**Andrzej Swiderski ´ 1, Anna Borucka 2,\*, Małgorzata Grzelak <sup>2</sup> and Leszek Gil <sup>3</sup>**


Received: 24 January 2020; Accepted: 20 February 2020; Published: 24 February 2020

**Abstract:** This article uses Markov and semi-Markov models as some of the most popular tools to estimate readiness and reliability. They allow to evaluate of both individual elements as well as entire systems—including production systems—as multi-state structures. To be able to distinguish states with varying degrees of technical readiness in complicated and complex objects (systems) allows to determine their individual impact on the tasks performed, as well as on the total reliability. The application of the Markov process requires, for the process dwell times in the individual states, to be random variables of exponential distribution and the fulfilling Markov's property of the independence of these states. Omitting these assumptions may lead to erroneous results, which was the authors' intention to show. The article presents a comparison of the results of the examination of the process of non-parametric distribution with an analysis in which its exponential form was (groundlessly) assumed. Significantly different results were obtained. The aim was to draw attention to the inconsistencies obtained and to the importance of a preliminary assessment of the data collected for examination. The diagnostics of the machine readiness operating in the studied production company was additionally performed. This allowed to evaluate its operational potential, especially in the context of solving process optimization problems.

**Keywords:** semi-Markov model; Markov model; empirical data distribution; readiness; production machines
