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    Production, Manufacturing and Logistics

    A study of repairable parts inventory system operating under

    performance-based contract

    H. Mirzahosseinian ⇑, R. Piplani

    Centre for Supply Chain Management, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore

    a r t i c l e i n f o

     Article history:

    Received 20 July 2010

    Accepted 27 April 2011

    Available online 4 May 2011

    Keywords:

    Logistics

    Base stock

    Component reliability

    Repair facility

    a b s t r a c t

    Performance-Based Logistics (PBL) is becoming a dominant logistics support strategy, especially in the

    defense industry. PBL contracts are designed to serve the customer’s key performance measures, while

    the traditional contracts for after-sales services, such as Fixed-price (FP) and Cost-plus (C+), only provide

    insurance or incentive. In this research, we develop an inventory model for a repairable parts system

    operating under a PBL contract. We model the closed-loop inventory system as an  M/M/m queue in which

    component failures are Poisson distributed and the repair times at the service facility are exponential.

    Our model provides the supplier and the customer increased flexibility in achieving target availability.

    Analysis of key parameters suggests that to improve the availability of the system with repairable spare

    parts, the supplier should work to improve the components reliability and efficiency of repair facility,

    rather than the base stock level, which has minimal impact on system availability.

     2011 Elsevier B.V. All rights reserved.

    1. Introduction

    The after-sales parts and services have become a key source of 

    revenue for firms selling capital goods. An Accenture (2003) study

    of General Motor indicated that $9 billion in after-sale revenue

    added $2 billion to profits whereas profits from the company’s

    $150 billion in car sales were relatively lower (Dennis and Kambil,

    2003). As further evidence, in 2001, IBM derived over $5 billion of 

    its revenue from maintenance and service (Cohen et al., 2006). This

    is especially so as over the life cycle of most systems, it has been

    estimated that about 30% of all dollars spent are used to acquire

    the system, while the remaining 70% are spent for support (Berko-

    witz et al., 2005).

    During the past few years, the after-sales contracts for servicing

    capital-intensive goods in both commercial and military fields

    (e.g., General Electric, Lockheed Martin, Rolls-Royce and Boeing)

    have become performance-based. ‘‘Performance-Based Logistics

    (PBL) is the purchase of support as an integrated, affordable, per-

    formance package designed to optimize system readiness and

    meet performance goals for a weapon system through long-term

    support arrangements with clear lines of authority and responsibil-

    ity’’ (Defense Acquisition University, 2004).

    While the traditional after-sales contracts in capital-intensive

    industries, such as Fixed-price and Cost-plus, are based on buying

    spare parts, repair action, equipment, transactional goods or

    services, the Performance-Based Logistics contracts focus on buy-

    ing the outcome performance. For example under PBL, mainte-nance and servicing of the engine is not paid according to the

    spare parts used, repairs or activities, but by how many hours

    the customer obtains power from the engine (Ng et al., 2009). Un-

    der PBL the supplier has more flexibility as the customer only spec-

    ifies the requirements, not the means of achieving it. On the other

    hand the customer can obtain the best performance by reimburs-

    ing the supplier based on the real outcome. Also, the PBL enhances

    the supplier’s ability by shifting his responsibility to control the

    service elements, such as packaging, handling, storage, transporta-

    tion and warehousing, required to successfully support the system.

    Application of Performance-Based Logistics may be at the sys-

    tem, subsystem, or major assembly level, depending upon the pro-

    gram’s unique circumstances and appropriate business case

    analysis (Defense Acquisition University, 2004). One of the earliest

    PBL implementation dates back to 1998 when Lockheed Martin of-

    fered a system to DoD for supporting F-117 Nighthawk, which tied

    its compensation to the fighter’s performance outcome. While

    there were about 100 acquisition programs supported by PBL be-

    fore October 2005 (Phillips, 2005), this number increased to more

    than 200 PBL contracts in place across the DoD by July 2006 (Geary,

    2006).

    Devries (2004)   studied the relationship between successful

    implementation of PBL and the barriers and enablers to its imple-

    mentation. A survey was conducted to collect data from 26 PBL 

    managers from different industries. Findings indicated that perfor-

    mance, metrics and incentives were the most frequent enablers of 

    PBL and enhancing them can lead to its successful implementation.

