Professor Michael Todinov

Abstract: The paper introduces a powerful method for developing lightweight designs and enhancing
the load-bearing capacity of common structures. The method, referred to as the ‘method of
aggregation’, has been derived from reverse engineering of sub-additive and super-additive algebraic
inequalities. The essence of the proposed method is consolidating multiple elements loaded in
bending into a reduced number of elements with larger cross sections but a smaller total volume of
material. This procedure yields a huge reduction in material usage and is the first major contribution
of the paper. For instance, when aggregating eight load-carrying beams into two beams supporting
the same total load, the material reduction was more than 1.58 times. The second major contribution
of the paper is in demonstrating that consolidating multiple elements loaded in bending into a
reduced number of elements with larger cross sections but the same total volume of material leads
to a big increase in the load-bearing capacity of the structure. For instance, when aggregating eight
cantilevered or simply supported beams into two beams with the same volume of material, the loadbearing
capacity until a specified tensile stress increased twice. At the same time, the load-bearing
capacity until a specified deflection increased four times.

The paper reveals that a prediction of system reliability on demand based on
average reliabilities on demand of components is a fundamentally flawed
approach. A physical interpretation of algebraic inequalities demonstrated that
assuming average component reliabilities on demand entails an overestimation
of the system reliability on demand for systems with components logically
arranged in series and series-parallel and underestimation of the reliability on
demand for systems with components logically arranged in parallel. The key reason
for these discrepancies is the variability of components from the same type.
Techniques for countering variability by promoting asymmetric response through
inversion have also been introduced. The paper demonstrates that variability during
assembly operations can affect negatively the reliability of mechanical systems.
Accordingly, techniques for reducing the variability of stresses during
assembly operations have been discussed. Finally, the paper provides a discussion
related to the reasons for the relatively slow adoption of domain-independent
methods for improving reliability despite their numerous advantages.

The paper examines the profound impact on the forecasted system reliability when one assumes average reliabilities on demand for components of various kinds but of the same type. In this paper, we use reverse engineering of a novel algebraic inequality to demonstrate that the prevalent practice of using average reliability on demand for components of the same type but different varieties to calculate system reliability on demand is fundamentally flawed.

This approach can introduce significant errors due to the innate variability of components within a given type.

Additionally, the paper illustrates the optimization of engineering processes using reverse engineering of sub-additive algebraic inequalities based on concave power laws. Employing reverse engineering on these sub-additive inequalities has paved the way for strategies that enhance the performance of diverse industrial processes. The primary advantage of these sub-additive inequalities lies in their simplicity, rendering them particularly suitable for reverse engineering.

The paper demonstrates a new domain-independent method for improving reliability and reducing risk including two fundamental approaches: the forward approach, based on deriving algebraic inequalities from real systems and processes; and the inverse approach, based on deriving new knowledge by meaningful interpretation of existing correct algebraic inequalities. The forward approach has been used to prove the domain-independent principle of the well-ordered systems which are characterised by the smallest possible risk of failure. The inverse approach has been used to generate new knowledge related to the relationship of the equivalent elastic constants of elements arranged in series and parallel and the upper and lower bounds of the percentage of faulty components in pooled batches of components with unknown sizes.

The reverse engineering of a valid algebraic inequality often leads to a projection of a novel physical reality characterized by a distinct signature: the algebraic inequality itself. This paper uses reverse engineering of valid algebraic inequalities for generating new knowledge and substantially improving the reliability of common series-parallel systems. Our study emphasizes that in the case of series-parallel systems with interchangeable redundant components, the asymmetric arrangement of components always leads to higher system reliability than a symmetric arrangement. This finding remains valid, irrespective of the particular reliabilities characterizing the components. Next, the paper presents novel system reliability inequalities whose reverse engineering enabled significant enhancement of the reliability of series-parallel systems with asymmetric arrangements of redundant components, without knowledge of the individual component reliabilities. Lastly, the paper presents a new technique for validating complex algebraic inequalities associated with series-parallel systems. This technique relies on permutation of variable values and the method of segmentation.

New results related to maximizing the reliability of common systems with interchangeable redundancies at a component level have been obtained by using the method of algebraic inequalities. It is shown that for systems with independently working components with interchangeable redundancies, the system reliability
corresponding to a symmetric arrangement of the redundant components is always inferior to the system reliability corresponding to an asymmetric arrangement of the redundant components, irrespective of the probabilities of failure of the different types of components. It is also shown that for series–parallel systems, the system reliability is maximized by arranging the main components in ascending order of their probabilities of failure, whereas the redundant components are arranged in descending order of their
probabilities of failure. Finally, this article derives rigorously the highly counterintuitive result that if two components must be selected from n batches containing reliable and faulty components with unknown proportions, the likelihood that both components will be reliable is maximized by selecting both components from a randomly selected batch.

