The Impact of Non-Constant Failure Rates on System Performance
This paper considers systems consisting of components that fail according to some given distribution. The focus of the paper is to study the difference in overall system performance, measured by the number of backorders in a spares inventory, for constant and non-constant failure rates. It is well known that, under fairly mild assumptions and if the number of components is large,
the process of generated failures tends to a Poisson process implying that, in steady state, the demand for spare parts can be considered to be caused by constant failure rates. This result is verified by simulation, but it is also demonstrated that if the number of components is small or if the process is not steady state the use of non-constant failure rates can be valid
THE PROBLEM
Most spares optimization models make a critical assumption: component failure rates remain constant over time. This assumption—rooted in analytical convenience rather than real-world evidence—can lead to dramatically suboptimal spares inventories and unpredictable system performance.
The Real Issue:
In steady-state systems, the number of spare parts required depends far more on whether failure rates change over time than on the number of components in the system. Yet most analytical optimization methods simply cannot handle non-constant failure rates, forcing organizations to choose between accuracy and analytical tractability.
The consequences are significant: inadequate spare inventory, increased system downtime, budget waste, and missed opportunities to optimize maintenance schedules. For defence and complex systems, this inefficiency is simply not acceptable.
WHAT THIS RESEARCH REVEALS
Systecon's research, authored by Thord Righard and Mats Werme, demonstrates that non-constant failure rates—modeled using Weibull distributions—can be both mathematically tractable and practically implementable in simulation-driven optimization frameworks.
The paper introduces the "bathtub curve" methodology: modeling component failure as three distinct phases:
• Early-Life Failures
Manufacturing defects and initial wear-in—decreasing failure rates
• Useful Life
Random, unpredictable failures—constant failure rates
• Wear-Out Phase
Age-related degradation—increasing failure rates
By constructing failure rate functions that transition between these phases using Weibull distributions, you can model real component behavior with mathematical precision—without sacrificing the ability to generate random failures for simulation and optimization.
WHO SHOULD READ THIS?
• Supply Chain & Logistics Leaders managing complex asset fleets and spare inventory budgets
• System Engineers & Maintainers responsible for availability and mean-time-to-recovery
• Defence & Aerospace Professionals where inventory efficiency and system reliability are both mission-critical
• Anyone Optimizing Spares Under Uncertainty who recognizes that one-size-fits-all assumptions no longer serve their operational needs
Get the full technical paper and discover how non-constant failure rates can transform your approach to spares planning and system performance management.