    0377-2217/$ - see front matter   2011 Elsevier B.V. All rights reserved.doi:10.1016/j.ejor.2011.04.035

    ⇑ Corresponding author. Tel.: +65 8374 1015; fax: +65 6792 4062.

    E-mail address:  [email protected] (H. Mirzahosseinian).

    European Journal of Operational Research 214 (2011) 256–261

    Contents lists available at  ScienceDirect

    European Journal of Operational Research

    j o u r n a l h o m e p a g e :   w w w . e l s e v i e r . c o m / l o c a t e / e j o r

    http://dx.doi.org/10.1016/j.ejor.2011.04.035mailto:[email protected]://dx.doi.org/10.1016/j.ejor.2011.04.035http://www.sciencedirect.com/science/journal/03772217http://www.elsevier.com/locate/ejorhttp://www.elsevier.com/locate/ejorhttp://www.sciencedirect.com/science/journal/03772217http://dx.doi.org/10.1016/j.ejor.2011.04.035mailto:[email protected]://dx.doi.org/10.1016/j.ejor.2011.04.035

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    Performance, the key goal of PBL, should be defined in terms of the

    system objectives such as operational availability. Metrics are the

    heart of PBL as the performance is linked to the metrics specified

    in the contract. Incentives (monetary/non-monetary, positive/neg-

    ative), on the other hand, motivate the suppliers to meet the cus-

    tomer performance objectives.

    Availability, one of the key performance criteria in defense PBL 

    contracts, enables mission capability (Wynne, 2004) and can be af-fected by various factors such as reliability, response time and

    logistics footprint (e.g. inventory). Controlling these factors and

    their relationship with availability is vital for the supplier to meet

    the performance level that satisfies the customer goals. The cus-

    tomer also needs effective metrics to monitor the supplier’s perfor-

    mance during the contract period and ensure PBL’s success.

    Against this backdrop, the following questions become impor-

    tant in the successful implementation of a PBL contract: How do

    inventory management, component reliability and repair facility

    efficiency influence the availability of systems under the PBL con-

    tract? How can customers monitor the supplier’s performance and

    ensure that the supplier provides the desired performance level?

    In this article, we model the PBL system as a queuing network

    by enhancing the classical repairable parts inventory model. Our

    model improves upon the classical model by relaxing some restric-

    tive assumptions, such as fixed failure rate, fixed repair rate and

    infinite capacity at repair facility. Our model focuses on the inter-

    action between inventory management, component reliability and

    repair facility efficiency. The model is then analyzed to determine

    the factors that have significant impact on the system availability.

    The results show that the base stock level of the spare parts has

    negligible effect on the system availability. Thus, to achieve a de-

    sired availability level, the supplier has to improve the component

    reliability and the repair time, rather than invest in building up a

    stock of spares. In addition, we formulate two metrics that allow

    the customer to monitor the key parameters affecting system

    availability.

    The rest of the paper is organized as follows: Section 2 discusses

    the relevant literature in repairable parts inventory and its applica-tion in the PBL contract. In Section 3 we present the structure of 

    the inventory system, and in Section 4 the Markov model of the

    system. The system metrics and the performance are discussed in

    Section 5. Section 6  presents the numerical study, followed by the

    parametric analysis in Section   7. Section  8   rounds off the paper

    with conclusions and future research directions.

    2. Literature review

    Our model represents an enriched repairable parts inventory

    management model operating under a PBL contract. Over the last

    40+ years, researchers have developed many models in repairable

    parts inventory. METRIC, as the first practical model in this area, isa mathematical model of a base-depot supply system with com-

    pound Poisson demand, which specifies stock levels at bases and

    depot to optimize system performance (Sherbrooke, 1968). Sher-

    brooke (1968)   used one-for-one replenishment inventory policy

    and modeled the system based on the mean repair time rather than

    its distribution. Muckstadt (1973) extends the METRIC model, call-

    ing it MOD-METRIC, to control a multi-item, multi-echelon, multi-

    indenture inventory system for repairable items. The model is used

    to compute the base stock levels of different echelons by consider-

    ing the logistical relationship between shop replaceable unit and

    line replacement unit. MOD-METRIC model was been implemented

    by Air Force to support the F-15 weapon system.   Sherbrooke

    (1986)  later developed a VARI-METRIC model which focused on

    the expected backorders. He changed the METRIC model fromfirst-order to second-order by incorporating variances of repair

    items. Simulation showed that the VARI-METRIC provides a more

    accurate estimate of the expected backorders. These three models

    are the fundamental models of repairable spare parts inventory

    systems. Many researchers later enhanced these models by relax-

    ing one or more of the assumptions.