This paper focuses on optimising processes and generating knowledge based on interpreting a new algebraic inequality. An interpretation of the new inequality yielded a strategy for reducing the amount of pollutants released from an industrial process. An alternative interpretation of the same inequality established that the deflection of n elastic elements connected in series is at least n^2 times larger than the deflection of the same elements connected in parallel, irrespective of the individual stiffness values of the elements. In addition, an
alternative interpretation of the new inequality yielded a counter-intuitive result concerning improving the chances of picking a winning lottery ticket. Finally, the paper introduces a method for improving reliability by increasing the level of balancing and novel interpretations of algebraic inequalities related to this method. This is done by assessing the probability of selecting items of the same variety and determining the lower and upper bounds of this probability.

Problems with the current methods for reliability improvement are discussed as well as two generic methods for
reliability improvement. The paper argues that reliability improvement is underpinned by common principles that
provide key input to the design process. The domain-independent methods change the way engineers and scientists
approach reliability improvement. The presented generic methods encourage simple low-cost solutions as opposed to
some traditional high-cost solutions based on introducing redundancy, condition monitoring, reinforcement and use of
expensive materials. The domain-independent methods allow engineers and scientists in a particular domain to access
excellent solutions and practices for eliminating failure modes in other domains. In this way, the constant ‘reinventing
of the wheel’ is avoided. As part of the presented approach, a generic method for increasing reliability by increasing the
level of balancing and by substitution have been presented. In addition, a new classification of techniques related to
increasing the level of balancing has been introduced and discussed for the first time. The paper also proves rigorously
that if two components must be selected from n batches containing reliable and faulty components with unknown
proportions, the likelihood that both components will be reliable is maximised by selecting the components from a
randomly selected batch.

The paper explores the probabilistic interpretations of algebraic inequalities and
presents several findings. First, the inequality of the additive ratios can be used
to increase the probability of an event occurring within a set of mutually exclusive
and exhaustive events. The interpretation of this inequality produced a
counter-intuitive result, that for suppliers delivering the same quantity of reliable
products alongside unknown numbers of unreliable products, the probability
of purchasing a reliable product from a randomly selected supplier is higher
than the probability of purchasing a reliable product from the market formed
by all suppliers. Next, the paper discusses how averaging the reliabilities of
components from different varieties can lead to a significant overestimation of
the calculated system reliability, as demonstrated by another algebraic inequality
interpretation. Finally, the paper derives tight bounds for the reliability of
demand in a load-strength interference model by interpreting the Hayashi’s
inequality. Notably, these bounds do not depend on the shape of the load distribution
and only require the strength distribution to be known in relatively small
vicinities of the lower and upper bound of the load.

A special class of general inequalities has been identified that provides the opportunity for generating new knowledge that can be used for optimising systems and processes in diverse areas of science and technology. It is demonstrated that inequalities belonging to this class can always be interpreted meaningfully if the variables and separate terms of the inequalities represent additive quantities. The meaningful interpretation of a new algebraic inequality based on the proposed general class of inequalities led to developing a light-weight design for a supporting structure based on cantilever beams, reducing
the maximum force upon impact, generating new knowledge about the deflection of elastic elements connected in parallel and series and optimising the allocation of resources to maximise expected benefit. The interpretation of the new inequality yielded that the deflection of elastic elements connected in parallel is at least n^2 times smaller than the deflection of the same elastic elements connected in series, irrespective of the individual stiffness values of the elastic elements. The interpretation of another algebraic inequality from the proposed general class led to a method for decreasing the stiffness of a mechanical
assembly by cyclic permutation of the elastic elements building the assembly. The analysis showed that a decrease of stiffness exists only if asymmetry of the stiffness values in the connected elements is present.

