Reliability prediction of adaptable-function machine by exploiting its similarity characteristics

Qiang Tu,

stud.,

Yi-min Deng,

Jun-yu Wang,

stud.,

Department of Mechanical Engineering, Ningbo University, Ningbo, China

The adaptable-function mechanical products are versatile in fulfilling multiple functions, hence are useful in various applications. The reliability of this kind of product is especially important if compared with single-function ones. Considering the similarity of its physical structure and behavioral process between its different adaptable functions, a method for reliability prediction was thus proposed. By analyzing the behavior similarity, the similarity of the reliability influence factors, and by exploiting the CBR (Case-Based Reasoning) theory and that of Fuzzy mathematics, this paper proposed a concept called comprehensive similarity, as well as the method for its quantification, which is subsequently used for the reliability prediction. The paper takes the reliability analysis of a micro-tillage machine with its function being cultivating soil as a case study to verify the feasibility of the proposed prediction method.

Introduction

The adaptable-function machine is capable of providing a different function from its existing one by varing part of its physical structure. The similarity of the behaviors in delivering different adaptable functions, as well as the similarity of structures thereof [1], are two of the main characteristics of the adaptable-function machines. Similarity is one of the commonly used concept in natural science. Former Soviet scholar Kirpichyov M. V. [2] put forward the three similar theorem, which laid the foundation of research on similarity. The similarity in product is a premise for product reliability prediction.

The reliability of mechanical products refers to the capacity of the products to complete the respecified conditions of use and within the stipulated time. The theory and the technology of reliability emerged during quired function under the Second World War, in order to solve the failure problem of military electronic components and equipment. The reliability of mechanical products is an important embodiment of product quality. In the reliability research Metler and Waller [3] discussed the Bayes estimation of reliability for complex systems. Johnson [4] studied the early multistage reliability model in complex system, Todinov [5] investigated the reliability synthesis problems of complex system. Menon [6] discussed the role of data mining techniques in the product development phase, further study [7] studied the data mining techniques for improving the reliability of system identification, and paper [8] focused on the life time information sharing research for complicated products.

The adaptable-function product is different as compared to the ordinary (non-adaptable) products, and the research on reliability of this kind of products is still rare. To address this problem, this paper attempts to make an investigation of this problem by focusing on an elaborated study of behavior similarity and other factors. The basic idea for reliability prediction to be presented is that, one may predict the reliability of an adaptable-function product in delivering an adaptable function if he or she knows the reliability of the product in delivering another adaptable function, i.e., if the benchmark has been specified. This is useful because an adaptable-function product may contain quite a number of functions. With the reliability of the product of any function being specified, the designers can thus predict the reliability of the product in delivering all other functions, which will provide the designer helpful information if he or she wishes to refine the design, e.g. by enhancing the reliability of the product for all functions.

1. Similarity analysis of adaptable-function machine

1.1 Analysis of behavior similarity

The adaptable-function machine exhibits similarity of the behaviors in delivering different adaptable functions. To study this behavior similarity, we adopt the “physical state change” method for behavior representation [9]. Take the similarity analysis of digging farmland, transport goods and spraying function of micro tillage machine for example. Tables 1-3 respectively express the three functions and their corresponding physics state changes of this machine. To facilitate elaboration, we indicate the function of digging farmland as F₁, the function of transforming goods as F₂, and the function of spraying pesticide as F₃.

Table 1

Physical state changes of the digging farmland function

Function	Digging farmland F1
Sub-behaviors	Press the switch	Turn on the circuit	Start the engine	Push the piston	Rotate the crankshaft	Rotate the small sprocket wheel
	Drive link chain	Rotate the big sprocket wheel	Transmit motion to small sprocket chain	Rotate the drive shaft	Drive the farming tool	The farming tool dig the farmland

Table 2

Physical state changes of the transforming goods function

Function	Transforming goods F2
Sub-behaviors	Press the switch	Turn on the circuit	Start the engine	Push the piston	Rotate the crankshaft	Rotate the small sprocket wheel
	Drive link chain	Rotate the big sprocket wheel	Transmit motion to small sprocket chain	Rotate the drive shaft	Drive the tire	The tire transport goods

Table 3

Physical state changes of the spraying pesticide function

Function	Spraying pesticide F3
Sub-behaviors	Press the switch	Turn on the circuit	Start the engine	Push the piston	Rotate the crankshaft	Spray device movement	Volume pressure changes	Suction drainage	Spraying pesticide

In order to compare similarity degree of these physical states changes more accurately, we introduce the similarity evaluation decision table (see Table 5), with the values given by domain expert. The Table 4 shows the details of “dive the farming tool ” and the “drive the tire ” sub-behaviors in energy, material and signal(mainly considered the outputs situation ).

