Wyniki wyszukiwania - BazTech

1

Preliminary approach to modelling eutrophication - anthropopressure impact on sea water quality

Bogalecka Magdalena

Safety and Reliability of Systems and Processes

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2023

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Summer Safety and Reliability Seminar 2023

19--31

EN

The chapter is devoted to the problem of eutrophication. Methods and parameters for its assessment are described. Furthermore, the eutrophication of the Baltic Sea is discussed in detailed. Finally, the semi-Markov model of the eutrophication process is proposed, and its characteristics are determined.

2

Modelling process of municipal wastewater quality - backgrounds and preliminary application

Bogalecka Magdalena, Dereszewska Alina

Safety and Reliability of Systems and Processes

|

2022

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Summer Safety and Reliability Seminar 2022

17--34

EN

The probabilistic model of municipal wastewater quality process is proposed in the chapter. The methods of its characteristics and parameters statistical identification and prediction are presented. Next the proposed model is practically applied to examine and characterized the quality of the municipal wastewater collected in the exemplary sewage treatment plant.

3

Semi-markovian approach to modelling air pollution

Bogalecka Magdalena

Safety and Reliability of Systems and Processes

|

2021

|

Summer Safety and Reliability Seminar 2021

31--44

EN

The air pollution assessment based on concentration’s changes of sulphur dioxide, carbon monoxide, nitrogen dioxide, ozone, benzene, and particulate matter is discussed in the chapter. The semi-Markov model of the environmental pollution process is introduced and its characteristics are determined. Next the proposed model is practically applied to examine and characterized air pollution in Gdańsk (Poland) as the exemplary industrial agglomeration. The main parameters and characteristics of the air pollution process are determined, such as concentration states of particular kinds of air pollutants, the limit values of transient probabilities and the mean total sojourn times staying at the air pollutants’ concentration states, for the fixed time interval.

4

Możliwość oszacowania czasu działania dowolnego okrętowego urządzenia energetycznego

Girtler Jerzy

Journal of Polish CIMEEAC

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2021

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Vol. 16, no 1

43--55

PL

W artykule przedstawiono propozycję modelu procesu eksploatacji dowolnego okrętowego urządzenia energetycznego w formie trójstanowego procesu semi-markowskiego {Y(t): t ≥ 0} o zbiorze stanów Z = {z1, z2, z3} i następującej interpretacji elementów tego zbioru: z1 – stan użytkowania urządzenia o stanie pełnej zdatności, (z2) – stan obsługiwania planowego (profilaktycznego) urządzenia będącego w stanie zdatności częściowej, (z3) – stan obsługiwania nieplanowego (wymuszonego uszkodzeniami) urządzenia, które jest wtedy w stanie niezdatności.. Przedstawiono uzasadnienie praktycznej przydatności takiego modelu z uwzględnieniem warunków eksploatacji okrętowych urządzeń energetycznych. Zasygnalizowano, że na bazie opracowanego modelu procesu eksploatacji o trzech stanach może być rozbudowany do tylu stanów eksploatacji ile musi uwzględnić użytkownik wspomnianych urządzeń, aby zapewnić racjonalną ich eksploatację.

5

Degrading systems availability analysis: analytical semi-Markov approach

Kumar Varun, Kumar Girish, Singh Rajesh Kumar, Soni Umang

Eksploatacja i Niezawodność

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2021

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Vol. 23, no. 1

195--208

EN

This paper deals with modeling and analysis of complex mechanical systems that deteriorate with age. As systems age, the questions on their availability and reliability start to surface. The system is believed to suffer from internal stochastic degradation mechanism that is described as a gradual and continuous process of performance deterioration. Therefore, it becomes difficult for maintenance engineer to model such system. Semi-Markov approach is proposed to analyze the degradation of complex mechanical systems. It involves constructing states corresponding to the system functionality status and constructing kernel matrix between the states. The construction of the transition matrix takes the failure rate and repair rate into account. Once the steady-state probability of the embedded Markov chain is computed, one can compute the steady-state solution and finally, the system availability. System models based on perfect repair without opportunistic and with opportunistic maintenance have been developed and the benefits of opportunistic maintenance are quantified in terms of increased system availability. The proposed methodology is demonstrated for a two-stage reciprocating air compressor with intercooler in between, system in series configuration.

