Electronic Journal of Polish Agricultural Universities (EJPAU) founded by all Polish Agriculture Universities presents original papers and review articles relevant to all aspects of agricultural sciences. It is target for persons working both in science and industry,regulatory agencies or teaching in agricultural sector. Covered by IFIS Publishing (Food Science and Technology Abstracts), ELSEVIER Science - Food Science and Technology Program, CAS USA (Chemical Abstracts), CABI Publishing UK and ALPSP (Association of Learned and Professional Society Publisher - full membership). Presented in the Master List of Thomson ISI.
Volume 10
Issue 2
Agricultural Engineering
Available Online: http://www.ejpau.media.pl/volume10/issue2/art-04.html


Czesław RzeĽnik, Karol Durczak
Institute of Agriculture Engineering, Agricultural University in Poznan, Poland



Quality, alongside economical and ecological effectiveness, is becoming one of the basic preconditions of functioning of companies on the market of material and service products. This also refers to companies carrying out machine processes in agricultural production which must implement and apply systems of quality management. One of the problems in this area is, among others, the number of criteria making up the global quality process which is not always rational. It happens fairly frequently that significant expenditures are necessary to fulfil certain criteria which are of little impact on the global quality. In the presented paper, the authors employed information entropy to present an original method which allows assessing sets of quality criteria of machine processes from the point of view of rationality of their application in the process of the quality system implementation.

Key words: agricultural machine, machine processes, quality, information entropy.


Processes of agricultural production are carried out with the assistance of machines. They are referred to as machine processes in contrast to, for example, biological and chemical processes. Machine processes, differing from one another as to their ‘content’, are dynamic systems carried out increasingly frequently in the form of services which are subject to evaluation according to different criteria. The most important among these criteria are those associated with economical but also ecological effectiveness. In addition, the quality of processes themselves, which for service processes is a highly subjective issue, is also becoming very important. The same service may be evaluated positively by one customer and negatively by another. Although customers’ expectations will always vary, they are always connected with technical and functional aspects of services. The technical aspect of services concerns the material domain and is of paramount importance in the case of the discussed services which are of production nature. The functional aspects include, among others: competence, reliability, trustworthiness, politeness of the service provider, keeping the agreed dates etc.

Łańcucki [8] describes service quality as a degree to which the majority of fundamental service properties meet the expectations of the customer who is the only and the most important judge of the service and selects and sets the criteria.

In the case of the analysed services, the functional aspect of the provided services should refer to the standard which the company operating on the service market must fulfil. On the other hand, the technical aspect of service quality constitutes a certain set of criteria (requirements) of varying importance which must be met by the service provider in the highest possible degree. The adopted quality criteria include significant properties of the service selected to determine the overall quality performance. The number of criteria adopted in order to evaluate its quality should be possibly high as it favours comprehensive assessment of its quality. On the other hand, this number should not be too high because this may hinder the effectiveness of the quality analysis and makes the implementation of quality systems difficult [4,7,9].

Irrespective of the formal requirements concerning quality associated with the introduction of ISO standards, each and every service provider should undertake steps aiming at the improvement of quality because it is the precondition for his operation on the market. Work in this area encounters a wide range of difficulties. The technical aspect of services, which is the most important consideration, requires the fulfilment of a certain set of requirements of which each appears to have a different impact on the global service quality. At the same time, the realisation of a specific requirement involves certain expenses and service providers may sometimes encounter problems. Not infrequently, the realisation of a requirement, which bears little significance for the global quality of the provided service, may incur considerable costs.

These issues are important for quality management [1,6]. One of the tools used in quality management is the Pareto-Lorenza method [5] which allows modifying the set of the most important requirements and determining the extent of the impact on quality. Its utilisation allows determining the percentage influence of each requirement on the global quality and next arranging them from the requirement which has the greatest share in the global quality to the one with the smallest share [3]. However, this method fails to evaluate the effect of the number of criteria and distribution of the share in global quality on the efficiency of the application of the set of criteria for quality management. Intuitively, it seems obvious that the smaller the number of criteria, the easier it is to implement and manage the quality system. At equal number of criteria in the set, the one in which some criteria are dominant and others less dominant will be easier to implement and operate than the one in which all criteria are of equal importance.

