This chapter is from: P. Sandborn and K. Feldman ...escml.umd.edu/Papers/WileyPHMBook-Sandborn.pdforganization is managed. In regards to specific organizational objectives such as

This chapter is from: P. Sandborn and K. Feldman Electronic System Prognostics and Health Management Wiley & Sons, 2008

Chapter 5

The Economics of Prognostics and Health Management

Prognostics and Health Management (PHM) provides an opportunity for lowering sustainment costs, improving maintenance decision-making and providing product usage feedback into the product design and validation process. The adoption of PHM approaches requires consideration and planning for integration into new and existing systems, operations, and processes. PHM must provide a significant advantage in order to add value for the maintenance process; commitments to implement and support PHM approaches cannot be made without the development of supporting business cases. The realization of PHM requires implementation at different levels of scale and complexity. The maturity, robustness, and applicability of the underlying predictive algorithms impact the overall efficacy of PHM within a technology enterprise. The utility of PHM to inform decision-makers within tight scheduling constraints and under different operational profiles likewise affects the cost avoidance that can be realized. This chapter discusses the determination of the benefits and potential cost avoidance offered by electronics PHM.

5.1 Return on Investment (ROI)

One important attribute of most business cases is the development of an economic justification. Return on investment (ROI) is a useful means of gauging the economic merits of adopting PHM.

ROI measures the ‘return,’ the cost savings, profit, or cost avoidance that result from a given use of money. Types of ROI include investment return, cost savings (or cost avoidance), and profit growth [1]. At the enterprise level, ROI may reflect how well an organization is managed. In regards to specific organizational objectives such as gaining more market share, retaining more customers, or improving availability, the ROI may be measured in terms of how a change in practice or strategy results in meeting these goals. In general, ROI is the ratio of gain to investment. Equation (1) is a way of defining a ROI calculation over a system life cycle.

Investment

InvestmentReturn ROI −= 1

−=Investment

CostAvoided (1)

The middle ratio in (1) is the classical ROI definition and the right ratio is the form of

ROI that is applicable to PHM assessment. ROI allows for enhanced decision-making regarding the use of investment money, and research and development efforts by enabling

Prognostics and Health Management of Electronics

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comparisons of alternatives. However, its inputs must be accurate and thorough in order for the calculation itself to be meaningful. In the case of PHM, the investment includes all the costs necessary to develop, install and support a PHM approach in a system, while the return is a quantification of the benefit realized through the use of a PHM approach.

Constructing a business case for PHM does not necessarily require that the ROI be greater than zero (ROI > 0 implies that there is a cost benefit), i.e., in some cases the value of PHM is not quantifiable in monetary terms but is necessary in order to meet a system requirement that could not otherwise be attained, e.g., an availability requirement. However, the evaluation of ROI (whether greater than or less than zero) is still a necessary part of any business case developed for PHM [2].

5.1.1 PHM ROI Analyses1

The determination of the ROI allows managers to include quantitative and readily interpretable results in their decision-making [3]. ROI analysis may be used to select between different types of PHM, to optimize the use of a particular PHM approach, or to determine whether to adopt PHM versus traditional maintenance approaches.

The economic justification of PHM has been discussed by several authors, e.g., [4-8]. The ROI associated with PHM approaches have been examined for specific non-electronic military applications, including ground vehicles, power supplies and engine monitors [9, 10]. NASA studies indicate that the ROI of prognostics in aircraft structures may be as high as 0.58 in 3 years for contemporary and older generation aircraft systems assuming a 35% reduction in maintenance requirements [11]. To generalize the costs of electronics PHM for commercial and military aircraft requires knowledge of industry practices and regulations, knowledge of phased and mission scheduling, understanding of the underlying PHM component technologies, and an assessment of their accuracy. Simple ROI analyses of electronic prognostics for high reliability telecommunications applications (power supplies and power converters) have been conducted, including a basic business case for the BladeSwitch voice telecommunications deployment in Malaysia [12].

The Joint Strike Fighter (JSF) program was the first implementation of PHM in a major multinational defense system [13]. PHM is the principle component in the JSF’s Autonomic Logistics2 system. ROI predictions of the costs of PHM implementation and the potential for cost avoidance have been evaluated and an analysis of PHM for JSF aircraft engines was developed using a methodology that employed Failure Modes, Effects, and Criticality Analysis (FMECA) to model hardware [15, 16]. The effectiveness of the PHM devices in detecting and isolating each of the failures was determined and evaluated against unscheduled maintenance and scheduled maintenance approaches. Ashby and Byer [16] employed a logistic simulation model to assess impacts on availability within military flight scheduling for an engine control unit (ECU) equipped with PHM for different subcomponents. PHM, when applied to suitable subcomponents, offered substantial monetary and non-monetary benefits, specifically in increased safety and improved sortie generation. Byer provides results showing maintenance and cost avoidance savings for a program using PHM over a five year period.

1 Warning, not all researchers that quote ROI numbers define ROI in the same way. Equation (1) is the standard definition used by the financial world for return on investment. 2 ‘Autonomic logistics’ describes an automated system that supports mission reliability and maximizes sortie generation while minimizing costs and logistical burden, [14].

The Economics of Prognostics and Health Management 3

Byer et al. [17] describe a process for conducting a cost-benefit analysis for prognostics applied to aircraft subsystems. The definition of a baseline system without PHM and the aircraft system with PHM is the first step in the analysis. Secondly, reliability and maintainability predictions for the components of the aircraft are developed. Next, the measures of PHM effectiveness are defined and the corresponding metrics associated with these measures of effectiveness are established. The impact of PHM on training, support equipment, the cost of consumables, and manpower are then assessed. The overall non-recurring and recurring costs of providing PHM are estimated. The results are then computed for the cost benefits. The process is then repeated for PHM benefits that are not denominated in monetary units, including sortie generation capability, reduction in the frequency of accidents, and the change in footprint.

As supplemental information and for model refinement, Byer et al. [17] use FMECA, line maintenance activity costing, and legacy field event rates in addition to scheduling matrices and cost data on parts to produce life cycle costs and operational impact assessments. The detailed inputs present an improvement over the more general information contained in typical military maintenance databases, which may have a great amount of historical data overall but lack specific data on fault diagnostic and isolation times needed to assess the cost avoidance of PHM. The methodology can be used to enhance the accuracy of operational and support costs, even in the absence of PHM technologies, by creating a more rigorous framework for the examination of maintenance costs.

The cost-benefit analysis of PHM for batteries within ground combat vehicles was modeled using the Army Research Laboratory’s Trade Space Visualizer software tool [18]. The analysis was performed by conducting a study of asset failure behavior, calculating the cost of PHM technology development and integration, estimating the benefits of the technology implementation, and calculating decision metrics. The initial analysis focuses on isolating the subcomponents that contribute to the degradation of the larger components or the system itself. FMECA can then be used to classify the failure mode and determine which prognostics technology could be used to monitor it. This information is then extended into a fleet operations framework in which a user can select variables of parameters, such as availability, battery failure rate, or the logistic delay time. These parameters can be optimized to achieve a given ROI, or the user can set values for these parameters and then calculate the ROI for different scenarios. Banks and Merenich [18] found that ROI was maximized when the time horizon (prognostic distance) was greatest and when the number of vehicles and the failure rates were largest.