6

Limiting distribution of the three-state semi-Markov model of technical state transitions of ship power plant machines and its applicability in operational decision-making

Girtler Jerzy

Polish Maritime Research

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2020

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nr 2

136--144

EN

The article presents the three-state semi-Markov model of the process {W(t): t > 0} of state transitions of a ship power plant machine, with the following interpretation of these states: s1 – state of full serviceability, s2 – state of partial serviceability, and s3 – state of unserviceability. These states are precisely defined for the ship main engine (ME). A hypothesis is proposed which explains the possibility of application of this model to examine models of real state transitions of ship power plant machines. Empirical data concerning ME were used for calculating limiting probabilities for the process {W(t): t > 0}. The applicability of these probabilities in decision making with the assistance of the Bayesian statistical theory is demonstrated. The probabilities were calculated using a procedure included in the computational software MATHEMATICA, taking into consideration the fact that the random variables representing state transition times of the process {W(t): t > 0} have gamma distributions. The usefulness of the Bayesian statistical theory in operational decision-making concerning ship power plants is shown using a decision dendrite which maps ME states and consequences of particular decisions, thus making it possible to choose between the following two decisions: d1 – first perform a relevant preventive service of the engine to restore its state and then perform the commissioned task within the time limit determined by the customer, and d2 – omit the preventive service and start performing the commissioned task.

7

Probabilistyczny model procesu obciążeń mocą okrętowego tłokowego silnika głównego i jego praktyczna przydatność

Girtler Jerzy

Journal of Polish CIMEEAC

|

2020

|

Vol. 15, no 1

46--61

PL

W artykule przedstawiono propozycję modelu widma obciążeń mocą okrętowego silnika głównego w formie czterostanowego procesu semi-Markoawa{D(t): t≥0}ciągłego w stanach i czasie o zbiorze stanów C= {c1, c2, c3, c4} i następującej interpretacji elementów tego zbioru: c1–obciążenie silnika mocą częściową, c2–obciążenie silnika mocą trwałą, c3–obciążenie silnika mocą znamionową, c4–obciążenie silnika mocą maksymalną. Określono rozkład graniczny wspomnianego procesu i wykazano możliwość oszacowania prawdopodobieństw tego rozkładu. Przedstawiono uzasadnienie potrzeby opracowania takiego modelu charakteryzując warunki eksploatacji okrętowych silników głównych. Wykazano, że zastosowanie w praktyce nawet tak prostego modelu może być przydatne do planowania zapasu paliwa niezbędnego do działania silnika podczas rejsu statku. Wykazano też, że model ten może być zmodyfikowany, w zależności od potrzeb eksploatacyjnych tak, aby uwzględnionych było w nim tyle stanów odzwierciedlających poszczególne rodzaje obciążeń mocą silnika głównego, ile musi znać użytkownik, aby zapewnić racjonalną jego eksploatację.

8

Identifying the issue of reducing the emission of harmful compounds in the exhaust gas from marine main engines and description of the emission process of these compounds in probabilistic approach

Łosiewicz Z.

Polish Maritime Research

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2017

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nr 2

89--95

EN

The article discusses the results of actions performed by marine engine manufacturers towards the reduction of emission of harmful substances in the exhaust gas from these engines. The discussion is limited to main engines produced by MAN B&W. A model is proposed to describe the process of emission of harmful substances from Diesel engines based on the semi-Markov process, discrete in states and continuous in the operating time. The states of this process are: engine ability state (s1) and engine inability state (s2). A method to calculate probabilities P1 and P2 of the appearance of states s1 and s2 is proposed. State s1 is interpreted as corresponding to the inequality ekek(dop), where ek represents the mass of harmful substances emitted by the engine during its operation and ek(dop) is the maximum mass of emission of these substances permitted by relevant regulations.

9

Determination of probabilities defining safety of a sea-going ship during performance of a transportation task in stormy weather conditions

Girtler J.

Journal of Polish CIMEEAC

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2017

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Vol. 12, no 1

21--30

EN

The paper presents the possibility of applying the theory of semi-Markov processes to determine the limiting distribution for the process of changes of technical states being reliability states of the systems of sea-going ships significantly affecting safety of such ships, which include main engine, propeller and steering gear. The distribution concerns the probabilities of occurrence of the said states defined for a long time of ship operation (t → ∞). The considered states are as follows: s0 – full ability state of the systems, i.e.: main engine, propeller and steering gear, s1 – inability state of the main engine, s2 – inability state of the propeller, s3 – inability state of the steering gear. Significance of the systems for safety of the ships at sea was demonstrated herein. General conditions for performing transportation tasks by the ships, with particular regard to stormy conditions, were also here described.

