Large-scale scientific equipment mentioned here refers to the scientific equipment with original value higher than 500 thousand RMB [7]. Platform Center of the Ministry of Science and Technology carried out survey, classification and analysis of China's utilization and sharing of large-scale scientific equipment in the past a few consecutive years. The data were screened. The large-scale engineering equipment at the affiliated base, those with annual average working hours exceeding 8640 (360*24), computers and auxiliaries, and equipment to be scraped, were excluded [8]. By the end of 2012, China had 43028 sets of large-scale scientific equipment in total, with the original value of as high as 57.17 billion RMB. They are distributed at 524 legal entities such as Chinese Academy of Sciences and Peking University as well as 39 national-level administrative departments such as Ministry of Education and Ministry of Industry and Information.

Fig. (1). Utilization and sharing of large-scale scientific equipment in China (2008-2012).

Here “utilization rate” of scientific equipment refers to the ratio of working hours of equipment to rated working hours within a specific time period. The annual rate working hours of the equipment is set as 8h*200d=1600h. In that case, the utilization rate of scientific equipment will exceed 100%. Therefore, we treat the calculated utilization rate above 100% as 100%. But this method will artificially reduce the differences between the utilization efficiencies of scientific equipment across the regions. So we do not make special treatment on utilization rate larger than 100%.

Furthermore, for the convenience of data acquisition, we only process data of large-scale scientific equipment in 30 provinces excluding Tibet, Hong Kong, Macau and Taiwan.

The indices of utilization and sharing of large-scale scientific equipment can reflect the status of scientific equipment utilization and sharing comprehensively. For each dimension, 3 secondary indices are selected to constitute an index system. The weight of each index is determined by expert grading.

(1) Equipped capacity of large-scale scientific equipment

Equipped level measures the scale, structure, development, allocation, R & D and centralized management of large-scale scientific equipment in a specific region.

Original value a₁₁ of equipment (ten thousand RMB): it is the sum of original value of all equipment in a specific region, and it reflects the equipment construction scale of this region. It also represents the potential of this region in equipment utilization and sharing, with the weight of 0.3.

Original value a₁₂ of newly added equipment (ten thousand RMB): it is the sum of original value of all newly added large-scale scientific equipment in a specific region in the past 3 years. The index reflects the equipment input scale of this region in the past 3 years as well as the equipment construction & input capacity, with the weight of 0.3.

Original value a₁₃ per staff engaged in scientific research (ten thousand RMB/per person): it is the original value of equipment in a specific region divided by the number of staff engaged in scientific research (here it does not refer to all people engaged in scientific research of the region). This index measures the degree of allocation of equipment among users in this region, with the weight of 0.4.

(2) Ability of utilization of large-scale scientific equipment

Utilization level comprehensive measures the status of utilization of large-scale scientific equipment in a specific region (including the utilization efficiencies of all equipment, newly added equipment and high-end equipment, as well as the total working hours, full-load operations and normal operations.

Utilization rate a₂₁ of equipment (%): the utilization rate of a single equipment is the ratio of annual working hours to annual rated working hours of an equipment (the annual rated working hours is 1600 h, that is, 8 hours for 200 days every year). The utilization efficiency of equipment in a specific region is the weighted sum of utilization rate of a single equipment according to the proportion of original value of the equipment. This index reflects the overall utilization efficiency of equipment in this region. It has the weight of 0.3.

Utilization rate a₂₂ of newly added equipment (%): the utilization rate of newly added equipment in a specific region in the past 3 years is the weighted sum by the proportion of original value. The index reflects the utilization efficiency of newly added equipment in this region, with the weight of 0.3.

Proportion a₂₃ of equipment operating under full load (%): it is the proportion of equipment with annual working hours equal or exceeding the rated working hours. This index reflects the situation of high-level operation of equipment in this region, with the weight of 0.4.