A comparison of the ROI of prognostics for two types of military ground vehicle platforms was performed using data from Pennsylvania State University’s battery prognostics program [7]. Non-recurring development costs were estimated for the prognostic units developed for the batteries of the Light Armored Vehicle (LAV) and the Stryker platform used in the Stryker Brigade Combat Team (SBCT) family of vehicles. ROI was calculated as 0.84 for the LAV and 4.61 for the SBCT based on estimates of the development and implementation costs. The difference in ROI is attributed to a shorter period of benefit over which the costs of PHM development would be absorbed for the LAV in addition to a smaller quantity of batteries. The implementation costs considered were manufacturing of the PHM sensors and their installation in each vehicle. The non-recurring development costs included algorithm development, hardware and software design, engineering, qualification, and testing, vehicle system integration, and the development of an integrated data environment (IDE) for data management. When combined with known data about battery performance across the Department of Defense (DoD), the total ROI of battery prognostics for the DoD was calculated as 15.25 over a 25-year period.


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The Boeing Company developed a life cycle cost model for evaluating the benefits of prognostics for the Joint Strike Fighter program. The model was developed by Boeing’s Phantom Works division to enable cost-benefit analysis of prognostics for the fighter’s avionics during system demonstration and then enhanced to permit life cycle cost assessment of prognostic approaches [19]. The model allowed for selection of standard mission profiles or definition of custom mission profiles. Cost influencing parameters in addition to economic factors were incorporated into a cost benefit analysis [20].

Although existing PHM ROI assessments contain valuable insight into the cost drivers, most cost analyses and cost-benefit analyses are application-specific; they do not provide a general modeling framework or consistent process with which to approach the evaluation of the application of PHM to a new system. Furthermore, existing approaches provide primarily “point estimates” of the value based on a set of fixed inputs when, in reality, the inputs are uncertain. For example, the reliability of a system is best represented as a probability distribution, as are many other inputs to the ROI analysis. Accommodating the uncertainties in the PHM ROI calculation is at the heart of developing realistic business cases that address prognostic requirements.

5.1.2 Financial Costs

Financial costs are part of the engineering economics of technology acquisitions. The business cases for the inclusion of PHM into systems are long-term propositions, i.e., for most types of systems, investments are made and cost avoidance is realized over many years. Because the ROI assessment spans a significant time period, the cost of money must be included in the ROI evaluation. In examining options for capital allocations, key financial concepts are used to evaluate alternatives and to determine the best use of an organization’s resources. The borrowing of money carries with it an interest charge, while examination of resource allocation and payments over a system life cycle may require consideration of the value of money over time, depreciation, and inflation. Economic equivalence correlates the cash flows associated with different usage alternatives to produce meaningful comparisons for investment decision-making. Concepts such as Present Value may be used to compare the value of money in the present to its value in the future. A dollar today is worth more than a dollar in the future, because money available today can be invested and grow while money spent today cannot. Ignoring inflation, the present value of Vn, n years from the present with a constant discount rate (rate of Return on Investment) of r is given by,

( )n

n

1+rVlue=Present Va (2)

Using (2), a cost of Vn can be shifted n years into past for comparison purposes. Other forms of the present value calculation exist for various assumptions about the growth of money over time; see [21] for an overview of engineering economics concepts.

5.2 PHM Cost Modeling Terminology and Definitions

This section provides some necessary definitions of several concepts that are central to the discussion of PHM costs in this chapter.


Line Replaceable Unit (LRU) is a general term referring to a generic ‘black box’ electronics unit that is usually designed to common specifications and are readily replaceable on the “line” (i.e., in the field). LRUs are distinguished from Shop Replaceable Units (SRUs) and Depot Replaceable Units (DRUs), which may require additional time, resources, and equipment for replacement and maintenance. A socket is a unique instance of an installation location for an LRU. One instance of a socket occupied by an engine controller is its location on a particular engine. The socket may be occupied by a single LRU during its lifetime (if the LRU never fails), or multiple LRUs if one or more LRUs fail and needs to be replaced.

Unscheduled maintenance refers to operating a system until failure and then taking appropriate maintenance actions to replace or repair the failure. The opposite of unscheduled maintenance is preventative maintenance in which a maintenance action is taken prior to failure at a scheduled interval or in response to an indication provided by a PHM approach. A fixed-schedule maintenance interval is the interval at which scheduled maintenance is performed. The fixed-schedule maintenance interval is kept constant for all instances of the LRUs occupying all socket instances throughout the system life cycle. The common wisdom that oil should be changed every 3,000 miles for personal vehicles represents a fixed-schedule maintenance interval policy. Precursor to Failure methodologies refer to methodologies that are dependent on the specific LRU instance they are applied to. Included in this category of PHM approaches are Health Monitoring (HM) and LRU-dependent fuses. LRU-dependent fuses are assumed to be fabricated concurrently with specific instances of LRUs, e.g., they would share LRU-specific variations in manufacturing and materials. LRU-independent methodologies are independent of the specific LRU instance they are applied to. Included in this category of PHM approaches are Life Consumption Monitoring (LCM) and LRU-independent fuses. LRU-independent fuses are fabricated separately from the LRUs and assembled into the LRUs, so they do not share any LRU-specific variations in manufacturing and materials.

The remainder of this chapter treats the total cost of ownership of PHM by discussing two major categories of cost-contributing activities that must be considered in an analysis of the ROI of PHM. These categories, implementation costs and cost avoidance, represent the ‘Investment’ portion and the ‘Return On’ portion of the ROI calculation respectively.

5.3 PHM Implementation Costs

Implementation costs are the costs associated with the realization of PHM in a system, that is, the achievement of the technologies and support necessary to integrate and incorporate PHM into new or existing systems. The costs of implementing PHM can be categorized as recurring, non-recurring, or infrastructural depending on the frequency and role of the corresponding activities. The implementation cost is the cost of enabling the determination of Remaining Useful Life (RUL) for the system. Implementation costs can be characterized as non-recurring, recurring, and infrastructural.

‘Implementation’ may be decomposed into many separate activities at different levels of complexity and detail. The following sections discuss the major groups of implementation costs while maintaining generality and breadth. This broadness reflects the incorporation of implementation costs into ROI models for PHM; an organization will likely not be able to put an exact ‘price tag’ on very specific activities. Implementation cost


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models can and should be adapted to meet the needs of a particular application and can be expanded as knowledge of the PHM devices and their use increases.

5.3.1 Non-Recurring Costs Non-recurring costs are associated with one-time only activities that typically occur at the beginning of the timeline of a PHM program — although disposal or recycling non-recurring costs would occur at the end. Non-recurring costs can be calculated on a per-LRU or per-socket basis, or per a group of LRUs or sockets. The development of hardware and software are the most prominent non-recurring costs. Hardware cost modeling will vary depending on manufacturing specifications, country of origin, level of complexity, and materials. LRU-dependent prognostics are manufactured concurrently with the device whose failure they are intended to indicate; if a general cost model can be developed for the electronic components of interest, it may be a reasonable assumption that the costs of materials, parts, and labor for the manufacturing of the prognostic device will be equivalent. This simplifies the cost modeling of the LRU-dependent prognostics but not the LRU-independent approaches, which need not have anything in common with the device they are monitoring.