10

Semi-Markov model of quality state changes of a selected transport system

Landowski B., Muślewski Ł., Knopik L., Bojar P.

Journal of KONES

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2017

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Vol. 24, No. 4

141--148

EN

The study deals with the problems connected with evaluation and analysis of transport systems operational quality. The research object is a real, sociotechnical system (of the type H-M-E) whose functional quality is affected by: operators, equipment and technical state of he operated vehicles and the environmental impact. A scheme of an assessment model was built on the basis of a developed concept of a system operational quality and a random process was defined to be used for the analysis. The assessment process involves investigating the variability degree of properties included in the resultant model in a given time and determining whether and to what degree the obtained values meet the requirements of the system appropriate operational quality. On the basis of the above assumptions and in result of experimental tests, four qualitative states of a transport system functioning, which represent intervals of values of the obtained grades in given time moments, were distinguished. The study presents a model of system operation qualitative state changes developed with the use of Markov chain inserted into a certain semi-Markov process. A graph and a matrix for probability of transition between the states were created and boundary distributions of the process were determined on the basis of experimentally obtained data. A system of equations was determined for the distinguished Markov chain, on the basis of which a mathematical model for assessment and control of operational quality of selected types of transport systems will be built.

11

Optimal age-replacement policy for non-repairable technical objects with warranty

Knopik L., Migawa K.

Eksploatacja i Niezawodność

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2017

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Vol. 19, no. 2

172--178

PL

W pracy bada się efekty wprowadzenia odnów prewencyjnych do systemu eksploatacji, realizowanych przez wymiany według wieku obiektów technicznych posiadających gwarancję producenta i nienaprawialnych. W tym celu bada się koszt przypadający na jednostkę czasu, wynikający z wykonywanych w systemie eksploatacji wymian profilaktycznych i napraw. Funkcję wyrażającą ten koszt w zależności od czasu wymiany zdefiniowano w oparciu o podstawy teorii procesów semi–Markowa. Sformułowano warunki dostateczne istnienia minimum kosztu wymian w przypadku, gdy czas do uszkodzenia ma niemalejącą funkcję intensywności uszkodzeń. W końcowej części artykułu przedstawiono przykład numeryczny ilustrujący przedstawione w pracy wyniki.

EN

This paper investigates the effects of introducing preventive replacement to maintenance system implemented by age-replacement of technical objects with valid manufacturer’s warranty and non-repairable. In order to examine this, the cost per unit time, resulting from the use of the preventive replacements and repairs system is investigated. The function expressing the cost depending on the time of replacement is defined on the basis of the foundations of the theory of semi-Markov processes. Sufficient conditions for the existence of the minimum of criteria function were formulated, in this case when the failure rate function is increasing. In the final part of the paper, a numerical example illustrating the findings of the paper was presented.

12

Concept of semi-Markov process

Grabski F.

Zeszyty Naukowe Akademii Marynarki Wojennej

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2016

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R. 57 nr 3 (206)

25--36

EN

This paper provides the definitions and basic properties related to a discrete state space semi-Markov process. The semi-Markov process is constructed by the so called Markov renewal process that is a special case the two-dimensional Markov sequence. The Markov renewal process is defined by the transition probabilities matrix, called the renewal kernel and an initial distribution or by another characteristics which are equivalent to the renewal kernel. The counting process corresponding to the semi-Markov process allows to determine concept of the process regularity. In the paper are also shown the other methods of determining the semi-Markov process. The presented concepts are illustrated a simple example.

PL

Artykuł przedstawia definicje i podstawowe cechy procesu semi-Markowa dyskretnego stanu przestrzeni. Proces semi-Markova jest zbudowany przez tzw. proces odnawiania Markova, który jest specjalnym przypadkiem dwuwymiarowego ciągu Markova. Proces odnawiania Markova jest zdefiniowany przez macierz prawdopodobieństw przejściowych, zwaną jądrem odnawiania, i początkowy rozkład lub przez inne charakterystyki, które są równe jądru odnawiania. Proces obliczeniowy odpowiadający procesowi semi-Markova pozwala na określenie koncepcji regularności procesu. W artykule przedstawiono również pozostałe metody określania procesu semi-Markova. Przedstawione koncepcje są zaprezentowane na prostym przykładzie.

13

A model of fuel combustion process in the marine reciprocating engine work space taking into account load and wear of crankshaft-piston assembly and the theory of semi-Markov processes

Girtler J.

