**1. Introduction**

Market success of a manufacturing company is shaped primarily by the demand for the manufactured products and the rate of return on capital employed [1,2]. Poor machine efficiency and frequent downtimes can lead to a reduction in production levels, resulting in lost market opportunities, increased operating costs and reduced profits [3]. It is therefore necessary to apply appropriate methods and tools to support management and to organize maintenance services in an adequate manner to ensure that the production system operates at the assumed levels of productivity and efficiency [4].

Effectiveness is an important element in the analysis of the production process [5–7], often considered in scientific publications. It is assessed on the basis of various measures. In practice, numerous mathematical models and tools are used to support the assessment of the performance of machinery. The most frequently used measures for analyzing the efficiency of technical facilities are those resulting from three general models of operation assessment, i.e., the reliability model, the operational efficiency OEE (overall equipment effectiveness) model and the organizational and technical KPI (key performance indicators) model [8]. In addition, methods and tools for its evaluation can be classified in five main areas, i.e., operational, market, financial, technical or dynamic [9,10]. Particularly important from the point of view of machinery efficiency diagnostics is operational efficiency, and the research in this area focuses primarily on the search for opportunities to reduce the consumption of production resources. These include analysis of labor productivity growth, cost reduction, minimization of losses and shortening of production cycles. Studies available in the literature indicate the application of a number of methods and tools in this area, such as methods of productivity and profitability indicators, analysis of efficiency and degree of work stations' utilization, cost calculation of activities, study of spatial efficiency of production organization and economic evaluation of the production structure [11].

Maintaining the company's machinery stock at an appropriate level requires continuous monitoring and evaluation of the adopted effectiveness indicators. A number of companies have MES (manufacturing execution system) systems in place, which enable ongoing control of the above parameters. There are also companies (including those examined by the authors) that do not have such software and therefore proper evaluation of efficiency parameters is difficult. Such analyses are supported by mathematical tools and methods, which also include modeling with the use of logistic regression, as presented in this article. The subject of this research was a plastics manufacturing company, while the main objective was to evaluate the effectiveness of the production process based on selected factors that may significantly affect the level of machinery efficiency. The analysis was carried out on the basis of information on the performance of the company's production system recorded from 1 September 2015 to 31 August 2017.

Monitoring the effectiveness of utilization of the available machinery allows production reserves or waste in the processes underway to be identified [12–14]. The basis for successful assessment is an appropriate selection of measures and indicators. The analysis of literature made it possible to distinguish those which were of the greatest importance both in theoretical and industrial-practical aspects. Three general models should be distinguished:


Within the operational efficiency model, a frequently employed parameter (which was monitored in the examined entity as well) is the overall equipment effectiveness (OEE) indicator, which is widely described in the literature [16–19]. The available studies most often present the theoretical aspects of its calculation and indicate the categories of losses that may occur during the process of machinery and equipment use in relation to ideal conditions [19–21]. Analyses are also available to demonstrate the practical implementation of this parameter in manufacturing companies [12,22,23].

The OEE index is a product of three components [23,24], i.e., readiness and efficiency of machinery and quality of the manufactured products. It is therefore a general, comprehensive assessment, most often presented in percentage form. According to Seichi Nakajime from the Japan Institute of Plant Maintenance [25,26], OEE should remain at 85.41%, but it should be stressed that each enterprise operates in a specific environment; thus, this indicator will be different for each entity, depending on its size, profile and industry, and will not take on the same value in two different operating units [9,27]. Therefore, in practice the above indicator has evolved into different forms of application depending on the sector in which a given entity operates, adjusting to the needs of the environment. The following indicators should be mentioned: OFE (overall factory effectiveness), OPE (overall plant effectiveness), OTE (overall throughput effectiveness), PEE (production equipment effectiveness), OAE (overall asset effectiveness) or TEEP (total equipment effectiveness performance) [21].

The reliability model allows measures in statistical terms to be determined, on the basis of a time analysis of the performance of technical facilities. In practice, these refer to the technical condition of machines, as well as to the activities of maintenance staff. These are MTBF (mean time between failures), MTTR (mean time to repair) or MTTF (mean time to failure) [15].

The organizational and technical KPI model includes a set of measures enabling a comprehensive assessment of the efficiency and effectiveness of the implemented processes. It includes 72 indicators classified in three areas: economic (e.g., total relative cost of maintenance), technical (availability of facilities for preventive works) and organizational (number of maintenance staff) [28].

In relation to the analyzed company, indicators associated with the operational effectiveness model, related to efficiency, will be preferable in the context of machinery stock management; therefore, they have become the subject of this analysis. Following the literature in this field [13,29], it was assumed that efficiency in production processes is the quotient of the actual efficiency to the nominal efficiency, as specified in the following ratio (1):

$$\mathcal{W}\_{\mathbb{Q}} = \frac{Q\_r}{Q\_{\mathbb{O}}} \, \, \, \, \tag{1}$$
