Evaluation of Machinery Readiness Using Semi-Markov Processes

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.

Analysis of Light Utility Vehicle Readiness in Military Transportation Systems Using Markov and Semi-Markov Processes

“…In operation, the most frequently used models are based on discrete processes in states, developed for both discrete and continuous time [8,16,24,28,29].…”

“…Some characteristics of the operation process may not meet it. From the point of view of the reliability of the mapping, this excludes the possibility of applying the Markov model [29,45]. The generalization of the Markov process is the semi-Markov process, which does not require the fulfilment of the condition of exponential distributions of interstate transition times.…”

“…The comparison of the values obtained by the six-state Markov and semi-Markov models, which the authors of the publication [29] developed for production machines, indicated that the unverified assumption of the exponential distribution of the time the object stays in states may lead to significant errors in the calculation of the readiness indices. In the presented case study, the difference between the results of the semi-Markov model and the erroneous Markov model was as much as 0.40, which is less than half of the actual value of the readiness index.…”

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“…A large number of criteria indicated by experts shows that the problem of a machine criticality assessment on a manufacturing system level is a complex multi-dimensional decision problem [79]In order to solve this problem, an enterprise has to consider different viewpoints from various stakeholders and, thus, include many (not always compatible) goals in a decision-making process. A possible strategy to deal with this problem is to combine multiple goals simultaneously into a hierarchical structure mapping the main stakeholder groups and the issues relevant to each of them.…”

Statistical Comparison of the Hardness and Scratch-Resistance of the PMMA Polymers Used in Orthodontic Appliances

“…The use of polymers is common, e.g. as thin packaging films and waste bags [5]. Scientific research includes issues related to the maintenance and operation of polymer medical devices [6,7] and orthodontic appliances [8,9].…”