(3) Capacity of sharing large-scale scientific equipment

Sharing level comprehensively measures the situation of external service rate (including the external service rates of total equipment and newly added equipment), total hours of external services, proportion of equipment with information publicity, average income from equipment services and regional sharing. It has the weight of 0.3.

External service rate a₃₁ of equipment (%): the external service rate of a single equipment is the proportion of external service hours of a single equipment in annual rated service working hours. The external service rate of a specific region is the weighted sum of external service rate of a single equipment by the proportion of its original value. This index reflects the overall external service level of the region, with the weight of 0.3.

External service rate a₃₂ of newly added equipment (%): the external service rate of newly added equipment in the past 3 years is the weighted sum by the proportion of its original value. This index measures the external service level of the newly added equipment in this region.

Proportion a₃₃ of equipment shared regionally (%): it is the proportion of original value of equipment for cross-regional external services [9]. The index measures the status of cross-regional sharing of the equipment in this region, with the weight of 0.4.

Evaluation based on multiple indices involves the actual values and assessment values of each index. The two values are different in dimension. Non-dimensionalization is to remove the differences in measurement units and the differences in order of magnitude. After non-dimensionalization, the indices can be synthesized. Benchmarking method is employed for non-dimensionalization of secondary indices, and the secondary index x_ij is obtained.

Then, integrated weighing is employed to calculate the primary index $y_i^k$.

where γ_ij is the weight of each secondary index, which is determined by expert grading.

The influence of the above-mentioned factors on the sharing of large-scale scientific equipment is evaluated and compared. Clustering is adopted for hierarchical assessment of the influence factors of three aspects.

The elements to be assessed are divided into p categories. Two most distant elements x_i1 and x_i2 are selected as the first two clustering points. That is to say, to choose x_i1 and x_i2 that makes .

Then the third clustering point is selected that makes the shortest distance from x_i3 to the first clustering points equal to the largest one among the shorter distance from x_i1 and x_i2:

By the same principle, x_i4 is selected, until k clustering points are selected, namely, x_i1, x_i2, ..., x_i4.

The selection process can be completed using recursion formula. If l clustering points are selected, then the principle for choosing the l+1-th clustering point can be expressed as

In the above clustering process, we select 3 clustering points for each category of influence factors, i.e. p=3 . Therefore, the equipped level is divided into high, moderate and low. The same applies to the grading of utilization level and sharing level.

Based on the analysis of equipped level, utilization level and sharing level of large-scale scientific equipment, the Hall's three-dimensional structure in system engineering methodology is referred to. The three-dimensional model for evaluating the utilization and sharing of the equipment is constructed as shown in the Fig. (2).

Fig. (2). Three-dimensional model for the evaluation of utilization and sharing status of large-scale scientific equipment.

In the above figure, the factors of three dimensions, namely, supply, operation and sharing construction of large-scale scientific equipment, are assigned with different scores. Thus, the utilization and sharing status of equipment are plotted under the coordinate system. Points A, B and C in the figure stand for this.

A: (X₁, Y₁, Z₁) = (weak equipped capacity, weak operating status, weak sharing construction capacity)= (1,1,1)

B: (X₂, Y₂, Z₂) = (moderate equipped capacity, moderate operating status, moderate sharing construction) = (2,2,2)

C: (X₃, Y₃, Z₃) = (strong equipped capacity, good operating status, good sharing construction) = (3,3,3)

If the three coordinates are synthesized by multiplication, then the synthetic scores of equipment utilization and sharing in a specific region are obtained and expressed as δ. Then,

In the formula of synthetic score proposed in this article, different elements represent different types, where Z represents the dimension of equipped level; Z₁, Z₂, Z₃ represent weak, moderate and strong levels, respectively. L represents the dimension of utilization; L₁, L₂, L₃ represent poor, moderate and good sharing construction capacity; G represents the dimension of sharing; G₁, G₂, G₃ represent poor, moderate and good sharing construction capacity, respectively. Thus, theoretically, δ_(i,j,k) has 27 combinations, with 10 different values.

