Monitoring time between events (TBE) is essential in many industrial settings. Traditional methods assume a time-invariant failure rate which is unsuitable for complex systems where the failure mechanism changes over time due to degradation. The NonHomogeneous Poisson Process (NHPP) better models these systems by allowing a time-varying failure intensity. Additionally, failure patterns of such systems are often influenced by risk factors like environmental conditions and human interventions. Restoration of such systems also imposes multiple cost constraints. This work proposes a novel approach: a risk-adjusted control chart based on the NHPP model, specifically designed for monitoring the ratio, Cost/TBE, called the average cost per time unit. Risk-adjustment enhances the chart’s detectability of shifts in the failure process by isolating the risk factors’ contribution. Moreover, incorporating cost-based monitoring statistics not only emphasizes the cost impacts beside the failures themselves but also improves the chart’s interpretability. The effectiveness of the proposed method is demonstrated through a comprehensive numerical study showing its superior performance compared to existing methods. The comparison study shows that ignoring the risk factors in the chart design leads to numerous false alarms, undermining the chart’s effectiveness. We also illustrated the proposed method through a case study on monitoring a network of oil pipeline accidents.

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