The development of PHM software may be outsourced and treated as a single contract amount or may be modeled according to standard software cost models such as COCOMO [22]. COCOMO and other software cost models provide cost estimates based on the Source Lines of Code (SLOC), the programming language used, and the manpower needed for development. Both hardware and software design include testing and qualification to ensure performance, compatibility with existing architectures, and compliance with standards and requirements.

Other non-recurring costs include the costs of training, documentation, and integration. Training costs arise from the need to develop training materials to instruct and educate maintainers, operators, and logistics personnel as to the use and maintenance of PHM, in addition to the cost of removing these workers from their ordinary duties to attend training. PHM hardware and software must have documentation to serve as guides and as usage manuals, while integration costs refer to the costs of modifying and adapting systems to incorporate PHM.

The specific non-recurring cost is calculated as: qualintdoctrainingdev_softdev_hard CCCCCCCostRecurringNon +++++=− (3) where Cdev_hard is the cost of hardware development; Cdev_soft is the cost of software development; Ctrain is the cost of training; Cdoc is the cost of documentation; Cint is the cost of integration; and Cqual is the cost of testing and qualification.

5.3.2 Recurring Costs

Recurring costs are associated with activities that occur continuously or regularly during the PHM program. As with non-recurring costs, some of these costs can be viewed as an additional charge for each instance of an LRU or for each socket (or for a group of LRUs or sockets).


The recurring cost is calculated as: installtestassemblyhard_addgroup) socket, LRU,(per CCCCCostRecurring +++= (4) where Chard_add is the cost of hardware in each LRU (e.g., sensors, chips, extra board area) and may include the cost of additional parts or manufacturing or the cost of hardware for each socket (such as connectors and sensors); Cassembly is the cost of assembly, installation, and functional testing of the hardware in each LRU or the cost of assembly of hardware for each socket or for each group of sockets; Ctest is the cost of functional testing of hardware for each socket or for each group of sockets; and Cinstall is the cost of installation of hardware for each socket or for each group of sockets, which includes the original installation and re-installation upon failure, repair, or diagnostic action.

5.3.3 Infrastructure Costs

Unlike recurring and non-recurring costs, infrastructure costs are associated with the support features and structures necessary to sustain PHM over a given activity period and are characterized in terms the ratio of money to a period of activity (i.e., dollars per operational hour, dollars per mission, dollars per year). During a mission or use period, the PHM device may be collecting, processing, analyzing, storing, and relaying data. These activities constitute the data management needed to implement PHM and are continual throughout the life of the PHM program. The addition of PHM to an LRU imposes a cost associated with the extra time for maintainers, diagnosticians, and other personnel to read and relay the information provided by PHM to render a decision about the timing and content of maintenance actions. As with the LRUs that they monitor, PHM devices may also require maintenance over their life cycles, including repairs and upgrades. Maintenance of the PHM devices may require the purchase of repair expendables (consumables) or ordering of new parts. The labor required for such maintenance contributes to the infrastructure costs. Lastly, re-training or ‘continuous education’ is an infrastructure cost, ensuring that personnel are prepared to use and maintain the PHM devices as intended.

The infrastructure costs are calculated as:

dataretrainingdecisionenanceprog_maint CCCCCost tureInfrastruc +++= (5) where Cdata is the cost of data management, including the costs of data archiving, data collection, data analysis, and data reporting; Cprog_maintenance is the cost of maintenance of the prognostic devices; Cdecision is the cost of decision support; and Cretraining is the cost of retraining costs to educate personnel in the use of PHM.

5.3.4 Non-Monetary Considerations and Maintenance Culture

The implementation of PHM imparts additional burdens onto systems that cannot always be easily measured and considered in monetary terms. The physical hardware apparatuses used in PHM will consume volumetric space and alter the weight (loading) of the systems where they are installed. The time needed for PHM data to be processed, stored,


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and analyzed to render a maintenance decision is an additional metric of importance. Space, weight, time, and cost (SWTC) are the dimensions in which PHM activities could be fully expressed. Considering each of these dimensions may not be useful or needed for a particular analysis; however, awareness of these physical and time-related factors can be leveraged to calculate the non-monetary impositions and potential benefits associated with PHM. Examples of these non-monetary quantities are given in Table 5.1.

Table 5.1: Categories of non-monetary considerations for PHM

Category Example

Footprint within the LRU Footprint of external equipment

needed to support PHM Space (Volume or Area) Dimensions of electronics content

and integration with existing equipment (e.g., number of

connector pins, boards per panel) Weight of PHM equipment on-

board or on system Weight Weight of external equipment needed to support PHM Time to collect data Time to analyze data

Time to render a decision Time to communicate decision

Time

Time to take action

Maintenance culture has been studied to identify areas of improvement following accidents or failures, to determine the most effective ways of training maintenance crews, and as part of resource management, with 12-15% of accidents in the commercial aviation industry attributable to maintenance errors [23]. Analyses of the maintenance culture underscore the complexity of decision-making within the industry and point to the underlying difficulties of effecting organizational changes [24, 25]. Organizations seeking to implement changes within their daily operations are confronted by direct and tangible impacts such as new equipment and fewer personnel that can be correlated to different costs. However, the role of seemingly intangible elements has proved important to the practices and business culture of productive and efficient organizations and has been studied within the contexts of industrial and organizational psychology, group dynamics, human factors, and team and training effectiveness [26].

The aviation workplace culture has been examined as an environment in which high-pressure, safety-critical decisions must be made in a team atmosphere. PHM represents a departure from traditional maintenance procedures; to implement it will require a change the maintenance culture such that maintainers are comfortable and educated to use PHM as intended. This cost of changing the maintenance culture may be quantified as a continuous education cost beyond standard training. System architects and designers would eventually transition to placing greater responsibility in PHM, ultimately to remove redundancy and to make other changes necessary to allow the full value of PHM to be realized. While this is not a tangible or engineering cost, it is nonetheless a real factor contributing to the adoption of PHM.


5.4 Cost Avoidance

Prognostics provide estimations of Remaining Useful Life (RUL) in terms that are useful to the maintenance decision making process. The decision process can be tactical (real-time interpretation and feedback) or strategic (maintenance planning). All PHM approaches are essentially the extrapolation of trends based on recent observations to estimate RUL, [27]. Unfortunately, the calculation of RUL alone does not provide sufficient information to form a decision or to determine corrective action. Determining the best course of action requires the evaluation of criteria such as availability, reliability, maintainability, and life cycle cost. Cost avoidance is the value of changes to availability, reliability, maintainability, and failure avoidance.

The primary opportunities for obtaining cost avoidance from the application of PHM to systems are failure avoidance and minimization of the loss of remaining system life. Field failure of systems is often very expensive. If all or some fraction of the field failures can be avoided, then cost avoidance may be realized by minimizing the cost of unscheduled maintenance. Avoidance of failures can also increase availability, reduce the risk of loss of the system, and may increase human safety depending on the type of system considered. Failures avoided fall into two types: 1) real-time failure avoidance during operation that would otherwise result in the loss of the system or loss of the function the system was performing (i.e., loss of mission), and 2) warning of future (but not imminent) failure that allows preventative maintenance to be performed at a place and time that are convenient.

PHM may allow minimization of the amount of remaining useful life thrown away when performing scheduled maintenance. Cost can be avoided if the system components are used for their full lifetimes rather than removing and disposing of system components while they still possess significant RUL.