By δ_(i,j,k), the equipment utilization and sharing status across the provinces is divided into different intervals; the provinces with 1 ≤ δ ≤ 3 are classified as category I; the provinces with 4 ≤ δ ≤ 9 are classified as category II; the provinces with 10 ≤ δ ≤ 27 are classified as category III.

According to the aforesaid formulas and three-dimensional evaluation model of the utilizing and sharing status, the development level of equipment, utilization and sharing in 30 provincial areas throughout China in 2012 was assessed. Please refer to Table 1(vide infra) for results.

Based on the grading results of all provincial areas in such three dimensions as equipment, utilization and sharing in Table 1, we classified the results by δ value according to (*) formula. The result is presented in Table 2.

On the basis of calculation and classification results in Figs. (1 and 2), we can reach the following conclusions:

• (1) As shown by the classification by value, the number of provincial regions that are included into Category I is 6. They can be further divided into two sub-categories. Beijing and Shanghai, the two municipalities directly under the Central Government, are the first category as they enjoy considerable advantages over other provincial areas in economy, science and technology, culture and other fields. In terms of large-scale scientific equipment, the two cities enjoy a more balanced development in all aspects. Especially, Beijing, with so many universities and research institutes, equips itself with abundant advanced large-scale scientific instruments that other provincial areas cannot catch up with. Another sub-category consists of Hunan, Yunnan, Ningxia and Xinjiang, in central and western China. It is not difficult to find by carefully analyzing their index values in the three dimensions that the major reason why they can be included in Category I is their high level of utilization and sharing, suggesting that developed economy and huge amount of large-scale scientific equipment do not mean high level of utilization and sharing. A good equipment sharing platform as well as high quality research and managerial staff members are the key aspects of the utilization and sharing of equipment.
• (2) By analyzing the regions that are classified into Categories II and III, we can discover that the development of large-scale scientific equipment in central China is better than that in western regions. The equipped level of large-scale scientific equipment in different provincial areas differs greatly, but the utilization and sharing levels are relatively balanced. We can see that the equipped level index in provincial areas that are classified into Category III is not higher than 20, which is also the major difference existing between them and Category III regions. From this we can conclude that the raising of absolute strength is urgently needed by the western areas where economy, science and technology are underdeveloped. Therefore, science and technology management organs should take them into consideration when allocating resources and making policies.
• (3) The development status of large-scale scientific equipment in some particular or typical regions among the 30 provincial areas has its own characteristics, which are worthy of consideration. One of the typical regions is Beijing. The equipped level of large-scale scientific equipment in Beijing is the highest but the utilization index only ranks the 13th among the 30, and the sharing index, the No. 15, both belonging to a moderate level. Although the total quantity of equipment is huge, there is redundancy of equipment and a low request for sharing; secondly, due to the lack of effective equipment sharing platform, there is a weak connection between owners and demanding parties. A considerable amount of equipment is left idle and wasted. Thirdly, the management professionals who have varying levels of skills and knowledge cannot provide proper maintenance for the equipment or make full use of the equipment.
• (4) Another typical region is Ningxia. In 2012, the original value of large-scale scientific equipment of Ningxia was only 91,730,000 yuan, less than 1% of that of Beijing. However, since 2005, Ningxia began to break the industrial boundaries by an easy access to large-scale scientific equipment. It was turned into reality that the management of large-scale scientific equipment resources had shifted from the mode of “segregation of departments” to “co-construction and - sharing”. Besides, Ningxia began to train managerial staff at all scientific research institutes and universities in batches, thus increasing the utilization rate to 79% and the sharing rate to 66.5%. Through integration, by 2010, the instruments included into the network of the whole region had reached 525, with 62 units involved in the network. The accumulated visits of the websites of large-scale scientific equipment amounted to 130,000. This further highlights the importance of management mode to the increase of instruments' utilization rate and sharing rate.