Table 4

Energy, material and signal details of two sub-behaviors

	Energy	Material	Signal
Dive the farming tool	kinetic energy	Farming tool	component motion
Drive the tire	kinetic energy	tire	component motion

Table 5

Similarity evaluation decision table

Number	Similar situation of energy, material and signal	similarity
1	Energy, material and signal are all the same in the physical state changes	1
2	Energy, material are the same, signals is different in physical state changes	0.8
3	Energy, signal are the same the flow of materials are different in physical state changes	0.7
4	Material, signal are the same，the flow of energy are different in physical state changes	0.6
5	The flow of energy are the same, the material and signal are different in physical state changes	0.5
6	The flow of material are the same, the energy and signal are different in physical state changes	0.4
7	The flow of signal are the same, the material and energy are different in physical state changes	0.3
8	The flow of material, energy and signal are all different	0

With the quantitated physical state changes of these three functions, we can employ the classic Jaccard coefficient to evaluate the similarity between their corresponding behaviors. Assume the behaviors corresponding to Function i and j are to be compared, whereby A_k is the similarity value of physical state changes, k is the serial number of the sub-behaviors, n is the total number of compare process, then we can get the similarity of i and j as Equation (1):

(1)

In fact, in the current example k is from 1 to 12 (n = 12). According to the similarity evaluation decision table, we can get the similarity matrix of these three functions as below.

By using Equation (1) to calculate, the similarity values of the behavior “digging farmland” and the others other two behaviors are S₁₂=0.93; S₁₃=S₁₂₃=0.67. The data show that, the higher the similar degree of material, energy and signal, the higher the similarity of the corresponding behaviors or behavioral processes.

1.2 Analysis of similarity of reliability influence factors

The characteristics of the reliability shows that the fault reasons of a mechanical product can be of diversity and complexity, determined by the working environment, the quality of the product itself, and so on, all of which are referred to as the reliability influence factors. The adaptable-function machine works with different functional components, and it changes its output function through the conversion of functional components. In order to consider the reliability influence factors of the adaptable-function machines more comprehensively, we select the working environment, product quality, working time, working load as the basic influence factors. The working environment factor include the environment temperature, acid and alkali conditions, lubrication conditions. The quality factor include materials quality, processing technology and others that may influence the quality of the constituent components. The factor of working time is used due to the fact that the adaptable functions may be used unevenly. The working load factor may be used according to the specific application, for example, in the previous example, the load for “transporting goods” function can be the weight of the goods,being transported, and the load corresponding to “spraying pesticide” function can be the amount of pesticide to be sprayed, etc. Table 6 shows an influence factor decision table given by the domain expert.

Table 6

Influence factor decision table

Influence factors	Hierarchical and scores
Environment	Very good (1)	Good (0.8)	General (0.6)	Poor (0.4)
Quality	Very good (1)	Good (0.8)	General (0.6)	Poor (0.4)
Working time	Short (1)	General time (0.8)	Long time (0.6)	Very long time (0.4)
Working load	Very light (1)	General weight (0.8)	Heavy (0.6)	Very heavy (0.4)

Note that the values given in Table 6 are only as a demonstration of the proposed methodology. The actual values depend on the specific domain of application and should be specified by the respective domain experts. For the above case of micro tillage machine, reliability influence factor values may be given as the one showed in Table 7.

