Radim Briš

New method to minimize the preventive maintenance cost of series -parallel systems

Abstract General preventive maintenance model for input components of a system, which improves the reliability to ‘as good as new,’ was used to optimize the maintenance cost. The cost function of a maintenance policy was minimized under given availability constraint. An algorithm for first inspection vector of times was described and used on selected system example. A special ratio-criterion, based on the time dependent Birnbaum importance factor, was used to generate the ordered sequence of first inspection times. Basic system availability calculations of the paper were done by using simulation approach with parallel simulation algorithm for availability analysis. These calculations, based on direct Monte Carlo technique, were applied within the programming tool Matlab. A genetic algorithm optimization technique was used and briefly described to create the Matlabs algorithm to solve the problem of finding the best maintenance policy with a given restriction. Adjacent problem, which we called ‘reliability assurance,’ was also theoretically solved, concerning the increase of the cost when asymptotic availability value conforms to a given availability constraint.

Parallel simulation algorithm for maintenance optimization based on directed Acyclic Graph

An efficient simulation algorithm for the quantification of reliability performance indicators of a complex system is demonstrated in the paper that is based on Monte Carlo method. A directed Acyclic Graph is used as a useful system representation. A parallel simulation technique is used in the algorithm which is based on the construction of the special course of life sequence of transformed transition times subjected to the corresponding part of the Acyclic Graph. The parts of the Acyclic Graph represent individual subsystems of a given system and may be effectively evaluated from the reliability point of view. The wide range of models for both deterministic and stochastic processes applied on the terminal nodes of the Acyclic Graph is allowed in the algorithm. The use of the algorithm for comparative theoretical calculations as well as for industrial applications is shown by a visual demonstration. A cost-optimization problem is shortly introduced which may be fully solved by the algorithm using additional genetic algorithms as an applicable optimization technique. The problem takes into account also additional objective that is defined as a prescribed constraint of a selected reliability performance indicator. The solution of the cost-optimization problem is demonstrated on two practical examples.

Exact reliability quantification of highly reliable systems with maintenance

When a system is composed of highly reliable elements, exact reliability quantification may be problematic, because computer accuracy is limited. Inaccuracy can be due to different aspects. For example, an error may be made when subtracting two numbers that are very close to each other, or at the process of summation of many very different numbers, etc. The basic objective of this paper is to find a procedure, which eliminates errors made by PC when calculations close to an error limit are executed. Highly reliable system is represented by the use of directed acyclic graph which is composed from terminal nodes, i.e. highly reliable input elements, internal nodes representing subsystems and edges that bind all of these nodes. Three admissible unavailability models of terminal nodes are introduced, including both corrective and preventive maintenance. The algorithm for exact unavailability calculation of terminal nodes is based on merits of a high-performance language for technical computing MATLAB. System unavailability quantification procedure applied to a graph structure, which considers both independent and dependent (i.e. repeatedly occurring) terminal nodes is based on combinatorial principle. This principle requires summation of a lot of very different non-negative numbers, which may be a source of an inaccuracy. That is why another algorithm for exact summation of such numbers is designed in the paper. The summation procedure uses benefits from a special number system with the base represented by the value 232. Computational efficiency of the new computing methodology is compared with advanced simulation software. Various calculations on systems from references are performed to emphasize merits of the methodology.

Bayes approach in RDT using accelerated and long-term life data

Abstract A common problem of reliability demonstration testing (RDT) is the magnitude of total time on test required to demonstrate reliability to the consumer’s satisfaction, particularly in the case of high reliability components. One solution is the use of accelerated life testing (ALT) techniques. Another is to incorporate prior beliefs, engineering experience, or previous data into the testing framework. This may have the effect of reducing the amount of testing required in the RDT in order to reach a decision regarding conformance to the reliability specification. It is in this spirit that the use of a Bayesian approach can, in many cases, significantly reduce the amount of testing required. We demonstrate the use of this approach to estimate the acceleration factor in the Arrhenius reliability model based on long-term data given by a manufacturer of electronic components (EC). Using the Bayes approach we consider failure rate and acceleration factor to vary randomly according to some prior distributions. Bayes approach enables for a given type of technology the optimal choice of test plan for RDT under accelerated conditions when exacting reliability requirements must be met. These requirements are given by a hypothetical consumer by two different ways. The calculation of posterior consumer’s risk is demonstrated in both cases. The test plans are optimum in that they take into account Var{ λ |data}, posterior risk, E { λ |data}, Median λ or other percentiles of λ at data observed at the accelerated conditions. The test setup assumes testing of units with time censoring.

Time-dependent risk modeling of accidental events and responses in process industries

Abstract Risk to safety of personnel in process industries is normally modeled in the application of event trees, where the risk is defined as a product of event frequency and its consequences. This method is steady state whilst the actual event is time dependent, comprising, for a gas release, as for example, the size of gas cloud being released, probabilities of ignition, fire or explosion, fatality, escalation to new releases and fire and/or explosion, and the probability of fatality, all varying with time. This Paper presents a method whereby the time-dependent events and the time-dependent probability of fatality are modeled by means of the direct Monte Carlo simulation method. Different accident scenarios are modeled and discussed resulting from event trees analysis. Using the simulation method the modeled scenarios change with relevant probabilities at defined times to configurations with appropriate probabilities of fatalities. Simple sensitivity analysis in dependency on most relevant events is also performed. The Paper uses a realistic example from the offshore industry for which the probability of fatality is quantified by the use of simulation method.

