# A decision support model for determining the applicability of prognostic health management (PHM) approaches to electronic systems

## SummaryĀ (3 min read)

### 1. INTRODUCTION

- Prognostics is the estimation of remaining life in terms that are useful to the maintenance decision process.
- Most approaches to PHM are focused on monitoring failure precursor indications (i.e., health monitoring), which does not require system failures to be deterministic in nature, but does require that the failure precursor have a deterministic link to the actual system failure.
- Modeling to determine the optimum schedule for performing maintenance for systems is not a new concept.
- Maintenance modeling has not been widely applied to electronic systems where presumed random electronics failure is usually modeled as an unscheduled maintenance activity, and wear-out is beyond the end of the systemās life.
- This boils down to determining optimal safety margins on life consumption monitoring predictions and prognostic distances1 for health monitoring.

### 2. MODEL FORMULATION

- The following model accommodates variable time-tofailure and LCM forecast distributions.
- The model considers only one LRU (Line Replaceable Unit) within a larger system.
- To assess PHM, relevant failure mechanisms must be segregated into two types: Failure mechanisms that are random from the view point of the PHM methodology.
- Note, the model formulation is presented based on ātimeā to failure measured in operational hours, however, the relevant quantity could be a non-time measure such as thermal cycles.
- Example results generated using all the approaches discussed in this section are presented in Section 3.

### 2.1 Fixed Scheduled Maintenance Interval

- This case is well understood, but included herein because it serves to define the general approach that will be used for assessing health monitoring and life consumption monitoring.
- In this case a fixed scheduled maintenance interval is selected that is kept constant for all instances of the LRU throughout the system life cycle.
- The following algorithm is used to accumulate life cycle costs (C) based on time stepping through the lifetimes of a statistically relevant set of LRUs where T is time: 1. Defined Time-to-Failure (TTF) distributions (subscript R = random, subscript P = predictable) 2. Sample the TTF distributions to get TTFR and TTFP 3.
- Repeat steps 2-5 until T > operation and support life of the system 7.
- To model the random failure rate, a uniform distribution with a height equal to the average random failure rate per year and a width equal to the inverse of the average random failure rate is created and sampled to get TTFR.

### 2.2 Life Consumption Monitoring (LCM)

- Life Consumption Monitoring is defined in this paper as the process by which a history of environmental stresses (e.g., thermal, vibration) is used in conjunction with physics of failure models to compute damage accumulated and thereby forecast life remaining.
- For this example, the LCM forecast was modeled as a symmetric triangular distribution with a most likely value set to the time-to-failure of the LRU instance and a fixed width measured in operational hours, (Fig. 2).
- The LCM distribution is then sampled and if the LCM sample minus the safety margin is less than the actual time-to-failure of the LRU instance then LCM was successful (failure avoided).
- If successful, a scheduled maintenance activity is performed and the timeline is incremented by the LCM sampled time-to-failure minus the safety factor.
- The Histograms allow us to choose safety margins that minimize mean life cycle cost or alternatively minimize the cumulative life cycle cost of all units sampled.

### 2.3 Health Monitoring (HM)

- Health monitoring is defined in this paper as monitoring for failure precursors.
- If the health monitoring distribution sample is greater than the actual time-to-failure of the LRU instance then health monitoring was unsuccessful.
- If successful, a scheduled maintenance activity is performed and the timeline is incremented by the health monitoring sampled time-tofailure.
- For both the LCM and HM approaches, the performance of the PHM methodology is modeled as a probability distribution taking into account uncertainties embedded in the methodology, sensors, models, etc.

### 3. MODEL RESULTS

- All of the variable inputs to the model can be treated as probability distributions or as fixed values, however, for example purposes, only the time to failure and performance of the PHM methodologies have been characterized by probability distributions.
- For long scheduled maintenance intervals virtually every instance of the LRU fails prior to the scheduled maintenance activity and the life cycle cost per unit becomes equivalent to a simple unscheduled maintenance model.
- The authors have also found that the effective life cycle cost is very sensitive to the width of the LCM forecasted timeto-failure distribution for the specific LRU (one case with a 2000 hour width is shown in Fig. 5).
- Figure 6 shows example results from a health monitoring solution for the example described in Table I. Figure 6 indicates that the health monitoring based methodology yields lower life cycle costs then either unscheduled maintenance or scheduled maintenance with a fixed interval.
- As the safety margin or prognostic distance increase (or fixed scheduled maintenance interval is small) the failures avoided limits to 100% in all cases (with and without random failures included).

### 4. DISCUSSION

- Previous PHM work on electronic systems has demonstrated life consumption monitoring for electronic systems, [4].
- Such an analysis becomes non-trivial when one considers the accuracy that life consumption monitoring results are likely to have (imperfect and partial monitoring conditions).
- The 1990ās perfected obtaining and storing large amounts of information, and as a result, the world is wading in a lot more information that it knows how to use.
- The single LRU model presented in this paper is being extended to treat multiple LRUs.
- Realistic PHM solutions for electronic systems will probably be mixtures of LCM, HM and scheduled maintenance Treatment of redundancy Second order uncertainty (uncertainty about uncertainty) may be a real issue in the treatment of this problem.

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##### Citations

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### Additional excerpts

...valves [14], and electronic devices [15]....

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### Cites background from "A decision support model for determ..."

...The literature on PHM solutions for aeronautical components comprises a wide range of applications, such as the monitoring of valves [3], pumps [4], engines [5], and electronic devices [6]....

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### Cites background from "A decision support model for determ..."

...Electronic systems, on the other hand, have traditionally not been subject to PHM since their time to wear-out has been longer than the life cycle of the whole system [21]....

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...Although many applicable models for single and multiunit maintenance planning have appeared [9,10], the majority of the models assume that monitoring information is perfect (without uncertainty) and complete (all units are monitored the same), i....

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### "A decision support model for determ..." refers background in this paper

...Although many applicable models for single and multiunit maintenance planning have appeared [9,10], the majority of the models assume that monitoring information is perfect (without uncertainty) and complete (all units are monitored the same), i....

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...All PHM approaches are essentially the extrapolation of trends based on recent observations to estimate remaining life, [1]....

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### "A decision support model for determ..." refers background or methods in this paper

..., thermal, vibration) is used in conjunction with physics of failure models to compute damage accumulated and thereby forecast life remaining, [4]....

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