    Gross et al. (1985)   describe a multi-echelon repairable-item

    inventory system using a closed-network queue. They consider a

    limited number of simultaneous repair channels and determinethe optimal combination of the number of spares and repair chan-

    nels to deliver service-level performance.   Gupta and Albright

    (1992)   model a two-echelon multi-indentured repairable item

    inventory system in which there exist similar machines at each

    base and each machine consists of several module types. They used

    Markovian approach to calculate the steady-state operating char-

    acteristics of the system.

    Dhakar et al. (1994) focus on the stocking levels of repairable

    spares from the point of view of cost and production scheduling.

    They develop a realistic model by considering the failure rate as

    a function of the number of machines in operation and determine

    the optimal stocking levels for expensive, low demand and critical

    repairable spares. Diaz and Fu (1997) relax the assumption of am-

    ple repair capacity in inventory model of repairable items and

    introduce an approximation to deal with limited repair capacity.

    They also conduct numerical experiments to show their model’s

    superiority against traditional models when faced with high repair

    facility utilization.   Wang et al. (2000)   consider a two-echelon

    repairable inventory system consisting of a central depot and mul-

    tiple stocking centers where depot replenishment lead times are

    independent. Sleptchenko et al. (2003) analyze the trade-off be-

    tween inventory levels and the number of servers at repair facili-

    ties in multi-echelon, multi-indentured service part supply

    systems. Lau and Song (2004)  study a repairable item inventory

    system under limited repair capacity and non-stationary Poisson

    demands to minimize the cost of the system. Wong et al. (2005)

    develop an analytical model to determine the spare stocking levels

    in a single-item, multi-hub, multi-company repairable inventory

    system. The model minimizes the total system cost consisting of holding, downtime and transshipment costs. Tao and Wen (2009)

    model a closed loop, multi-echelon repairable inventory system

    to evaluate the effect of repair capacity on expected backorders,

    and optimize spares location. Their results illustrate their model’s

    superiority over METRIC.

    In recent years, researchers have also studied the repairable

    spare parts inventory system under PBL contract.  Kang et al.

    (2005) find that many PBL contracts concentrate on the contractual

    agreement for improving component level performance goal, while

    what really matters is the total system operational availability.

    They develop a methodology to calculate the system operational

    availability based on the component-level reliability and maintain-

    ability data. They find that the time- between- failure, the spare

    inventory and the time- to- repair are three key metrics whichhave higher impact on the availability of the system. In a follow-

    up paper, Kang et al. (2006) extend a simulation model to consider

    both ‘‘availability’’ (the average percentage of assets that are avail-

    able for operations) and ‘‘readiness risk’’ (the probability that a

    vendor will fail to deliver a desired threshold of operational avail-

    ability) as two key measures of performance. This approach intro-

    duces the most effective alternative for increasing the availability

    and reducing readiness risk of the system simultaneously. Their re-

    sults show that the readiness risk is affected by failure rate and

    logistics delay.

    Kim et al. (2007a) study N  identical systems where each system

    consists of  n   subsystems. The customer contracts with individual

    suppliers who maintain the inventory and repair facilities to sup-

    port each of the subsystems. They assume a fixed failure rate foreach subsystem and a fixed repair lead time at the repair facility.

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    For compensation, the customer pays a part of the supplier’s hold-

    ing cost, which can be reduced by the supplier’s efforts, and penal-

    izes the supplier depending upon the number of backorders. To

    prevent a backorder, the supplier may resort to higher inventory

    holding, which may not be optimal for the customer. To close this

    gap, Kim et al. (2007b) focus on the tradeoff between spare asset

    management and investment into product reliability, by consider-

    ing a variable failure rate. They find that the spare asset ownershipplays a key role in achieving a good balance between inventory and

    reliability levels.

