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To establish a more flexible and accurate reliability model, the reliability modeling and solving algorithm based on the meta-action chain thought are used in this thesis. Instead of estimating the reliability of the whole system only in the standard operating mode, this dissertation adopts the structure chain and the operating action chain for the system reliability modeling. The failure information and structure information for each component are integrated into the model to overcome the given factors applied in the traditional modeling. In the industrial application, there may be different operating modes for a multicomponent system. The meta-action chain methodology can estimate the system reliability under different operating modes by modeling the components with varieties of failure sensitivities. This approach has been identified by computing some electromechanical system cases. The results indicate that the process could improve the system reliability estimation. It is an effective tool to solve the reliability estimation problem in the system under various operating modes.

During recent decades, the electromechanical systems have been widely used in the industrial field. Therefore, the importance of the reliability of electromechanical systems has increased accordingly. On the other hand, the growing complexity of systems has made the job of reliability modeling more challenging. Many qualitative and quantitative techniques have been proposed to analyze the reliability. Traditional methods are effective under the hypothesis that system reliability can be described by macroscopic stochastic models while pure probability models only describe the stochasticity of failures in system level without considering failure mechanism. This paper is proposed to identify the connection between macroscopic system failure probability and microscopic failure cause. System operation information and structure information are integrated into the model to describe the state changes for a given system. In fact, macroscopic system operation is the input of the microscopic failure processes of each component in the system. On the other hand, the microscopic failure processes make up the macroscopic stochastic model. Herein, meta-action structure chain and operating series chain are proposed in this paper to combine these two aspects.

System reliability modeling has been widely used in researches in recent years [

In addition, the fuzzy set theory and Bayesian approach have been widely used especially in the cases that the systems have small sample [

In this paper, system operation is expressed as state transitions versus time dimension and the state of the system is expressed with all the status of meta-actions. State transitions of the specific meta-action are utilized to combine the information of failure modes. Traditional reliability modeling estimates the system reliability with system operating time. In fact, the operating time of each component in the system has an implicit function to the total operating time of the whole system and some failures are even not sensitive to the operating time (e.g., sensitive to rotation numbers and total travel). System structure information, operating information, and failure information should be integrated into one reliability model to make reliability estimation more practical.

Thus, the impact of the paper can be summarized as follows:

The rest of the thesis is organized as follows: Section

The Pedigree-Function-Movement-Action (PFMA) structural decomposition shown in Figure

PFMA structural decomposition for electromechanical system.

The meta-action theory has been utilized in the study of precision control and assembly reliability analysis. This method focuses on the minimum fault analytical unit to precisely control the reliability of the electromechanical system as shown in Figure

Meta-action assembly unit.

Meta-action of gear shaft rotation assembly unit.

Markov method has been widely applied in the research of the random process [

As meta-action focuses on the basic moving unit of the system, this method is used to analyze the system precisely. However, the reliability and precision are controlled by optimizing the sensitive parameters of the single essential meta-action in the former research. The failure mechanism and work mode effect are not included in the traditional modeling. On the one hand, the meta-action chain methodology (MCM) is put forward in this chapter to solve these problems. On the other hand, the traditional Markov chain methods in the reliability research only focus on the failure probability in the given states of the system. The relationship between the states selection and system operation has not been established. In the MCM model proposed by this study, the system operating states are represented by the meta-actions matrix and the mapping matrix. The meta-actions in each state have their own computing chains to ensure the consistency with the failure mechanism.

The definition of a meta-action chain is a series of ordered meta-actions that is driven by the same power input to describe the states of specific function in given condition and operating mode. Two kinds of information are considered in the meta-action chain. One is structure information and the other is operating state information. Meta-action chain includes two parts, the structure chain and operating series chain. The operating series chain can be mapped into the Markov chain for different working modes.

In structure chain, there are _{i}. For example, the number of outputs for the first input power is

Meta-action structure chain.

To realize specific operation cycle, electromechanical systems work orderly action by action as shown in Figure

Meta-action operating series chain.

To determine the reliability of each state for the system, the operating meta-action chain is expressed by the Boolean variable matrices. The universal set of the metaactions

Herein,

For example, if

Figure

State transition directed graph.

Take one column as an example in Figure

States change of specific meta-action.