A method for optimising the design of systems and processes has been introduced that consists of interpreting the left- and the right-hand side of a correct algebraic inequality as the outputs of two alternative design configurations delivering the same required function. In this way, on the basis of an algebraic inequality, the superiority of one of the configurations is established. The proposed method opens wide opportunities for enhancing the performance of systems and processes and is very useful for design in general. The method has been demonstrated on systems and processes from diverse application domains.
The meaningful interpretation of an algebraic inequality based on a single-variable sub-additive function led to developing a light-weight design for a supporting structure based on cantilever beams. The interpretation of a new algebraic inequality based on a multivariable sub-additive function led to a method for increasing the kinetic energy absorbing capacity during inelastic impact. The interpretation of a new inequality has been used for maximising the mass of deposited substance during electrolysis and for generating new knowledge about the deflection of elastic elements connected in parallel and series.

The paper introduces a method for increasing the impact of additive quantities by meaningful interpretation of multivariate sub-additive and super-additive functions. The paper demonstrates that the segmentation of additive quantities through sub-additive and super-additive functions can be used to generate new knowledge and optimise systems and processes and the presented algebraic inequalities are applicable to any area of science and technology. The meaningful interpretation of the modified Cauchy-Schwarz inequality, led to a method for increasing of the power output from a voltage source and to a method for increasing the capacity for absorbing strain energy of loaded mechanical components. It was found that the existence of asymmetry is essential to increasing the strain energy absorbing capacity and the power output. Loaded elements experiencing the same displacement do not yield an increase of the absorbed strain energy. Similarly, loaded resistances experiencing the same current do not yield an increase of the power output. Finally, the meaningful interpretation of an algebraic inequality in terms of potential energy, resulted in a general necessary condition for minimising the sum of powers of distances to a fixed number of points in space.

The paper develops an important method related to using algebraic inequalities for uncertainty and risk reduction and enhancing systems performance. The method consists of creating relevant meaning for the variables and different parts of the inequalities and linking them with real physical systems or processes. The paper shows that inequalities based on multivariable sub-additive functions can be interpreted meaningfully and the generated new knowledge used for optimising systems and processes in diverse areas of science and technology. In this respect, an interpretation of the Bergstrom inequality, which is based on a sub-additive function, has been used to increase the accumulated strain energy in components
loaded in tension and bending. The paper also presents an interpretation of the Chebyshev’s sum inequality that can be used to avoid the risk of overestimation of returns from investments and an interpretation of a new algebraic inequality that can be used to construct the most reliable series-parallel system. The meaningful interpretation of other algebraic inequalities yielded a highly counter-intuitive result related to assigning devices of different types to missions composed of identical tasks. In the case where the probabilities of a successful accomplishment of a task, characterising the devices, are unknown, the best strategy for a successful accomplishment of the mission consists of selecting randomly an arrangement including devices of the same type. This strategy is always correct, irrespective of existing
uknown interdependencies among the probabilities of successful accomplishment of the tasks characterising the devices.

The paper demonstrates for the first time uncertainty reduction and attaining superior performance through segmentation based on algebraic inequalities. Meaningful interpretation of algebraic inequalities has been used for generating new knowledge in unrelated application domains. Thus, the method of segmentation through an abstract inequality led to a new theorem related to electrical circuits. The power output from a source with particular voltage, on elements connected in series, is smaller than the total power output
from the segmented sources applied to the individual elements. Segmentation attained through the same abstract inequality led to another new theorem related to electrical capacitors. The energy stored by a charge of given size on a single capacitor is smaller than the total energy stored in multiple capacitors with the same equivalent capacity, by segmenting the initial charge over the separate capacitors. Finally, inequalities based on sub-additive and superadditive functions have been introduced for reducing uncertainty and obtaining
superior performance by a segmentation or aggregation of controlling factors. By a meaningful interpretation of sub-additive and super-additive inequalities, superior performance has been achieved for processes described by a powerlaw dependence.

The paper discusses applications of the domain-independent method of algebraic inequalities, for reducing uncertainty and risk. Algebraic inequalities are used for revealing the intrinsic reliability of competing systems and ranking the systems in terms of reliability in the absence of knowledge related to the reliabilities of their components. An algebraic inequality has also been used to establish the principle of the well-ordered parallel-series systems which, in turn, has been applied to maximise the reliability of common parallel-series systems.

The paper introduces a method of linking an abstract inequality to a real process by a meaningful interpretation of the variables entering the inequality and its left- and right-hand part. The meaningful interpretation of a simple algebraic inequality led to a counter-intuitive result. If two items from varieties are present in a large batch, the probability of selecting randomly two items of different variety does not exceed 0.5.