The two opportunities discussed above are the primary targets for most PHM business cases; however, other cost avoidance opportunities, discussed in the remainder of this section, may exist depending on the application of the system.

Logistics footprint reduction: Reduction in the system’s logistics footprint may be possible through better spares management (quantity, refreshment, and locations), better use of and control over inventory, and minimization of external test equipment. Note, this does not necessarily imply that the quantity of spares required will be reduced, if fact, a successful PHM program could increase the number of spares needed compared to a non-PHM unscheduled maintenance approach.

Repair cost reduction: PHM may reduce the costs of repair by enabling better fault isolation (decreased inspection time, decreased trouble shooting time, less equipment removal [28]). PHM may also reduce collateral damage during repair because of better fault isolation.

Reduction in redundancy: In the long term, it may be possible to reduce critical system redundancy for selected subsystems. This will not happen until and unless PHM approaches are proven effective for the subsystems.

Reduction in no-fault-founds:3 PHM approaches may be able to reduce the quantity or reduce the cost of resolving no-fault-founds. A substantial portion of the maintenance cost

3 No-fault-founds (NFFs), also known as can-not-duplicates (CNDs) or no-trouble-founds (NTFs), occur when an originally reported mode of failure cannot be duplicated and therefore the potential defect cannot be fixed. Many organizations have policies regarding the management of NFFs that, depending on the number of occurrences of an NFF in a specific LRU, the NFF LRUs are put back in service or contributed back into the spares pool.


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of many systems is due to no-fault-founds. It may be possible to construct an entire business case for electronics PHM based on only the reduction in no-fault-founds.

Eased design and qualification of future systems: The data collected through the use of PHM is an extremely valuable resource for understanding the actual environmental stresses and product usage conditions seen by a product during its field use. This knowledge can be used to refine the design, refine reliability assessments, improve uncertainty estimates, and to enhance knowledge of failure modes and behaviors. Designers of a product often cannot anticipate how that product is actually used, e.g., designers rated the maximum load of High Mobility Multipurpose Wheeled Vehicles (HMMWVs) at 2,500 lbs.; in combat zones, they have been loaded to more than 4,530 lbs, that is, 181 percent of their maximum load [29]. Warranty verification: PHM can be used to verify the field usage conditions for products returned for warranty claims, thereby allowing products that have been used in environmental conditions that void the warranty to be readily identified and warranty claims for them appropriately managed.

Reduced waste stream: For some systems, PHM may lead to a reduction in the end-of-life disposal costs for the system and thereby a reduction in product take-back costs.

Not all of the opportunities listed above are applicable to every type of system, however, a combination of the opportunities has to be targeted or a business case cannot be substantiated.

Several key concepts differentiate the cost avoidance modeling from implementation cost modeling. First, the temporal order of events in the lifetime of an LRU or socket affect the calculation of cost avoidance (this is true whether financial costs are included or not). The cost avoidance is heavily influenced by the sequencing (in time) of failures and maintenance actions, whereas implementation costs are not time-sequence dependent and can be modeled independently of each other in many cases, despite sharing cost-contributing factors. Secondly, irrespective of the combination of criteria for cost avoidance under consideration, corresponding measures of the uncertainty associated with the calculation must be incorporation. It is the inclusion and comprehension of the corresponding uncertainties —decision making under uncertainty— that is at the heart of being able to develop a realistic business case that addresses prognostic requirements.

The next subsection addresses the use of PHM for maintenance planning. It quantifies how to determine the cost avoidance associated with PHM for the realization of failure avoidance and the minimization of the loss of RUL.

5.4.1 Maintenance Planning Cost Avoidance

The modeling discussed in this subsection is targeted at finding the optimum balance between avoiding failures and throwing away RUL with fixed interval scheduled maintenance. Two systems, fielded and used under similar conditions, will not generally fail at exactly the same time due to differences in their manufacturing and materials, and due to differences in the environmental stress history they experience. Therefore, system reliability is generally represented as a probability distribution over time or in relation to an environmental stress driver. Likewise, the ability of a PHM approach to accurately predict RUL is not perfect due to sensor uncertainties, sensor gaps, sensor locations, uncertainties in algorithms and models used, or other source. Practically speaking, these uncertainties make 100% failure avoidance impossible to obtain; optimal maintenance planning for systems effectively becomes a tradeoff between the potentially high costs of failure and the costs of throwing away remaining system life in order to avoid failures.


Although many applicable models for single and multi-unit maintenance planning have appeared [30, 31], the majority of the models assume that monitoring information is perfect (without uncertainty) and complete (all units are monitored identically), i.e., maintenance planning can be performed with perfect knowledge as to the state of each unit. For many types of systems, and especially electronic systems, these are not good assumptions and maintenance planning, if possible at all, becomes an exercise in decision making under uncertainty with sparse data. The perfect monitoring assumption is especially problematic when the PHM approach is life consumption monitoring (LCM) because LCM does not depend on precursors. Thus, for electronics, LCM processes do not deliver any measures that correspond exactly to the state of a specific instance of a system. Previous work that treats imperfect monitoring includes [32] and [33]. Perfect, but partial monitoring has been previously treated in [34].

This section describes a stochastic decision model [35] that enables the optimal interpretation of LCM damage accumulation or HM precursor data, and applies to failure events that appear to be random or appear to be clearly caused by defects. Specifically the model is targeted at addressing the following questions. First, how do we determine on an application-specific basis when the reliability of electronics has become predictable enough to warrant the application of PHM-based scheduled maintenance concepts? Note that predictability in isolation is not necessarily a suitable criterion for PHM vs. non-PHM solutions, e.g., if the system reliability is predictable and very reliable, it would not make sense to implement a PHM solution. Secondly, how can PHM results be interpreted so as to provide value, i.e., how can a business case be constructed given that the forecasting ability of PHM is subject to uncertainties in the sensor data collected, the data reduction methods, the failure models applied, the material parameters assumed in the models, etc.? The interpretation boils down to determining an optimal safety margin on LCM prediction and prognostic distance for HM.

5.4.2 Discrete Event Simulation Maintenance Planning Model

The maintenance planning model discussed here accommodates variable time-to-failure (TTF) of LRUs and variable RUL estimates associated with PHM approaches implemented within LRUs. The model considers both single and multiple sockets within a larger system. Discrete event simulation is used to follow the life of individual socket instances from the start of their field lives to the end of their operation and support.4 Discrete event simulation allows for the modeling of a system as it evolves over time by capturing the changes as separate events (as opposed to continuous simulation where the system evolves as a continuous function). The evolutionary unit need not be time; it could be thermal cycles, or some other unit relevant to the particular failure mechanisms addressed by the PHM approach. Discrete event simulation has the advantage of defining the problem in terms of an intuitive basis, i.e., a sequence of events, thus avoiding the need for formal specification. Discrete event simulation is widely used for maintenance and operations modeling, e.g., [36-38], and has also previously been used to model PHM activities, [39].

The model discussed in this chapter treats all inputs to the discrete event simulation as probability distributions, i.e., a stochastic analysis is used, implemented as a Monte Carlo simulation. Various maintenance interval and PHM approaches are distinguished by how

4 Alternatively, one could follow the lifetime of LRUs through their use, repair, reuse in other sockets, and disposal.


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sampled TTF values are used to model PHM RUL forecasting distributions. To assess PHM, relevant failure mechanisms are segregated into two types. Failure mechanisms that are random from the view point of the PHM methodology are failure mechanisms that the PHM methodology is not collecting any information about (non-detection events). These failure mechanisms may be predictable, but are outside the scope of the PHM methods applied. The second type are failure mechanisms that are predictable from the view point of the PHM methodology. A probability distribution can be assigned for these failure mechanisms.