In different operating modes, the state changes of the meta-actions are different. The operating mode information can be used in the modeling just as the failure mode information shown in Figure

Failure modes on different meta-actions.

The common failure modes include degradation, switch fault, and alternating stress. The failure mechanism can be reflected on the meta-actions as clearly shown in the figure. If the meta-action is designed to always run during the operation, the column is full of 1 as the normal operation column in the figure. When the degradation failures happen, the continuous state changes from 1 to 0. The second type of failure is the switch fault. The reliability of such kind of meta-action depends on the probability of successful action. The failure occurs when the state is not able to change. The third kind of failure is the alternating stress failure. The state change frequency of such type of meta-action is high, which may cause additional degradation to the function units. Thus, the reliability calculations for the three kinds of meta-actions are different.

In the degradation process, the reliability of meta-action depends on the operating time. The operating time is expressed as the discrete variable. In the given time interval

PLP (Power Law Process) is utilized to model the failure density function in the degradation process.

The failure rate of switch failure

LND (Logarithmic Normal Distribution) is used to model the probability density function in the alternating stress process.

The correction coefficient

On the other hand, the reliability of the whole system at time

Reliability transfer matrix

A flow chart is shown in Figure

Flow chart of reliability calculation.

The subsystem of a CNC machine tool is used to illustrate the method proposed by this thesis. The structure is presented in Figure

NC rotary table structure diagram.

The subsystem is used to realize the indexing rotation function of the rotary table. And the meta-action structure chain is established in Figure

Meta-action structure chain of NC rotary table.

The universal set of meta-actions

A typical work circle of the system concludes 2 functions, including the exchanging worktable and indexing table. The operating series chains of the functions are shown in Figure

Operating series chains of the functions.

Figure

Timing sequence diagram of the system.

The operation time of this cycle is 1 hour (3600 seconds) and the worktable needs to be exchanged before each cycle in 5 minutes (300 seconds). Thus, the sampling interval

Operating states matrix

The failure modes of each meta-action can be determined by the operating states matrix and the previous failure data. Table

Failure modes of each meta-action.

Meta-action | Degradation | Alternating | Switch |
---|---|---|---|

| Y | Y | Y |

| Y | Y | N |

| Y | Y | N |

| Y | Y | N |

| Y | Y | N |

| N | N | Y |

| Y | N | Y |

| Y | Y | Y |

| Y | N | N |

| Y | N | N |

| Y | N | Y |

| Y | N | N |

Degradation failure distribution function parameters of each meta-action.

Meta-action | | |
---|---|---|

| | 1.21 |

| | 1.43 |

| | 1.12 |

| | 1.44 |

| | 1.25 |

| | 1.31 |

| | 1.35 |

| | 1.17 |

| | 1.03 |

| | 1.24 |

| | 1.12 |

Switch failure rate of each meta-action.

Meta-action | |
---|---|

| |

| |

| |

| |

| |

Alternating stress failure distribution function parameters of each meta-action.

Meta-action | | |
---|---|---|

| 9.5 | 2.8 |

| 10 | 2.3 |

| 9.9 | 3.1 |

| 10.1 | 3.4 |

| 10.2 | 3.2 |

| 9.8 | 2.9 |

Pseudocodes of the solving algorithm are as follows:

for

for

for

if switch

if alternating stress

end;

The original failure data of the given system are obtained from experiments, customer survey, and customer service data. The parameters of reliability models are determined by the fitting probability density function. They are listed in Table

At the beginning of the curve, the reliability of the system decreases smoothly as the main failure mode is degradation. After 3000 hours, the number of alternating stress cycles reaches the critical value. Thus, the reliability of the system decreases sharply for the reason that the main failure mode changes into the alternating stress. This curve is smooth and the turning point is clear. The solving accuracy is acceptable.

The traditional reliability estimation models the system reliability curve with Weibull distribution as shown in Figure

Reliability estimation for the NC rotary table with MCM and Weibull distribution.