Polish Maritime Research

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2016

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nr 3

50--57

EN

The article analyses the operation of reciprocal internal combustion engines, with marine engines used as an example. The analysis takes into account types of energy conversion in the work spaces (cylinders) of these engines, loads of their crankshaft-piston assemblies, and types of fuel combustion which can take place in these spaces during engine operation. It is highlighted that the analysed time-dependent loads of marine internal combustion engine crankshaftpiston assemblies are random processes. It is also indicated that the wear of elements of those assemblies resulting from their load should also be considered a random process. A hypothesis is formulated which explains random nature of load and the absence of the theoretically expected detonation combustion in engines supplied with such fuels as Diesel Oil, Marine Diesel Oil, and Heavy Fuel Oil. A model is proposed for fuel combustion in an arbitrary work space of a marine Diesel engine, which has the form of a stochastic four-state process, discrete in states and continuous in time. The model is based on the theory of semi-Markov processes.

14

Application of semi-Markov processes for evaluation of diesel engines reliability with regards to diagnostics

Girtler J.

Journal of Polish CIMEEAC

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2016

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Vol. 11, no 1

47--53

EN

The paper presents semi-Markov models of technical state transitions for diesel engines, useful for determination of their reliability, as a result of the conducted statistical empirical studies. Interpretation of technical states provided for this sort of engines refers to ship main engines, i.e. engines employed in propulsion systems of sea-going ships. The considerations recognize diesel engine as a diagnosed system (SDN), of which state can be identified by a diagnosing system (SDG). Both of the systems: SDN and SDG compose a diagnostic system (SD). Examples of three-state semi-Markov models were applied to demonstrate that in case of use of proper diagnosing systems (SDG) for identification of technical states of such engines as SDN, by classification of the states to the relevant class of the reference states, it is possible to make use of a Markov model to determine reliability of the engines. For developing a Markov model of state transitions for the engines, there were applied functions of the risk of damage: λ12 that causes transition from state s1 to state s2, and λ13 that causes transition from state s1 to state s3, as well as intensity functions of recovery (restitution): λ21 that causes transition from state s2 to state s1, and λ31 that causes transition from state s3 to state s1.

15

Analysis of operation efficiency of selected transport systems

Muślewski Ł., Lewalski M., Aleksandrowicz P., Landowski B.

Journal of KONES

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2016

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Vol. 23, No. 3

351--358

EN

This study deals with the problems connected with evaluation of technical systems efficiency of particular transport systems. The main goal of such a system operation is its effective functioning, through rational control of its particular activities and subsequent processes. A literature analysis of the definition of the efficiency term has been made. A real transport system has been accepted to be the research object. The system belongs to the group of sociotechnical systems in which evaluation of its operation efficiency depends on performance of operators, transport means and the impact of environmental factors. Criteria and methods of operation efficiency evaluation have been determined in this study as well as assessment indexes for transport systems. It has been shown that evaluation of a repair efficiency has a large influence on the efficiency of the whole system operation, especially the influence of secondary failure repairs, on the values of particular efficiency indexes. A semi-markov model of operation and maintenance of transport means used in the research object has been developed. This model provides the basis for evaluation of the influence of the processes involved in preparing transport means for service on the system operation efficiency. Moreover, the research also describes how to verify the developed model and present its simulation tests. The study is summarized with conclusions formulated based on the evaluation of the influence of the operation and maintenance processes on the investigated transport system operation efficiency.

16

On simulation of maintenance costs for water distribution system with fuzzy parameters

Romaniuk M.

Eksploatacja i Niezawodność

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2016

|

Vol. 18, no. 4

514--527

EN

In this paper we propose a model for evaluation of maintenance costs of a water distribution system (WDS). The set of possible states of each connection (i.e. a pipeline in the WDS) is related to various possible degrees of quality of the pipe and types of its malfunctions. The process of transitions between these states forms a semi-Markov process. Using Monte Carlo simulations, the length of services and the times of necessary replacements and repairs of the connections are obtained. These values are then used as an input for estimation of the maintenance costs of the whole WDS. During this step we take into account the concept of present value of money. Contrary to other approaches, instead of a constant yield, a stochastic process (the one-factor Vasicek model) of an interest rate is assumed. Then various simulated measures of reliability and the maintenance costs can be analysed, like an influence of various parameters of the pipes (e.g. intensities of damages) on the final costs of the performed services. They can be crucial in the analysis of risk for various possible decisions. Apart from the crisp approach, the Monte Carlo simulations are also applied, if some of the parameters of the WDS are fuzzified. Therefore uncertainty and experts’ knowledge can be easily incorporated into the proposed procedure of the estimation of the maintenance costs. Observed differences between the crisp and the fuzzy output are highlighted. Simulation algorithms, necessary for both of these approaches, are also provided.