The paper introduces two fundamental approaches for reliability improvement and risk reduction by using nontrivial algebraic inequalities: (a) by proving an inequality derived or conjectured from a real system or process and (b) by creating meaningful interpretation of an existing nontrivial abstract inequality
relevant to a real system or process. A formidable advantage of the algebraic inequalities can be found in their capacity to produce tight bounds related to reliability-critical design parameters in the absence of any knowledge about the variation of the controlling variables. The effectiveness of the first approach has
been demonstrated by examples related to decision-making under deep uncertainty and examples related to ranking systems built on components whose reliabilities are unknown. To demonstrate the second approach, meaningful interpretation has been created for an inequality that is a special case of the Cauchy-Schwarz inequality. By varying the interpretation of the variables, the same inequality holds for elastic elements, resistors, and capacitors arranged in series and parallel. The paper also shows that meaningful interpretation of superadditive and subadditive inequalities can be used with success for optimizing various systems and processes. Meaningful interpretation of superadditive and subadditive inequalities has been used for maximizing the stored elastic strain energy at a specified total displacement and for optimizing the profit from
an investment. Finally, meaningful interpretation of an algebraic inequality has been used for reducing uncertainty and the risk of incorrect prediction about the magnitude ranking of sequential random events.

The deliberate weaknesses are points of weakness towards which a potential failure is channelled in order to limit the magnitude of the consequences from failure. The paper shows that reducing risk by deliberate weaknesses is a powerful domain-independent method which transcends mechanical engineering and works in various unrelated areas of human activity. A classification has been proposed of categories and classes of deliberate weaknesses reducing risk as well as discussion related to the underlying mechanisms of risk reduction. It is shown that introducing and repositioning existing weaknesses is an effective risk-reduction strategy which transcends engineering and can be applied in many unrelated domains. The paper shows that in the case where the cost of failure of the separate components in a system varies significantly, an approach based on deliberate weaknesses has a significant advantage to the equal-reliability/equal-strength design approach.

The paper introduces a powerful domain-independent method for improving reliability and reducing risk based on algebraic inequalities, which transcends mechanical engineering and can be applied in many unrelated domains. The paper demonstrates the application of inequalities to reduce the risk of failure by producing tight uncertainty bounds for properties and risk-critical parameters. Numerous applications of the upper-bound-variance inequality have been demonstrated in bounding uncertainty from multiple sources, among which is the estimation of uncertainty in setting positioning distance and increasing the robustness of electronic devices. The rearrangement inequality has been used to maximise the reliability of components purchased from suppliers. With the help of the rearrangement inequality, a highly counter-intuitive result has been obtained. If no information about the component reliability characterising the individual suppliers is available, purchasing components from a single supplier or from the smallest possible number of suppliers maximises the probability of a high-reliability assembly. The Cauchy-Schwartz inequality has been applied for determining sharp bounds of mechanical properties and the Chebyshev's inequality for determining a lower bound for the reliability of an assembly. The inequality of the inversely correlated random events has been introduced and applied for ranking risky prospects involving units with unknown probabilities of survival.

The paper introduces new domain-independent methods for improving reliability and reducing risk based on algebraic inequalities and chain-rule segmentation. Two major advantages of algebraic inequalities for reducing risk have been demonstrated: (i) ranking risky prospects in the absence of any knowledge related to the individual building parts and (ii) reducing the variability of a risk-critical critical output parameter. The paper demonstrates a highly counter-intuitive result derived by using inequalities: if no information about the component reliability characterising the individual suppliers is available, purchasing components from a single supplier or from the smallest possible number of suppliers maximises the probability of a high-reliability assembly. The paper also demonstrates the benefits from combining domain-independent methods
and domain-specific knowledge for achieving risk reduction in several unrelated domains: decision-making, manufacturing, strength of components and kinematic analysis of complex mechanisms. In this respect, the paper introduces the chain rule segmentation method and applies it to reduce the risk of computational errors in kinematic analysis of complex mechanisms. The paper also demonstrates that combining the domain-independent method of segmentation and domain-specific knowledge in stress analysis leads to a significant reduction of the internal stresses and reduction of the risk of overstress failure.