For the purposes of cost model formulation, PHM approaches are categorized as (defined in detail in Section 5.2): (a) a fixed-schedule maintenance interval; (b) a variable maintenance interval schedule for LRU instances that is based on inputs from a Precursor to Failure methodology; and (c) a variable maintenance interval schedule for LRU instances that is based on an LRU-independent methodology. Note, for simplicity, the model formulation is presented based on “time” to failure measured in operational hours; however, the relevant quantity could be a non-time measure.

5.4.3 Fixed-Schedule Maintenance Interval

A fixed-schedule maintenance interval is selected that is kept constant for all instances of the LRU that occupy a socket throughout the system life cycle. In this case the LRU is replaced on a fixed interval (measured in operational hours), i.e., time-based prognostics. This is analogous to mileage-based oil changes in automobiles.

5.4.4 Precursor to Failure Monitoring

Precursor to failure monitoring approaches are defined as a fuse or other monitored structure that is manufactured with or within the LRUs or as a monitored precursor variable that represents a non-reversible physical process, i.e., it is coupled to the manufacturing or material variations of a particular LRU. Health Monitoring (HM) and LRU-dependent fuses are examples of precursor to failure methods. The parameter to be determined (optimized) is prognostic distance. The prognostic distance is a measure of how long before system failure the prognostic structures or prognostic cell is expected to indicate failure (in operational hours for example). The precursor to failure monitoring methodology forecasts a unique time to failure (TTF) distribution for each instance of an LRU based on the instance’s TTF.5 For illustration purposes, the precursor to failure monitoring forecast is represented as a symmetric triangular distribution with a most likely value (mode) set to the TTF of the LRU instance minus the prognostic distance, Figure 5.1.

The precursor to failure monitoring distribution has a fixed width measured in the relevant environmental stress units (e.g., operational hours in our example) representing the probability of the prognostic structure correctly indicating the precursor to a failure. As a simple example, if the prognostic structure was a LRU-dependent fuse that was designed to fail at some prognostic distance earlier than the system it protects, then the distribution on the right side of Figure 5.1 represents the distribution of fuse failures (the TTF distribution of the fuse). The parameter to be optimized in this case is the prognostic distance assumed for the precursor to failure monitoring forecasted TTF. 5 In this model, all failing LRUs are assumed to be maintained via replacement or good-as-new repair, therefore, the time between failure and the time to failure are the same.


The model proceeds in the following way: for each LRU TTF distribution sample (t1) taken from the left side of Figure 5.1, a precursor to failure monitoring TTF distribution is created that is centered on the LRU TTF minus the prognostic distance (t1-d). The precursor to failure monitoring TTF distribution is then sampled and if the precursor to failure monitoring TTF sample is less than the actual TTF of the LRU instance, the precursor to failure monitoring is deemed successful. If the precursor to failure monitoring distribution TTF sample is greater than the actual TTF of the LRU instance then precursor to failure monitoring was unsuccessful. If successful, a scheduled maintenance activity is performed and the timeline for the socket is incremented by the precursor to failure monitoring sampled TTF. If unsuccessful, an unscheduled maintenance activity is performed and the timeline for the socket is incremented by the actual TTF of the LRU instance. At each maintenance activity, the relevant costs are accumulated.

5.4.5 LRU-Independent Methods

In LRU-independent PHM methods, the PHM structure (or sensors) are manufactured independent of the LRUs, i.e., the PHM structures are not coupled to a particular LRU’s manufacturing or material variations. An example of a LRU-independent method is Life Consumption Monitoring (LCM). LCM is the process by which a history of environmental stresses (e.g., thermal, vibration) is used in conjunction with physics of failure (PoF) models to compute damage accumulated and thereby forecast RUL. The LRU-independent methodology forecasts a unique TTF distribution for each instance of an LRU based on its unique environmental stress history. For illustration purposes, the LRU-independent TTF forecast is represented as a symmetric triangular distribution with a most likely value (mode) set relative to the TTF of the nominal LRU and a fixed width measured in operational hours, Figure 5.2. Other distributions may be chosen and [40] has shown how this distribution may also be derived from recorded environment history. The shape and width of the LRU-independent method distribution depends on the uncertainties associated

Figure 5.1: Precursor to failure monitoring modeling approach

Symmetric triangular distributions are chosen for illustration. Note, the LRU TTF probability density function (pdf) (left) and the Precursor to failure TTF pdf

(right) are not the same (they could have different shapes and sizes).


14

with the sensing technologies and uncertainties in the prediction of the damage accumulated (data and model uncertainty). The variable to be optimized in this case is the safety margin assumed on the LRU-independent method forecasted TTF, i.e., the length of time (e.g., in operation hours) before the LRU-independent method forecasted TTF the unit should be replaced.

The LRU-independent model proceeds in the following way: for each LRU TTF distribution sample (left side of Figure 5.2), an LRU-independent method TTF distribution is created that is centered on the TTF of the nominal LRU minus the safety margin – right side of Figure 5.2 (note, the LRU-independent methods only know about the nominal LRU, not about how a specific instance of a LRU varies from the nominal). The LRU independent method TTF distribution is then sampled and if the LRU-independent method TTF sample is less than the actual TTF of the LRU instance then LRU-independent method was successful (failure avoided). If the LRU-independent method TTF distribution sample is greater than the actual TTF of the LRU instance then LRU-independent method was unsuccessful. If successful, a scheduled maintenance activity is performed and the timeline for the socket is incremented by the LRU-independent method sampled TTF. If unsuccessful, an unscheduled maintenance activity is performed and the timeline for the socket is incremented by the actual TTF of the LRU instance.6

In the maintenance models discussed, a random failure component may also be superimposed as discussed in [35]. The fixed scheduled maintenance, precursor to failure monitoring and LRU-independent method models are implemented as stochastic simulations, in which a statistically relevant number of sockets are considered in order to construct histograms of costs, availability, and failures avoided. Again, at each maintenance activity, the relevant costs are accumulated.

The fundamental difference between the precursor to failure and LRU-independent models is that in the precursor to failure models the TTF distribution associated with the 6 LRU-independent fuses and canary devices may require replacement for each alert that they provide whether that alert is a false positive or not. After the PHM devices are removed for maintenance, to download data, or for other activities, re-installation follows.

Figure 5.2: LRU-independent modeling approach Symmetric triangular distributions are chosen for illustration. Note, the LRU TTF pdf (left) and the LRU-independent method TTF pdf (right) are not the same (they

could have different shapes and sizes).


PHM structure (or sensor) is unique to each LRU instance, whereas in the LRU independent models the TTF distribution associated with the PHM structure (or sensor) is tied to the nominal LRU and is independent of any manufacturing or material variations between LRU instances.