PL

W niniejszym artykule przedstawiono model obliczający koszty utrzymania i konserwacji dla systemu dystrybucji wody (WDS). Zbiór możliwych stanów każdego połączenia (tzn. odcinku rurociągu w WDS) jest zdefiniowany przez różne poziomy jakości rury oraz występujące typy uszkodzeń. Proces przejść pomiędzy tymi stanami jest opisany procesem semi-Markowa. Wykorzystując symulacje Monte Carlo, uzyskano długości okresów obsługi oraz momenty niezbędnych wymian i napraw. Wartości te są następnie wykorzystywane do estymowania kosztów utrzymania całego WDS. W kroku tym brana jest pod uwagę wartość pieniądza w czasie. W przeciwieństwie do innych podejść, zamiast stałej stopy procentowej, założono stochastyczny proces stopy (dany jednowymiarowym modelem Vasicka). Następnie na podstawie przeprowadzonych symulacji wykonano analizę opartą o różne miary niezawodności i obliczone koszty obsługi, np. zbadano wpływ parametrów połączenia (takich jak intensywność uszkodzeń) na ostateczne koszty konserwacji. Analizy tego typu mogą pełnić istotną rolę w ocenie ryzyka dla różnych możliwych do podjęcia decyzji. Poza podejściem typu crisp, zastosowano również symulacje Monte Carlo gdy niektóre z parametrów WDS zostały określone w sposób rozmyty. Dzięki temu można wykorzystać niepewność oraz wiedzę ekspercką w proponowanej metodzie estymacji kosztów obsługi. Zwrócono uwagę na różnice występujące pomiędzy podejściem crisp i rozmytym. Zostały również opisane niezbędne dla obydwu podejść odpowiednie algorytmy symulacyjne.

17

Identification of damages of tribological associations in crankshaft and piston systems of two-stroke internal combustion engines used as main propulsion in sea-going vessels and proposal of probabilistic description of loads as causes of these damages

Girtler J.

Polish Maritime Research

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2015

|

nr 2

44--54

EN

The article discusses damages of essential tribological associations in crankshaft and piston systems of large power two-stroke engines used as main engines, which take place during transport tasks performed by those ships. Difficulties are named which make preventing those damages impossible, despite the fact that the technical state of engines of this type is identified with the aid of complex diagnostic systems making use of advanced computer technology. It is demonstrated that one of causes of the damages is the lack of research activities oriented on recognising random properties of the loads leading to those damages. A proposal is made for the loads acting at a given time ton tribological associations in crankshaft and piston systems of internal combustion engines used as main engines to be considered as random variables Qt. At the same time the loads examined within a given time interval tr ≤ t ≤ tz would be considered stochastic processes {Q(t): t ≥ 0}. Essential properties of the loads of the abovementioned tribological associations are named and explained by formulating hypotheses which need empirical verification. Interval estimation is proposed for estimating the expected value E(Qt) of the load Qt acting at time t. A relation is indicated between the mechanical load and the thermal load acting on tribological associations in the ship main engine crankshaft and piston system. A suggestion is formulated that a stochastic form of the relation between these types of load is to be searched for, rather than statistic relation, and a proposal is made to measure the intensity (strength) of the stochastic relation using the Czuprow’s convergence coefficient.

18

Metoda wyznaczania strategii sterowania procesem eksploatacji

Migawa K., Knopik L., Neubauer A.

Logistyka

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2015

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nr 4

2006--2015, CD2

PL

W pracy przedstawiono metodę wyznaczania strategii sterowania procesem eksploatacji obiektów technicznych, w której wybór decyzji sterujących realizowany jest z zastosowaniem decyzyjnych procesów semi-Markowa oraz algorytmu genetycznego. W prezentowanej metodzie wyznaczenie strategii sterowania procesem eksploatacji obiektów technicznych dotyczy wyboru ciągu decyzji sterujących, podejmowanych w poszczególnych stanach modelowanego procesu. Metoda ta polega na wyborze spośród możliwych wariantów decyzyjnych, najlepszej strategii sterowania procesem eksploatacji, dla której funkcja stanowiąca kryterium oceny osiąga wartość ekstremalną. W pracy przedstawiono przykład wyznaczenia strategii sterowania (ciągu decyzji), w przypadku, gdy funkcję kryterialną stanowi średni jednostkowy dochód. Całość rozważań przedstawiono na przykładzie procesu eksploatacji realizowanego w rzeczywistym systemie autobusowego transportu miejskiego.

