital module of the system as many spare units as possible in order to ensure high reliability. On the other hand, it is essential not to have an excessively costly, heavy or bulky system. In this paper we determine the optimal number of spare units which minimizes the expected total system cost. A numerical example is provided to illustrate the methods.

Evaluation of reliability and safety of long-term unmaintained computer systems

In many applications such as critical life-saving systems, safety is an important design issue as well as reliability. Among various commonly-used approaches in the implementation of on-line unrepairable fault-tolerant systems, standby systems achieve the most satisfactory reliability figure, followed by duplex systems, hybrid systems and triple modular redundancy. Nevertheless, the safety figure of duplex systems is superior to that of the standby approach. In this paper, the failure rate of system modules and hard core is predicted by the M1L-HDBK-217E model, and we show that the reliability and safety figure of cold standby systems can be further dramatically improved by increasing the number of spare units. Furthermore, comparative measures such as the reliability improvement factor, the safety improvement factor and the mission time improvement factor are proposed for showing that long-term unmaintained systems have reliability and safety as high as other systems that must be repaired.

Optimal Inventory Problem of a Repairable K-out-of-N:G System

The optimal inventory problem of a repairable K-out-of-N:G system is discussed. When a unit fails, it is repaired or discarded according to the extent of damage. Spare units are replenished at the replenishment times. The optimal inventory problem is to determine the number of spare units replenished at each replenishment time, which minimizes the total system cost constrained by system availability. This problem is formulated as a nonlinear integer programming problem. A new algorithm which is a modification of an algorithm proposed earlier by the authors is used for the problem.

Reliability of 2-out-of-3 System Considering Number of Spares and Exchange Time

The reliability of a simplified model of ractor instrumentation possessing redundancy in its system is studied. The unreliability is obtained for a 2-out-of-3 system with a limited number of spare units, for the case where the replacement of the failed unit by a spare unit is not instantaneous. Two methods for the solution are obtained. The results are then compared with that obtained from Jacobs' formula for a rate of false scrams, and the accuracy of Jacobs' formula is discussed. It is shown that Jacobs' formula can be used only when the duration of operation is larger than several times the reset time, which must be a constant. But in actuality this reset time depends on such factors as the number of spare units provided, and the time required for replacement.