Effective computing algorithm for maintenance optimization of highly reliable systems

This paper describes a new iterative numerical algorithm for optimal maintenance strategy respecting a given reliability constraint. It stems from the previous authors research work which brings a new direct analytical method that enables exact reliability quantifications of highly reliable systems with maintenance (both preventive and corrective), i.e. the instantaneous unavailability function is computed in full machine accuracy. The method takes into account systems with highly reliable and maintained components, including repairable components undergoing to hidden failures. The new numerical algorithm for maintenance optimization introduced in this article fully respects previously developed exact computing methodology to solve a cost optimization problem where decision variable is maintenance. The algorithm, which is based on merits of a high performance language for technical computing MATLAB, results from linear approximation of total system cost that is supposed to be a linear function of frequency of maintenance and from limiting unavailability approximation in each iteration step. The optimization method is demonstrated on two systems from practice—a real power distribution network and high pressure injection system of a nuclear power plant.

Coloured Petri nets and a dynamic reliability problem

One of the major problems of the system reliability calculation is an implementation of a dynamic behaviour. One way to show a possible representation of dynamic systems is by using coloured stochastic Petri nets (CSPNs). In this paper this approach is applied to one benchmark on the dynamic reliability taken from the literature. The system consists of a tank containing some liquid where the liquid level is controlled by suitable detectors acting on three hardware components that work independently. The modelled system is consequently used as an input for the calculation of the cumulative distribution functions and other characteristics (e.g. reliability of the system). As the next step, this benchmark will be modified. The first system modification is the maintenance action inclusion. The second one is the enhancement of the system by adding another process variable (the liquid temperature within the tank that is dependent on time). The CSPN approach is used to find a suitable representative scheme of these modifications.

Discrete maintenance optimization of complex multi-component systems

Abstract A complex multi-component system consists of finite number of non-identical components that can be realized as maintained components with different maintenance modes. We distinguish between four component models: non-repairable components, repairable components with corrective maintenance, repairable components with latent failures that are identified by means of preventive maintenance and component with preventive maintenance policy in which the component is restored (either repaired or renewed). The paper describes a new method for optimal maintenance strategy of a complex system respecting a given reliability constraint. It is based on our previously developed direct analytical method that enables exact reliability quantifications of highly reliable systems with maintenance. The method takes into account complex systems with maintained components, including all above models. Cost-optimization problem is solved where decision variables are changeable maintenance parameters that are optimally selected from a set of possible realistic maintenance modes. As a discrete maintenance model in this paper is considered such a model, where each maintained component can be operated in one or few discrete maintenance modes. One maintenance mode is characterized by fixed decision variables that affect maintenance cost of the mode. If a system hypothetically contains k components with 5 independent maintenance modes, in total we have 5 k maintenance configurations of the system, from which the optimal is found. The optimization method is demonstrated on real system from practice – a complex power distribution network.

Evaluation of the production availability of an offshore installation by stochastic Petri nets modeling

The purpose of this article is to illustrate the combination of stochastic Petri nets and Monte Carlo simulation approach for the evaluation of the production availability of a multi-state, multi-output offshore installation with operational loops. The presented test case comprises a great number of the problems encountered when dealing with probabilistic studies related to production processes. The reason for using of Petri net modeling is that it provides the necessary flexibility to describe the complexity of the plant and the realistic aspects of system behavior, such as a degradation of components, standby of components, corrective and preventive maintenance with stochastic or deterministic durations, a limited number of repair teams and associated component repair priorities, which determine the system stochastic evolution and which are not easily captured by analytical models. Different production levels of the multi-state system are assessed and evaluated from both reliability and production efficiency point of view. Four selected configurations of the system are computed and discussed in detail to investigate how the production efficiency and average availability are influenced by applying of a preventive maintenance and an additional cold standby of component.

A nonparametric approach to medical survival data: Uncertainty in the context of risk in mortality analysis

Abstract Medical survival right-censored data of about 850 patients are evaluated to analyze the uncertainty related to the risk of mortality on one hand and compare two basic surgery techniques in the context of risk of mortality on the other hand. Colorectal data come from patients who underwent colectomy in the University Hospital of Ostrava. Two basic surgery operating techniques are used for the colectomy: either traditional (open) or minimally invasive (laparoscopic). Basic question arising at the colectomy operation is, which type of operation to choose to guarantee longer overall survival time. Two non-parametric approaches have been used to quantify probability of mortality with uncertainties. In fact, complement of the probability to one, i.e. survival function with corresponding confidence levels is calculated and evaluated. First approach considers standard nonparametric estimators resulting from both the Kaplan–Meier estimator of survival function in connection with Greenwoods formula and the Nelson–Aalen estimator of cumulative hazard function including confidence interval for survival function as well. The second innovative approach, represented by Nonparametric Predictive Inference (NPI), uses lower and upper probabilities for quantifying uncertainty and provides a model of predictive survival function instead of the population survival function. The traditional log-rank test on one hand and the nonparametric predictive comparison of two groups of lifetime data on the other hand have been compared to evaluate risk of mortality in the context of mentioned surgery techniques. The size of the difference between two groups of lifetime data has been considered and analyzed as well. Both nonparametric approaches led to the same conclusion, that the minimally invasive operating technique guarantees the patient significantly longer survival time in comparison with the traditional operating technique.