Table 7

Reliability influence factor values for micro tillage machine

	Environment	Quality of artifacts	Working time	Working load
Digging farmland	0.65	0.86	0.83	0.87
Transform goods	0.76	0.81	0.79	0.65
Spraying pesticide	0.67	0.73	0.70	0.75

To study the similarity degree of the reliability influence factors among these functions, this paper uses the concept of closeness degree in Fuzzy mathematics. Set the A₁, A₂ as the two functions to be compared, U=is reliability influence factors,is the corresponding feature vector sets, is the weight of each influence factors. For the ease of calculation, we chose equal weights for the current example. The closeness degree between function 1 and function 2 is thus given as below.

(2)

By using Equation (2), the reliability influence factor closeness degree between digging farmland and transforming goods is 0.87, and that between digging farmland and spraying pesticide is 0.88.

1.3 Calculation of comprehensive similarity

As mentioned before, the prediction of the reliability of an adaptable-function machine is applicable if its reliability in delivering one of the adaptable functions has been known a priori. This in turn is applicable by exploiting the similarity of physical state changes and that of the reliability influence factors between the one to be predict and the one that is specified (the benchmark). For example, we may make use of the reliability of the function “digging farmland” to predict the reliability of others functions for the micro tillage machine. To implement this idea, this paper introduces the concept of “comprehensive similarity”, which incorporates both the similarity of physical state change and that of influence factors. The comprehensive similarity formula is

(3)

where is behavior similarity weight coefficient, is the influence factors closeness degree weight coefficient. To simplify the calculation, we again use equal weights, i.e. both 0.5 for the micro tillage machine. In this way, we can get the comprehensive similarity between digging farmland and the other two functions as,

ST1,2 =0.5*0.93+0.5*0.87=0.90, ST1,3=0.78.

2. Reliability prediction of the adaptable-function machine

According to the reliability prediction model of mechanical products [10], the failure effects of a partial system to the whole system can be classified according to the following types of system configuration.

(1) Serial system. This means an failure at any part will result in the failure of the whole system.

(2) Parallel system. Paralleling system means all the points and institutions failure, the system will failure.

(3) Mixed system. Such a system contains both serial parts and parallel parts.

As discussed above, an adaptable-function machine includes shared (common) parts and separate functional components (for individual adaptable functions respectively), hence the shared parts can be regarded as the serial-type system, and the functional components can be regarded as the parallel-type system. This provides us the theoretical basis for the above strategy in predicting the product reliability for one adaptable function by exploiting the reliability of the product for another adaptable function. Figure 1 shows the configuration of micro tillage machine, from the perspective of the above classification criterion, when it works normally.

Fig. 1 System configuration of the micro tillage machine

To measure the reliability of micro tillage machine, we propose to use the life time of the machine under normal working condition. For example, we can randomly select 5 micro tillage machines with the same brand and the same model, analyze and record the life time of digging farmland function (we have used the digging farmland function to predict the other two functions), as shown in Table 8.

Table 8

Life times of five micro tillage machines

Name	A1	A2	A3	A4	A5
Life time (*10^4h)	3.68	4.59	5.55	3.36	5.23

The average life time is hence 44820 hours. According to the comprehensive similarity values showed above, we can calculate the life time of transforming goods function as 44820*0.90h=40338h, and the spraying pesticide function life time as 44820*0.78h=34960h.

The above solution shows that the accuracy of the reliability prediction is not only affected by the comprehensive similarity results, but also by the benchmark reliability value. To improve the accuracy of benchmark reliability measurement and that of the similarity calculation are both important to increasing the accuracy of the reliability prediction.

Conclusion

The above sections have presented a strategy of reliability prediction of a specific type of machine, namely the adaptable-function machine. This prediction method is based on similarity of the product behaviors by which different adaptable functions are delivered, as well as the similarity of reliability influence factors. With this strategy as well as the implementation methodology, the designer can predict the reliability of the product under all situations once its reliability for any one adaptable function is known, hence it can considerably reduce the workload of reliability test for all of its adaptable functions. As for the specification of an initial reliability value, i.e. the benchmark reliability, we proposed to use the life time test as a measurement. Future work should include a study of other methods for the benchmark reliability specification, as well as on how to use more subjective evaluation method for the similarity of product behaviors (via physical state changes) and that of the reliability influence factors.

Acknowledgement

The authors gratefully acknowledge the supported by National Science Foundation of China (Grant NO.51375246).

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