5.4.6 Discrete Event Simulation Implementation Details

The model follows the history of a single socket or a group of sockets from time zero to the end of support life for the system. To generate meaningful results, a statistically relevant number of sockets (or systems of sockets) are modeled and the resulting cost and other metrics are presented in the form of histograms. The scheduled and unscheduled costs computed for the sockets are given by, VTfVfTCffCC irepairireplacerepairiLRUiLRUisocket )1()1( −++−+= (6) where Csocket i is the life cycle cost of socket i; CLRU i is the cost of procuring a new LRU; CLRU repair i is the cost of repairing an LRU in socket i; f is the fraction of maintenance events on socket i that require replacement of the LRU in socket i with a new LRU; Treplace iis the time to replace the LRU in socket i; Trepair i is the time to repair the LRU in socket i; and V is the value of time out of service.

Note, the values of f and V generally differ depending on whether the maintenance activity is scheduled or unscheduled. For simplicity, (6) is written assuming that quantity of replaced LRUs in socket i is one; however, in general, the socket could receive many LRUs during its lifetime. As the discrete event simulation tracks the actions that affect a particular socket during its life cycle, the implementation costs are inserted at the appropriate locations, Figure 5.3. At the beginning of the life cycle, the non-recurring cost is applied. The recurring costs at the LRU level and at the system level are first applied here and subsequently applied at each maintenance event that requires replacement of an LRU (CLRU i, as in (6)). The recurring LRU-level costs include the base cost of the LRU regardless of the maintenance approach. Discrete event simulations that compare alternative maintenance approaches to determine the ROI of PHM must include the base cost of the LRU itself without any PHM-specific

Time

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• LRU/socket associated non-recurring cost

• System recurring cost

Infrastructure cost (charged periodically)

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• Base LRU recurring cost• PHM LRU recurring cost

Figure 5.3: Temporal ordering of implementation cost inclusion in the discrete event simulation.


16

hardware. If discrete event simulation is used to calculate the life cycle cost for a socket under an unscheduled maintenance policy, then the recurring LRU-level cost is reduced to the cost of replacing or repairing an LRU upon failure. Under a policy involving PHM, the failure of an LRU results in additional costs for the hardware, assembly, and installation of the components used to perform PHM. The infrastructure costs are distributed over the course of the socket’s life cycle and are charged periodically.

The model assumes that the time-to-failure (TTF) distribution represents manufacturing and material variations from LRU to LRU. The range of possible environmental stress histories that sockets may see are modeled using an environmental stress history distribution. Note, the environmental stress history distribution need not be used if the TTF distribution for the LRUs includes environmental stress variations. The environmental stress history distribution is not used with the precursor to failure or LRU-independent models. Random TTFs are characterized by 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.

Uncertainty, which must be propagated throughout the life cycle simulations of systems, is present at multiple levels in the calculation of RUL. The data collected by the prognostic devices, the material inputs reliability modeling depends on, and the underlying assumptions of electronic failure behavior that are applied to produce reliability estimates may not always be accurate.

Uncertainties can be handled using different approaches, however, the most general method of handling uncertainties is to use a Monte Carlo analysis approach in which each input parameter is optionally represented as a probability distribution. The CALCE implementation of the maintenance modeling discussed in this chapter is implemented as a Monte Carlo analysis that follows a statistically relevant number of sockets over their support lives.

Additional model implementation details, including a flow chart that describes the discrete event simulation process, are available in [35].

5.4.7 Operational Profile

The operational profile of systems equipped with PHM dictates how the information provided by PHM may be used to affect the maintenance and usage schedules. The effective costs associated with maintenance actions depend on when (and where) actions are indicated relative to some operational cadence. Cadences may be proscribed by business constraints, regulations or mission requirements, and may be subject to change as user requirements shift. The cadence may be best described according to a probabilistic model rather than a timeline, i.e., a defined probability of a maintenance request being issued before, during, or after a mission or particular type of use. The implications of the safety margins or prognostics distances will vary with the difference in cadence to affect the timing of maintenance actions.

The operational profile is reflected in the maintenance modeling by varying the value of the parameter V in (6). V, the value of an hour out of service, is set to a specific value if the maintenance is scheduled, but if the maintenance is unscheduled, the value of V is given by the data in Table 5.2.


Table 5.2: Data defining unscheduled maintenance operational profile

Probability V Maintenance event before mission (during preparation) Pb Vb Maintenance event during mission Pd Vd Maintenance event after mission (during downtime) Pa Va

“Before mission” represents maintenance requirements that occur while preparing to

place the system into service, i.e., while loading passengers onto the aircraft for a scheduled commercial flight. “During mission” means that the maintenance requirement occurs while the system is performing a service and may result in interruption of that service, i.e., making an emergency landing, or abandoning a High Mobility Multipurpose Wheeled Vehicle (HMMWV) by the side of the road during a convoy. “After mission” represents time that the system is not needed, i.e., the period of time from midnight to 6:00 am when the commercial aircraft could sit idle at a gate.

When an unscheduled maintenance event occurs, a random number generator is used to determine the portion of the operational profile the event is in and the corresponding value (V) is used in the analysis. This type of valuation in the discrete event simulation is only useful if a stochastic analysis that follows the life of a statistically relevant number of sockets is used.

5.5 Example PHM Cost Analysis

The baseline data assumptions used to demonstrate the model in this chapter are given in Table 5.3. All of the variable inputs to the model can be treated as probability distributions or as fixed values, however, for example purposes, only the TTFs of the LRUs and the PHM structures have been characterized by probability distributions. Note, all of the life cycle cost results provided in the remainder of this chapter are the mean life cycle costs from a probability distribution of life cycle costs generated by the model.

Table 5.3: Data assumptions for example cases presented in this section

Variable in the model Value used for example analysis Production cost (per unit) $10,000

Time to failure (TTF) 5000 operational hours = the most likely value (symmetric triangular distribution with variable distribution width)

Operational hours per year 2500 Sustainment life 25 years

Unscheduled Scheduled Value of each hour out of service $10,000 $500

Time to repair 6 hours 4 hours Time to replace 1 hour 0.7 hours

Cost of repair (materials cost) $500 $350 Fraction of repairs requiring

replacement of the LRU (as opposed to repair of the

LRU)

1.0 0.7


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5.5.1 Single Socket Model Results

Figure 5.4 shows the fixed scheduled maintenance interval results. 10,000 sockets were simulated in a Monte Carlo analysis and the mean life cycle costs were plotted. The general characteristics in Figure 5.4 are intuitive: for short scheduled maintenance intervals, virtually no expensive unscheduled maintenance occurs, but the life cycle cost per unit is high because large amounts of RUL in the LRUs are thrown away. For long scheduled maintenance intervals virtually every LRU instance in a socket fails prior to the scheduled maintenance activity and the life cycle cost per unit becomes equivalent to unscheduled maintenance. For some scheduled maintenance interval between the extremes, the life cycle cost per unit is minimized. If the TTF distribution for the LRU had a width of zero, then the optimum fixed scheduled maintenance interval would be exactly equal to the forecasted TTF. As the forecasted TTF distribution for the LRU becomes wider (i.e., the forecast is less well defined), a practical fixed scheduled maintenance interval becomes more difficult to find and the best solution approaches an unscheduled maintenance model.