The popular domain-specific approach to risk reduction created the illusion that efficient risk reduction can be delivered successfully solely by using methods offered by the specific domain. As a result, many industries have been deprived from efficient risk reducing strategy and solutions. This paper argues that risk reduction is underlined by domain-independent methods and principles which, combined with knowledge from the specific domain, help to generate effective risk reduction solutions. In this respect, the paper introduces a powerful method for reducing the likelihood of computational errors based on combining the domain-independent method of segmentation and local knowledge of the chain rule for differentiation. The paper also demonstrates that lack of knowledge of domain-independent principles for risk reduction misses opportunities to reduce the risk of failure even in such mature field like stress analysis. The domain-independent methods for risk reduction do not rely on reliability data or knowledge of physical mechanisms underlying possible failure modes and are particularly well suited for developing new designs, with unknown failure mechanisms and failure history. In many cases, the reliability improvement and risk reduction by using the domain-independent methods reduces risk at no extra cost or at a relatively small cost. The presented domain-independent methods work across totally unrelated domains and this is demonstrated by the supplied examples which range from various areas of engineering and technology, computer science, project management, health risk management, business and even mathematics. The domain-independent risk reduction methods presented in this paper promote building products and systems characterised by high-reliability and resilience.

The paper also demonstrates that the successive shortest path strategy for minimising the total length of transportation routes from multiple interchangeable origins to multiple destinations fails to minimise the total length of the routes. It is demonstrated that even in a network with multiple origins and a single destination, the successive shortest path strategy could still fail to minimise the total length of the routes. By using the developed theoretical framework, it is shown that a minimum total length of the transportation routes in a network with multiple interchangeable origins, is attained if and only if no closed parasitic flow loops and dominated flow loops exist in the network. Accordingly, an algorithm for minimising the total length of the transportation routes by eliminating all dominated parasitic flow loops is proposed. 

The paper provides for the first time a comprehensive introduction into the mechanisms through which the method of separation achieves risk reduction and into the ways it can be implemented in engineering designs. The concept stochastic separation of critical random events on a time interval, which consists of guaranteeing with a specified probability a specified degree of distancing between the random events, is introduced. Efficient methods for providing stochastic separation by reducing the duration times of overlapping critical random events on a time interval are presented. The paper shows that the probability of overlapping of critical events, randomly appearing on a time interval, is practically insensitive to the distribution of their duration times and to the variance of the duration times as long as the mean of the duration times remains the same. A rigorous proof is presented that this statement is valid even for two random events on a time interval. The paper also provides insight into various mechanisms through which deterministic separation improves reliability and reduces risk. It is demonstrated that the separation on properties is an efficient technique for compensating the drawbacks associated with homogeneous properties. It is demonstrated that improving reliability by including redundancy, improving reliability by segmentation and some of the deliberate weak link techniques and stress limiters techniques for reducing risk are effectively special cases of a deterministic separation. Finally, the paper demonstrates that in a number of cases, the way to extract benefit from the method of separation is to build and analyse a mathematical model based on the method of separation. A comprehensive classification of the discussed methods for stochastic and deterministic separation is also presented.

The concept ‘stochastic separation’ of random events and methods for providing a stochastic separation have been introduced. It is shown that separation of properties is an efficient technique for compensating the drawbacks associated with a selection based on homogeneous properties. It is also demonstrated that the method of deliberate weak links and the method of segmentation can be considered as a special case of the method of separation. Finally, the paper demonstrates that the traditional reliability measure ‘safety margin’ is misleading and should not be used as a measure of the relative separation between load and strength

associated with transportation losses, congestion and increased pollution of the environment and are highly undesirable in real flow networks.

The paper derives a necessary and sufficient condition for the non-existence of dominated parasitic flow loops in the case of presence of paths with zero and non-zero flow. The necessary and sufficient condition is at the basis of a method

for determining the probability of a dominated parasitic flow loop. The results demonstrate that the probability of a dominated parasitic flow loop is very large and increases very quickly with increasing the number of flow paths.

Dominated parasitic flow loops can be drained by augmenting them with flow, which results in an overall decrease of the transportation cost, without affecting the quantity of delivered commodity from sources to destinations. Accordingly, an

efficient algorithm for removing dominated parasitic flow loops has been presented and a number of important applications have been identified. The presented algorithm has the potential to save a significant amount of resources to the world economy.

Accordingly, a new formulation of the (0-1) knapsack resource allocation model is proposed where the weighted sum of thebenefit and the remaining budget is maximised instead of the total benefit. The proposed optimisation model produces solutionssuperior to both – the standard (0-1) dynamic programming approach and the cost-benefit approach.

