Cumulative damage sequential preventive maintenance strategy for shock resilient machines with prior usage and non-constant shock magnitude

Purpose This study aims to develop a modified cumulative damage sequential preventive maintenance (CDSPM) model that addresses the limitations of traditional cumulative shock sequential models by incorporating three realistic factors often ignored in maintenance planning: prior damage in used machines, shock dampening effects and non-constant shock magnitudes. The research seeks to provide a more practical decision-making tool for industries, particularly in developing countries, that rely heavily on fairly-used equipment exposed to complex shock environments. Design/methodology/approach The study modifies the existing CDSPM model by introducing a non-zero initial damage state (R0 > 0), a shock dampening factor αl which is defined as the proportion of shock damage absorbed by the machine. This provides a mathematical mechanism for representing the protective effect of built-in shock-resistance components. The effective shock damage transmitted to the machine is represented by 1-αl100% with 0⩽αl⩽1. This formulation distinguishes between the physical magnitude of an external shock and the actual damage transmitted to the machine. It therefore provides a theoretical basis for incorporating mechanical protection into stochastic reliability models rather than assuming that the entire shock magnitude contributes directly to cumulative damage. Also, the Gamma-distributed shock magnitudes replace the traditional exponential distribution. The modified model formulates total expected cost functions for both infinite and finite time horizons, derives optimality conditions using Lagrange optimization, and develops a comprehensive availability model. The methodology is validated through application to a used Caterpillar 320BL hydraulic excavator using empirical field data, with the algorithm implemented in Python programming language. Findings The modified CDSPM model demonstrates that accounting for prior damage and shock resistance leads to shorter, effective and more realistic maintenance intervals with lower expected maximum cost rate compared to classical models. The optimal policy recommends P* = 12 maintenance intervals with a maximum expected cost rate of 26.99 million Naira and system availability of 98.51%, whereas the classical model (assuming pristine condition) suggests P** = 14 intervals with 58.98 million Naira cost and 99.18% availability for the case study used Caterpillar excavator. The 15% reduction in intervals and significantly lower lifecycle costs confirm the fact that classical models overestimate equipment longevity and underestimate maintenance requirements for fairly-used machines. Research limitations/implications The model's parameters are estimated from a single machine type and operational context, which may limit generalizability. The assumption of a constant shock dampening factor and fixed improvement factor may not capture all operational complexities. These identified baseline conditions are essential for real-world model development. Therefore, future research should explore time-varying dampening factors, multiple failure mechanisms and application to diverse equipment types across different industrial sectors. Practical implications The modified CDSPM model provides maintenance planners with a practical tool for scheduling sequential preventive maintenance (PM) on used equipment, enabling more accurate prediction of maintenance intervals, cost optimization and availability estimation that could not have been appropriate with fixed interval PM. The approach helps reduce unplanned failures, minimize downtime and extend equipment life through evidence-based decision-making that reflects actual machine conditions. Social implications By improving cumulative damage sequential maintenance practices for fairly-used equipment, particularly in developing countries where second-hand machinery is prevalent, the model supports sustainable industrial operations, reduces resource waste and enhances productivity and workers' safety through more reliable equipment performance. This cost-effective maintenance strategy contributes to economic efficiency in resource-constrained environments. Originality/value This research presents an integrated CDSPM model that simultaneously incorporates prior damage, shock dampening and Gamma-distributed shock magnitudes. The work extends Nakagawa and Mizutani’s (2008) foundational model as a special case while providing a more realistic model for used equipment maintenance. The availability model and finite horizon optimization approach offer novel contributions to reliability engineering practice.