Figure 5.5 shows example results for various widths of the LRU TTF distribution as a function of the safety margin and prognostic distances associated with the precursor to failure and LRU-independent models. Several general trends are apparent. First, the width of the LRU TTF distribution has little effect on the precursor to failure PHM method results. This result is intuitive in that the precursor to failure case the PHM structures are coupled to the LRU instances and track whatever manufacturing or material variation they have, thereby also reflecting the LRU TTF distribution. The degree to which the LRU-to-LRU variations are removed from the problem depends on the degree of coupling between the LRU manufacturing and materials and the PHM structure manufacturing and materials. Alternatively, the LRU-independent PHM method is sensitive to the LRU TTF distribution

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Figure 5.4: Variation of the effective life cycle cost per socket with the fixed scheduled maintenance interval (10,000 sockets simulated with no random failures

assumed).


width because it is uncoupled from the specific LRU instance and can only base its forecast of failure on the performance of a nominal LRU. A second observation is that the optimum safety margin decreases as the width of the LRU TTF distribution decreases. This is also

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Figure 5.5: Variation of the effective life cycle cost per socket with the safety

margin and prognostic distance for various LRU TTF distribution widths and constant PHM structure TTF width (10,000 sockets simulated)

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Figure 5.6: Variation of the effective life cycle cost per socket with the safety margin and prognostic distance for various PHM structure TTF and constant

LRU TTF distribution widths (10,000 sockets simulated).


20

intuitive because as the reliability becomes more predictable (i.e., a narrower forecasted LRU TTF distribution width), the safety margin that needs to be applied to the PHM predictions also drops. Figure 5.6 shows example results for various widths of the PHM associated distribution (constant LRU TTF distribution width) as a function of the safety margin and prognostic distances associated with the precursor to failure and LRU-independent models. In this case, both PHM approaches are sensitive to the width of their distributions.

General observations from Figures 5.5 and 5.6 are that 1) the LRU-independent model is highly dependent on the LRU’s TTF distribution, while 2) precursor to failure methods are approximately independent of the LRU’s TTF distribution. With all other factors being equal (ceteris paribus), 3) optimal prognostic distances for precursor methods are always smaller than optimal safety margins for LRU-independent methods, and therefore, precursor to failure PHM methods will always result in lower life cycle cost solutions than LRU-independent methods. The assumption in 3) is that equivalency is maintained between the LRUs and between the shapes and sizes of the distribution associated with the PHM approach. Any comparison between the precursor to failure approach and the LRU-independent approach should be performed with the assumption that both are possible choices, i.e., that there is a precursor to failure method that is applicable — there may not be (especially for application to electronic systems). An example business case construction for the single socket case is given in Section 5.5.3.

Figure 5.7 shows an example with a random failure rate of 10% included in the simulation. Figure 5.7 also includes the associated failures avoided. In all cases the failures avoided when random failures are included is lower than when random failures are not included, however, the change in the optimum safety margin or prognostic distance is small. As the safety margin or prognostic distance increase the failures avoided limits to 100% in all cases (with and without random failures included). However, for the example data used in this paper, safety margins or prognostic distances must be increased substantially beyond the range plotted in Figure 5.7 for the cases with random failures to approach 100%.

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Figure 5.7: Variation of the effective life cycle cost per socket and failures avoided,

with the safety margin and prognostic distance for 2000 hour LRU TTF distribution widths and 1000 hour PHM distribution widths, with and without

random failures included (10,000 sockets simulated).


5.5.2 Multiple Socket Model Results

Typical systems are composed of multiple sockets, where the sockets are occupied by a mixture of LRUs, some with no PHM structures or strategies, and others with fixed interval strategies, precursor to failure structures or LRU independent structures. Maintenance, even when it is scheduled, is expensive. Therefore, when the system is removed from service to perform a maintenance activity for one socket it may be desirable to address multiple sockets (even if some have not reached their most desirable individual maintenance point).

First, we address how to use the single socket models developed in Section 5.4 to optimize a system composed of multiple sockets, where we are assuming that all the LRUs that occupy a particular socket have the same PHM approach (but approaches can vary from socket to socket). To address this problem we introduce the concept of a coincident time. The coincident time is the time interval within which different sockets should be treated by the same maintenance action. If

action emaintenanc currenti LRU on actionemaintenanc requiredcoincident Time-TimeTime > (7) then the LRU i is addressed at the current maintenance action. A coincident time of 0 signifies that each socket is treated independently. A coincident time of infinity signifies that whenever any LRU in any socket in the system demands to be maintained, all sockets are maintained regardless of their remaining life expectancies. In the discrete event simulation, the time of the current maintenance and the future times for the required maintenance actions on other LRUs are known or forecasted and application-specific optimum coincident times can be found.

Implementation of the above constraint in the discrete event simulation is identical to the single socket simulation except we follow more than one socket at a time (see Section 5.4.6 and [35]). When the first LRU in the multiple socket system indicates that it needs to be maintained by RUL forecast or actually does fail, a maintenance activity is performed on all sockets in which the LRUs forecast the need for maintenance within a user specified coincident time, e.g., Figure 5.8. The model assumes that LRUs replaced at a maintenance

Socket 2 Timeline

CumulativeTimeline LR

U in socket 1 and

LRU

in socket 2 replaced

< Coincident time

LRU instance-specific “fix me” requests originating from failures, scheduled maintenance intervals, or PHM structures

> Coincident time

LRU

in socket 2 replaced

< Coincident time

Etc… to end of support

Socket 1 Timeline

LRU

in socket 1 and LR

U in socket 2

replaced

Figure 5.8: Multi-socket timeline example.


22

event are good-as-new and that portions of the system where damage occurred that was not addressed by any maintenance are not otherwise affected by the maintenance event. Costs are accumulated for scheduled and unscheduled maintenance activities and a final total life cycle cost computed. In practice, the future maintenance actions times for LRUs, other than the one indicating the need for maintenance, need to be determined from reliability forecasting. However, there is greater uncertainty in these forecasts as the time distance increases.

Analysis of multi-socket systems demonstrates that three types of system responses are possible for three types of systems: dissimilar LRUs, similar LRUs, and mixed systems of LRUs for which optimization can be performed. Consider systems built from the two different sockets shown in Figure 5.9. For the examples in this section, with the exception of the LRU TTF distribution, all the data is given in Table 5.3. With LRU TTFs defined as shown in Figure 5.9, a system composed of sockets #1 and #2 is considered to be dissimilar (LRUs with substantially different reliabilities and different PHM approaches). The first step in analyzing a multi-socket system is to determine what prognostic distance/safety margins to use for the individual sockets – we have observed no differences between the optimum prognostic distance/safety margins determined analyzing individual sockets or the sockets within larger systems. For the case shown in Figure 5.9, the optimum prognostic distance for the LRU in socket #1 was 500 hours.

Figures 5.10-5.12 display plots of the mean life cycle cost for a system of sockets. The mean life cycle cost is the mean of a distribution of life cycle costs computed for a population of 10,000 systems. Figure 5.10 shows the most common life cycle cost characteristic for dissimilar systems. For small coincident times, both sockets are being maintained separately, for large coincident times, LRUs in both sockets are replaced whenever either socket requires maintenance. It follows that mean life cycle costs are smaller for dissimilar systems when coincident times are small.