However, some questions arise:

The aim of this study is to try and find answers to the above-formulated questions. The performed analyses and investigations indicate that these questions may find positive answers. Farming machines of increasingly better quality employed to carry out machining processes now fulfil some requirements even without the operator’s involvement, e.g. cutting at a set height by a combine harvester. The quality improvement of machine processes in agriculture is also influenced by other positive changes in agriculture, such as: effective weed control, cultivation of cereal cultivars resistant to lodging, better field conditions etc. Such trends in the occurring changes facilitate the introduction of quality systems in the area of utilisation of agricultural machines.


The aim of this study is to elaborate a method which will allow calculating the impact of the number and share of individual requirements on the quality of machining processes in plant production. This, in turn, will allow the arrangement of the requirements according to their decreasing impact on the global quality of the machine services and possible elimination from the set of the least significant requirements. The elaborated method will allow numerical evaluation and comparison of different sets of quality requirements regarding the effectiveness of their implementation. In addition, it will also make it possible to asses accurately the applied sets of requirements needed for the quality evaluation of the machining processes and to introduce appropriate corrections in order to facilitate the implementation of quality systems into machine processes.


To begin with, it is essential to formalise the object of our investigations. The quality of machine processes can be treated as the fulfilment of a k set of partial requirements (criteria) together making up the global quality. Then the quality of a machine process J can be presented in a form of an equation as a set of partial criteria:

J = {k1, k2, ..., kn}          (1)

where: k1 designates i-th partial criterion (i = 1, 2, ...., n).

Each partial criterion has a certain share pi, i = 1, 2, ..., n, in the global quality of the machine process. The pi values will be determined on the basis of questionnaire surveys of farmers. However, it is also possible to determine pi using other method, for example, on the basis of expert opinions.

For purposes of this study, the following assumptions were adopted:

The authors adopted information entropy [2] as a measure allowing the assessment of the set of the partial quality criteria whose values was expressed by the following equation:


Information entropy increases together with the increase of the number of partial criteria making up the global quality of the machine process and with the levelling out of the proportion of individual partial criteria in this quality. Information entropy assumes the greatest value:


when the relative proportion of individual partial criteria in the global quality of the machine process is identical, i.e. p1 = p2 = ... = pn.

Information entropy allows numerical valuation of the properties of the set of the quality criteria of the machine process earlier expressed intuitively.


The development of the method required the authors to prepare sets of partial quality criteria and the participation of each of them in the global quality of machine processes. That is why they elaborated a questionnaire concerning processes using the following farming machines: grain drills, grain combine harvesters, potato planters and potato harvester. Using the System of Agricultural Machines, Polish Standards and farmers' opinions, the authors elaborated sets of requirements of their quality (Table 1).

Table 1. Sets of quality requirements of machine processes


Machines realizing the process

Standard number

Partial quality requirements of the machine process


Grain drills

with amendments (91.07.04)

1. Sowing depth
2. Seed coverage
3. Seed damage
4. Unequal sowing of seeds


Grain combine harvester


1. Uniform cutting
2. Seed losses caused by the reaper, leader and thresher
3. Grain damage
4. Purity of grain and seeds in the container


Potato planters


1. Planting depth
2. Coverage of potatoes
3. Allowable side deviation of potatoes from the row axis
4. Distance between potatoes in row
5. Acceptable number of single and multiple empty places
6. Acceptable mean potato damage
7. Acceptable number of broken sprouts in relation to the total number of sprouts when planting with potato planters for sprouted potatoes


Potato harvesters

PN-86/R-36500 with amendments “1” (88.06.13) and “2” (90.12.12)

1. Potato losses
2. Damaged potatoes
3. Contamination of the harvest

Next, another questionnaire was elaborated with the aim to arrange partial quality criteria of each machine process according to a decreasing impact on the global quality of the service. The presented investigations were carried out at the end of 2004 and beginning of 2005 using the method of direct questionnaire on 50 private farms specialising in cereal and potato production situated in Wielkopolska. An appropriate number of points from Table 2 were assigned to each place on the ranking list.