On the basis of common parallel-series systems, the paper also demonstrates that because of synergistic effects, sets includingthe same number of identical options could remove different amount of total risk. The existence of synergistic effects doesnot permit the application of the (0-1) dynamic programming approach. In this case, specific methods for optimal resource allocation should be applied. Accordingly, the paper formulates and proves a theorem stating that the maximum amount of removed total risk from operations and systems with parallel-series logical arrangement is achieved by using preferentially the available budget on improving the reliability of operations/components belonging to the same parallel branch. Improving the reliability of randomly selected operations/components not forming a parallel branch leads to a sub-optimal risk reduction.The theorem is a solid basis for achieving a significant risk reduction for systems and processes with parallel-series logical arrangement.

In this paper, we also raise awareness of a fundamental flaw of algorithms for maximising the throughput flow published since 1956. They all leave highly undesirable parasitic flow loops in the optimised networks and are unsuitable for network optimisation without an additional stage aimed at removing them.

Finally, unlike heuristic optimisation algorithms, the proposed algorithm for a topology optimisation of the network always determines the optimal solution.

The high computational speed of the developed production availability solver created the possibility for embedding it in simulation loops, performing a topology optimisation of large and complex repairable networks, aimed at attaining a maximum average availability within a specified budget for building the network. An exact optimisation method has been proposed, based on pruning the full-complexity network by using the branch and bound method as a way of exploring possible network topologies. This makes the proposed algorithm much more efficient, compared to an algorithm implementing a full exhaustive search. In addition, the proposed method produces an optimal solution compared to heuristic optimisation methods.

The application of the bound and branch method is possible because of the monotonic dependence of the production availability on the number of the edges pruned from the full-complexity network.

Methods have also been developed for specifying the maximum acceptable level of the flaw number density and the maximum size of the stressed volume which guarantee that the probability of failure initiated by flaws remains below a maximum acceptable level. An important parameter referred to as ‘detrimental factor’ is also introduced. Components with identical geometry and material, with the same detrimental factors are characterised by the same probability of failure. It is argued that eliminating flaws from the material should concentrate on types of flaws characterised by large detrimental factors.

The equations proposed avoid conservative predictions resulting from equating the probability of failure initiated by a flaw in a stressed region with the probability of existence of the flaw in that region.

An efficient discrete-event simulation model and algorithm have been proposed for reliability analysis based on the losses from failure for production systems with complex topology. The model links reliability with losses from failures. A new algorithm has also been developed for system reliability analysis related to productions systems based on multiple production units where the absence of critical failure means that at least m out n production units are working.

The parametric study conducted on the basis of the developed models revealed that a dual-control production system is characterized by enhanced production availability, which increases with increasing the number of production units in the system. A production unit from a dual-control production system including multiple production units is characterized by a larger availability compared to a production unit from a dual-control production system including a single production unit.

The proposed approach has been demonstrated by comparing the losses from failures and the net present values of two competing design topologies: one based on a single-channel control and the other based on a dual-channel control. The proposed models have been successfully applied and tested for reliability value analysis of productions systems in deepwater oil and gas production.

It is also argued that the reliability allocation in a production system should be done to maximize the net profit/value obtained from the system. Consequently, a method for setting reliability requirements and reliability allocation maximizing the net profit by minimizing the sum of the capital costs and the expected losses from failures has been proposed. Reliability allocation which maximizes the net profit in case of a system consisting of blocks arranged in series is achieved by determining for each block individually, the reliabilities of the components which minimize the sum of the capital costs and the expected losses from failures.

– The aim of this paper is to propose efficient models and algorithms for reliability value analysis of complex repairable systems linking reliability and losses from failures.

Design/methodology/approach

– The conventional reliability analysis is based on the premise that increasing the reliability of a system will decrease the losses from failures. In this paper it is demonstrated that a system with larger reliability does necessarily mean a system with smaller losses from failures. In other words, a system reliability improvement, which is disconnected from the losses from failures does not necessarily reduce the losses from failures. An efficient discrete‐event simulation model and algorithm are proposed for tracking the losses from failures for systems with complex topology. A new algorithm is also proposed for system reliability analysis related to productions systems based on multiple production units where the absence of a critical failure means that at least m out n production units are working.

Findings

– A model for determining the distribution of the net present value (NPV) characterising the production systems is developed. The model has significant advantages compared to models based on the expected value of the losses from failures. The model developed in this study reveals the variation of the NPV due to variation of the number of critical failures and their times of occurrence during the entire life‐cycle of the systems.

Practical implications

– The proposed models have been successfully applied and tested for reliability value analysis of productions systems in deepwater oil and gas production.

Originality/value

– The proposed approach has been demonstrated by comparing the losses from failures and the NPVs of two competing design topologies: one based on a single‐channel control and the other based on a dual‐channel control.