Figure 5.11 shows the cases of two and three similar LRUs in a system. In this case, the multiple sockets that make up the system are all populated with LRU #1 in Figure 5.9. The solution in this case is favorable to maintaining the LRUs in all the sockets at the same time, i.e., when the LRU in one socket indicates that it needs to be maintained, the LRUs in

TTF distribution for LRUs in Socket #1

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Socket #2 LRUs with Unscheduled Maintenance

Socket #1 LRUswith Health MonitoringC

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Time to FailureTime to Failure

Figure 5.9: Time to failure (TTF) distributions for LRUs used in multi-socket analysis examples. The plot on the right shows the cost of single socket systems

made from these two LRUs as a function of time using a prognostic distance of 500 hours for the LRU in socket #1 (note, the results for 10,000 instance of each socket

are shown). All data other than the LRU TTF is given in Table 5.3.


all the sockets are maintained. Note that the height of the step depends on the number of hours to perform scheduled maintenance and the cost of those hours.

Figure 5.12 shows the results for a mixed system that has a non-trivial optimum in the coincident time. In this case there is a clear minimum in the mean life cycle cost that is neither at zero nor infinity.

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Socket #1 LRU, location parameter = 19900 hours (health monitoring); socket #2 LRU, FFOP = 9900 hours (unscheduled maintenance); 10,000 systems simulated.

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Figure 5.11: Mean life cycle cost per system of two or three similar sockets

All LRUs, location parameter = 19900 hours (health monitoring); 10,000 systems simulated.


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5.5.3 Example Business Case Construction

Commitments to implement and support PHM approaches cannot be made without the development of a supporting business case justifying it to acquisition decision makers. One important attribute of most business cases is the development of an economic justification. The economic justification of PHM has been previously discussed, e.g., [41, 42]. These previous business case discussions provide useful insight into the issues influencing the implementation, management, and return associated with PHM and present some application-specific results, but do not approach the problem from a simulation or stochastic view. The following example presents an application of the discrete event simulation model to contribute to business case development. The objective of this example is to determine what the cost of implementing a PHM structure has to be in order for it to be viable from a life cycle cost viewpoint. Consider a single socket containing instances of an LRU characterized by the TTF distribution shown in Figure 5.13.

The sockets that are occupied by instances of this LRU experience a range (distribution) of environmental stress profiles. Figure 5.13 shows a fixed maintenance interval analysis performed using the process described in Section 5.4.6. We will use the best fixed interval maintenance solution as the metric that the PHM approaches must achieve.

The second step in the business case construction is shown in Figure 5.14. In Figure 5.14 we show four example PHM approaches, two with a precursor to failure approach (costing either $0 or $1000 per LRU instance to implement) and two with a LRU independent approach (again, costing either $0 or $1000 per LRU instance to implement). The right side of Figure 5.14 also generalizes the result by considering a continuum of PHM implementation costs and plotting the minimum life cycle cost solution corresponding to

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Figure 5.12: Mean life cycle cost per system of mixed sockets (10,000 systems simulated).


each one. Figure 5.14 also shows the life cycle cost of the best fixed interval maintenance solutions for the ±5000 hour triangularly distributed environmental stress distribution case from Figure 5.13. The intersection of the fixed interval maintenance line and the precursor

+

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Figure 5.13: Single-socket timeline example. This result indicates that the mean unscheduled maintenance cost per socket is $61,696 with 10,000 sockets simulated.

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Figure 5.14: The effective life cycle cost associated with precursor to failure and LRU independent PHM approaches. The left plot shows PHM approaches that cost either $0 or

$1000 per LRU instance to implement. Note, from Table 5.3, $1000/LRU = 10% of the LRU’s recurring cost. The right plot shows a generalization of the left plot in which only the lowest life cycle cost solutions are plotted. The small arrows indicate points on the left

plot that are mapped to (in common with) points on the right plot. (10,000 sockets simulated).


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to failure and LRU independent lines in the graph on the right side of Figure 5.14 tells us what we can spend on the PHM approaches. The precursor to failure method is economically practical if it can be implemented for < $730 per LRU (7.3% of recurring LRU cost); LRU independent methods are practical if they can be implemented for < $400 per LRU (4% of recurring LRU cost). It should be stressed that these are application-specific results.

5.6 Summary

PHM can be used within the maintenance decision-making process to provide failure predictions, to lower sustainment costs by reducing the costs of downtime, for inspection, for inventory management, to lengthen the intervals between maintenance actions, and to increase the operational availability of systems. PHM can be used in the product design and development process to gather usage information and to provide feedback for future generations of products.

The potential benefits of prognostics are significant for the military and commercial sectors; the U.S. Air Force estimates that successful health monitoring of the Minuteman III strategic missile fleet could cut its life cycle costs in half [43]. Proponents of PHM have prophesied that its success may one day obviate the need for redundant components in systems, but the transition to a full PHM approach will require extensive validation and verification before that can happen.

To determine the ROI requires an analysis of the cost-contributing activities needed to implement PHM and a comparison of the costs of maintenance actions with and without PHM. Analysis of the uncertainties in the PHM ROI calculation is necessary for developing realistic business cases. Allowance for variability in cadence, false alarm, and random failure rates, and system size enables a more comprehensive calculation of ROI to support acquisition decision making.

5.7 References 1. Friedlob, G. T., Plewa, F. J., Jr., Understanding Return on Investment, John Wiley and

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Computer-Aided Civil and Infrastructure Engineering, 2001, Vol. 16, pp. 71-78. 3. Sandborn, P.A., Course Notes on Manufacturing and Life Cycle Cost Analysis of

Electronic Systems, CALCE EPSC Press, College Park, MD, 2005. 4. Spare, J. H., “Building the Business Case for Condition-Based Maintenance,”

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5. Goodman, D. L., Wood, S., Turner, A. “Return-on-investment (ROI) for Electronic Prognostics in Mil/Aero Systems,” Proceedings of the IEEE Autotestcon, Orlando, FL, pp. 1-3, September 2005.

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17. Byer, B., Hess, A., Fila, L., “Writing a Convincing Cost Benefit Analysis to Substantiate Autonomic Logistics,” Proceedings of the IEEE Aerospace Conference, Big Sky, MT, Vol. 6, pp. 3095-3103, March 2001.

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19. Keller, K., Simon, K., Stevens, E., Jensen, C., Smith, R., Hooks, D., “A Process and Tool for Determining the Cost/Benefit of Prognostic Applications,” Proceedings of the IEEE Autotestcon, Valley Forge, PA, pp. 532-544, August 2001.

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22. Jones, T. C., Estimating Software Costs, McGraw-Hill, New York, 1998. 23. Patankar, M. S., Taylor, J. C., Risk Management and Error Reduction in Aviation

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25. Gopalan, R., Talluri, K. T., “The Aircraft Maintenance Routing Problem,” Operations Research, 1998, Vol. 46, No. 2, pp. 260-271.

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33. Barros, A., Berenguer, C., Grall, A., “Optimization of Replacement Times Using Imperfect Monitoring Information,” IEEE Transactions on Reliability, 2003, Vol. 52, No. 4, pp. 523-533.

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36. Raivio, T., Kuumola, E., Mattila, V. A., Virtanen, K., Hämäläinen, R. P., “A Simulation Model for Military Aircraft Maintenance and Availability,” Proceedings of the European Simulation Multiconference, pp. 190-194, September 2001.

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43. Ruderman, G., “Health management issues and strategy for Air Force missiles,” Proceedings of the Fifth International Workshop on Structural Health Monitoring, Stanford, CA, September 2005.

Documents

This chapter is from: P. Sandborn and K. Feldman ...escml.umd.edu/Papers/WileyPHMBook-Sandborn.pdforganization is managed. In regards to specific organizational objectives such as