EN

The paper presents a method of determining the strategy for control of technical objects operation and maintenance process, where semi-Markov decision processes and genetic algorithm are used for control. In the presented method, determining of strategy for control of technical objects operation and maintenance process involves the choice of a sequence of control decisions made in individual states of the modeled process. The method involves a choice, out of the possible decision options, of the best strategy for operation and maintenance process control for which the function constituting the evaluation criterion has extreme value. The paper presents an example of determining strategy for control (decision sequence) when the criterion function includes average unit profit. The study has been based on the operation and maintenance process of a real bus municipal transportation system.

19

Efektywnościowa analiza jakości działania wybranego systemu transportowego z zastosowaniem modelu semi-Markowa

Muślewski Ł., Lewalski M., Migawa K.

Journal of KONBiN

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2015

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No. 1 (33)

187--196

PL

Rozważania w niniejszym opracowaniu dotyczą problematyki oceny, analizy i zapewnienia odpowiedniej jakości działania systemów transportowych. Zidentyfikowano obiekt badań, którym jest rzeczywisty system transportowy, zaprezentowano schemat modelu ocenowego oraz opisano proces losowy, na podstawie którego dokonuje się jego oceny. W wyniku zrealizowanych badań eksploatacyjnych, wyróżniono stany jakościowe działania systemu, odwzorowujących przedziały wartości otrzymanych ocen w danych chwilach czasu. W dalszej części artykułu przedstawiono model oceny efektywności działania systemu eksploatacji rozpatrywanych obiektów technicznych, zbudowany z zastosowaniem teorii procesów semi-Markowa.

EN

This study deals with the problems connected with quality assurance for transport systems operation. The research was performed using data from a real transport system. The concept of a system operation quality was defined on the basis of which a schematic assessment model was developed and a random process was described to be used for its evaluation. Qualitative states of a system operation reflecting value ranges of the obtained evaluations in given times were identified in result of the experimental tests performed as part of the research. A model of a system operation efficiency evaluation was developed for the analyzed technical objects with the use of semi-Markov theory.

20

Possibility of estimating the reliability of diesel engines by applying the theory of semi-Markov processes and making operational decisions by considering reliability of diagnosis on technical state of this sort of combustion engines

Girtler J.

Combustion Engines

|

2015

|

R. 54, nr 4

57--66

EN

The paper presents semi-Markov models of technical state transitions for diesel engines, useful for determining the reliability of engines. A possibility of application of a three-state model with a simplified matrix function, or even a two-state model, to determine reliability of the engines, has been described herein on examples of known from literature semi-Markov models, for the case when appropriate diagnosing systems (SDG) are used to identify the technical condition of the engines considered as diagnosed systems (SDN). A risk function and a renewal (restitution) function have been proposed for developing a two-state model of engine state transitions. An opportunity for considering the reliability of diagnosis for making operational decisions by applying the statistical decision theory, has also been presented. Conditional probability P(si/Ki) is recognized as a measure of reliability of diagnosis.

PL

W artykule przestawiono semimarkowskie modele zmian stanów technicznych silników o zapłonie samoczynnym, przydatne do określenia niezawodności tych silników. Wykazano, na przykładzie znanych z literatury modeli semimarkowskich, że do określenia niezawodności tych silników możliwe jest zastosowanie modelu trójstanowego o uproszczonej macierzy funkcyjnej, a nawet modelu dwustanowego, przy zastosowaniu odpowiednich systemów diagnozujących (SDG) do identyfikacji stanu technicznego wspomnianych silników jako systemów diagnozowanych (SDN). Do opracowania dwustanowego modelu zmian stanów silników zaproponowano wykorzystanie funkcji ryzyka i funkcji intensywności odnowy (restytucji). Przedstawiono także możliwość uwzględnienia wiarygodności diagnozy przy podejmowaniu decyzji eksploatacyjnych w sytuacji zastosowania statystycznej teorii decyzji. Za miarę wiarygodności diagnozy przyjęto prawdopodobieństwo warunkowe P(si/Ki).