Table 2. Applied point scores for criterion ranking

Number of criterial of the machine process quality

Place in the ranking and the assigned number of points

Total number of assigned points for the machine process


1 position – 2 pnts
2 position – 1 pnt
3 position – 0 pnts

3 points


1 position – 3 pnts
2 position – 2 pnts
3 position – 1 pnt
4 position – 0 pnts

6 points


1 position – 6 pnts
2 position – 5 pnts
3 position – 4 pnts
4 position – 3 pnts
5 position – 2 pnts
6 position – 1 pnt
7 position – 0 pnts

21 points

Considering auxiliary character of the results obtained from the questionnaire with regard to the aim of this study, which is to elaborate a method, there are presented only these results, which are essential to comprehension of the matter of the method. The detailed results of research are presented in study of Durczak and Rzeznik [3].

On the basis of the results obtained from the questionnaire and number of points from Table 2, the authors calculated the total number of points assigned to individual criteria as well as the relative share of each criterion pi in the global quality of the machine process. Next, for the set of quality criteria, the authors calculated the maximum information entropy Emax (assuming the equal share of each criterion in the global quality) as well as the apparent information entropy Er (assuming the true share of each criterion obtained from questionnaire). The calculations were carried out using equations 2 and 3 and the results are presented in Table 3. In addition, the Table presents differences between the maximum and apparent entropy as well as the ratio of the latter to the former.

Table 3. List of share values and entropy for the examined machines

Type of machine

Share of criteria in global quality

Maximum entropy
Emax (bit)

Apparent entropy
Er (bit)


Grain drill

p1 = 0.43
p2 = 0.31
p3 = 0.17
p4 = 0.09





Grain combine harvester

p1 = 0.09
p2 = 0.35
p3 = 0.22
p4 = 0.34





Potato planter

p1 = 0.26
p2 = 0.20
p3 = 0.03
p4 = 0.12
p5 = 0.17
p6 = 0.15
p7 = 0.07





Potato harvester

p1 = 0.50
p2 = 0.38
p3 = 0.12





The analysis of the results presented in Table 3 allows drawing the following generalisations:


Value We was called the effectiveness coefficient of the implementation of quality systems in machine processes. The analysis of these processes (tab. 3) reveals that the set of criteria of the potato harvester is characterised by the highest effectiveness (We = 0.12), while the potato planter – by the lowest (We = 0.07), which confirms the logical correctness of the line of thought


When we introduce quality systems into machine processes, two contradictory requirements must be reconciled. At first, it is necessary to assume the highest possible number of partial requirements, so that they comprise all important features of the machine process impacting its quality. Next, we must analyse the adopted criteria and assess their influence on the global quality of the process and costs of their implementation. For this purpose, it is possible to utilise the effectiveness coefficient of the implementation of quality systems as this will allow evaluating the impact of each criterion on the global quality of the process and next eliminating or possible merger of non-significant criteria.

Practical use of the elaborated method will allow rationalization of number and importance of quality criteria set by omission of less important ones or their inclusion to others. It will make easier the quality system implementation in machine processes.


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Accepted for print: 12.03.2007

Czesław RzeĽnik
Institute of Agriculture Engineering,
Agricultural University in Poznan, Poland
Wojska Polskiego Street, 60-625 Poznan, Poland
email: rzeznik@au.poznan.pl

Karol Durczak
Institute of Agriculture Engineering,
Agricultural University in Poznan, Poland
Wojska Polskiego Street, 60-625 Poznan, Poland
email: kdurczak@au.poznan.pl

Responses to this article, comments are invited and should be submitted within three months of the publication of the article. If accepted for publication, they will be published in the chapter headed 'Discussions' and hyperlinked to the article.