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This paper aims to overcome the inability of both comparing loss costs and accounting for production resource losses of Overall Equipment Effectiveness (OEE)-related approaches.

The authors conducted a literature review about the studies focusing on approaches combining OEE with monetary units and/or resource issues. The authors developed an approach based on Overall Equipment Cost Loss (OECL), introducing a component for the production resource consumption of a machine. A real case study about a smart multicenter three-spindle machine is used to test the applicability of the approach.

The paper proposes Resource Overall Equipment Cost Loss (ROECL), i.e. a new KPI expressed in monetary units that represents the total cost of losses (including production resource ones) caused by inefficiencies and deviations of the machine or equipment from its optimal operating status occurring over a specific time period. ROECL enables to quantify the variation of the product cost occurring when a machine or equipment changes its health status and to determine the actual product cost for a given production order. In the analysed case study, the most critical production orders showed an actual production cost about 60% higher than the minimal cost possible under the most efficient operating conditions.

The proposed approach may support both production and cost accounting managers during the identification of areas requiring attention and representing opportunities for improvement in terms of availability, performance, quality, and resource losses.

Fractional order nonlinear evolution equations (FNLEEs) pertaining to conformable fractional derivative are considered to be revealed for well-furnished analytic solutions due to their importance in the nature of real world. In this article, the autors suggest a productive technique, called the rational fractional (DξαG/G)-expansion method, to unravel the nonlinear space-time fractional potential Kadomtsev–Petviashvili (PKP) equation, the nonlinear space-time fractional Sharma–Tasso–Olver (STO) equation and the nonlinear space-time fractional Kolmogorov–Petrovskii–Piskunov (KPP) equation. A fractional complex transformation technique is used to convert the considered equations into the fractional order ordinary differential equation. Then the method is employed to make available their solutions. The constructed solutions in terms of trigonometric function, hyperbolic function and rational function are claimed to be fresh and further general in closed form. These solutions might play important roles to depict the complex physical phenomena arise in physics, mathematical physics and engineering.

The rational fractional (DξαG/G)-expansion method shows high performance and might be used as a strong tool to unravel any other FNLEEs. This method is of the form U(ξ)=∑i=0nai(DξαG/G)i/∑i=0nbi(DξαG/G)i.

Achieved fresh and further abundant closed form traveling wave solutions to analyze the inner mechanisms of complex phenomenon in nature world which will bear a significant role in the of research and will be recorded in the literature.

The rational fractional (DξαG/G)-expansion method shows high performance and might be used as a strong tool to unravel any other FNLEEs. This method is newly established and productive.