Compared with the Weibull distribution, the MCM curve contains more failure modes information. In fact, in the given working condition, alternating stress failures occur more frequently than degradation failures after 3000 hours. On the other hand, the Weibull distribution curve is still smooth after the occurrence of the critical value. The traditional modeling methods cannot describe such kind of trend. If the MCM method is set as the benchmark, a cumulative relative error of Weibull distribution is shown as follows:

This value shows the difference between the two methods directly. Generally, the two methods can reflect the overall trend of the failure rate of the given system. According to some specific details, the maximum error of these two methods is observed in

The system reliability in different operating modes is estimated to show the failure effects from each operating parameter. In other operating modes, the timing sequence diagrams of the system are different from the standard operating mode. Hence, the operating states matrices are also different. Three typical operating modes are utilized to illustrate the MCM model as Figure

Timing sequence diagrams of the system.

In operating mode 2, the degradation time of the system decreases into half of the standard and the number of alternating stress cycle numbers decreases into quarter. In operating mode 3, the number of the alternating stresses decreases into half while in operating mode 4, the alternating stress cycle number increases to 2.5 times.

The results in Figure

The reliability estimation for the NC rotary table in different operating modes with MCM.

The operating modes influence the system reliability evidently. However, the traditional reliability estimation only focuses on system reliability in the particular working condition and operating mode. Operating parameters and structure information are not used. This limits the application of the modeling. The meta-action chain method uses the structure chain and operating chain to solve the problem.

Figure

Structure sketch of the lifting part of a tray automatic exchanging device.

As the function of this system is not complex (only exchanging tray), its failure rate is sensitive to the exchange frequency. According to the former failure data, only three meta-action failures were observed during the service life as shown in Table

Failure modes of the lifting part.

Meta-action | Failures | Failure modes |
---|---|---|

Rack moving: | Stuck rack | Degradation |

Gear shaft rotation: | Broken shaft | Alternating stress |

Worn shaft | Degradation | |

Lift hydraulic cylinder moving: | Stuck cylinder | Switch |

Both the MCM and Weibull distribution are utilized to estimate the system under the y 8 min^{−1}, 10 min^{−1}, and 12 min^{−1} exchange frequency. The results are presented in Figure

The reliability estimation for the lifting part of a tray automatic exchanging device.

Cumulative relative errors and maximum errors are presented in Table

Cumulative relative errors and maximum errors.

Exchange frequency | | |
---|---|---|

8 min^{−1} | 0.0032 | 0.0087 |

10 min^{−1} | 0.0044 | 0.0070 |

12 min^{−1} | 0.0108 | 0.1481 |

As the failure mechanisms of this example are simpler than the former one, there exists the difference between the two methods, as shown in Table ^{−1}, at 2000 h, the shape parameter

This paper presents the meta-action chain method to identify the connection between microscopic failure mechanism and microscopic system reliability calculation. The main scientific novelties are the modeling technique of the meta-action structure chain and operating series chain, reliability calculation modeling with Markov transferring matrices, and solving algorithm for industrial application.

The meta-action chain modeling technique defines system operation according to the states of each meta-action instead of the traditional reliability block diagram. The transitions of these states cause failures directly and the failure mechanism could be researched independently as failure sensitivity is much clearer. On the other hand, this method remains consistent with the traditional reliability modeling methods. Existing researches could be further developed and expanded by using microscopic failure data to obtain more precise and practical results.

Reliability calculation modeling uses the discretization approach to solve the discontinuous time interval. Solving algorithm and numerical examples are presented to illustrate the model. Case study shows that this algorithm is easy to realize and is appropriate for industrial application. In standard operating mode, the main failure mode of the given system changes from degradation to alternating stress after the critical value (3000 hours) and reliability decrease sharply. Meta-action method can express this trend instead of the totally smooth reliability curve calculated by the traditional Weibull distribution. Besides, reliability estimations for the system under different operating modes are also presented to prove the effectiveness of the proposed method. The system maintenance strategy would benefit from the results as more precise failure mode information can be acquired from the reliability curve.

The disadvantage of this method is that the state definition of each action should be discussed further. For example, the worm rotation with a 500 N load is much different from the one with a 1000 N load. In this paper, the states of these two situations are all 1. Future researches aim to use states matrices to describe the states of each meta-action instead of Boolean variable. States transition should be described more precisely and the failure mechanism information should be integrated more accurately.

The authors declare that they have no conflicts of interest.

This project is supported by National Major Scientific and Technological Special Project for “High-Grade CNC and Basic Manufacturing Equipment,” China (nos. 2013ZX04011-013 and 2013ZX04012-051).