    Nowicki et al. (2008) test three kinds of contracts (linear, expo-

    nential and step) in a multi-echelon, multi-item supply chain to

    show the significant impact the revenue function has on the inven-

    tory level, availability and total profit. Finally, Oner et al. (2010) fo-

    cus on the reliability level of a critical component during the design

    phase and demonstrate that the value of components, number of 

    systems, downtime penalty rate and length of exploitation phase

    influence the reliability of the component.

    While most of the earlier models in the literature aim to find

    optimal (cost minimizing) base stock subject to satisfying a speci-

    fied service level using a centralized approach, PBL considers the

    system in a decentralized framework to satisfy both the customer

    and the supplier’s requirements, simultaneously. Recently some

    studies have been done to close this gap (Kang et al., 2006; Kim

    et al., 2007a,b; Nowicki et al., 2008; Oner et al., 2010), but their

    models still have restrictive assumptions which decrease the sup-

    plier’s flexibility and may give indication of unrealistic perfor-

    mance to the customers. Firstly, they ignore the dependency of 

    subsystem failure rate to the number of operational units in a

    closed-loop system. Secondly, they do not consider the influence

    the supplier’s effort may have on component reliability and effi-

    ciency of the repair facility. PBL should empower the provider with

    the authority and responsibility to control those elements required

    to successfully support the program (NAVAIRINST 4081.2A, 2004).

    Relaxing these assumptions, thus, offers an opportunity to develop

    a robust model which may influence the contractual elements,

    especially metric formulation.Our research incorporates two major innovations. Firstly, we re-

    lax three restrictive assumptions of previous repairable spare parts

    inventory models under PBL, such as fixed failure rate, fixed repair

    rate and infinite repair facility capacity, and model it using queuing

    theory. Secondly, we formulate two effective metrics which allow

    the customer to monitor the supplier’s performance during the

    execution of the PBL contract. This allows both the parties to en-

    sure that the delivered performance at the end of the contract

    meets or exceeds the target.

    3. Repairable parts inventory system

    We consider a closed-loop inventory system consisting of a re-pair facility and a single warehouse, to support the customer sys-

    tems under a PBL contract, similar to the one used in Gross et al.

    (1985), Dhakar et al. (1994) and Kim et al. (2007a). Each system

    (such as an air vehicle) consists of several major repairable compo-

    nents (e.g. engine, avionics, weapon system). For simplicity, we

    model the system with one supplier who supports one specific

    repairable component for N   identical systems. The inventory sys-

    tem is illustrated in Fig. 1.

    We assume that a component’s failure follows an independent

    Poisson distribution with constant rate (k); the airline industry

    data supports the validity of this assumption (Timmers, 1999).

    Based on this assumption, the component failure distribution in a

    closed-loop system with N  systems follows a Poisson process with

    the variable rate   k( z ), where   z   is the number of operational sys-tems. We model the repair facility as an  M/M/m queue. The repair

    lead time of each server in the repair facility, which consists of the

    repair time and transportation delay, is assumed to be an indepen-

    dent exponential random variable with mean (l)1. This assump-tion is common in the literature (Wong et al., 2005);  Alfredsson

    and Verrijdt (1999) also show that the performance of the inven-

    tory system is insensitive to lead-time distribution. The time be-

    tween replacement of components from repair facility to the

    warehouse follows Exponential distribution with the variable rate-

    l( y, m), which is a function of the number of components in repair

    facility ( y) and the number of servers (m).A one-for-one base stock (S ) replenishment policy is followed at

    the warehouse. As per this policy, a failed component is immedi-

    ately replaced by a ready-to-use component (new or refurbished)

    from the warehouse and the failed one is sent to the repair facility.

    A backorder takes place when the warehouse is out of stock. The

    warehouse triggers a replenishment order immediately and the

    information lead time is assumed to be zero.

    The inventory level in the warehouse is represented by ‘ x’,

    which can change from  N  to  S  (N 6 x 6 S ), with negative value

    of ‘ x’ representing the number of backorders. The relationship be-

    tween inventory level ( x), on-order inventory ( y) (the number of 

    components at the repair facility) and the number of operating sys-

    tems ( z ) is formulated in Eq. (1).

     z  ¼   N    if   xP 0;N  þ x   otherwise;

      y ¼  S   x   for    N 6  x 6 S    ð1Þ

    The component failure rate and the component replacement rate in

    the system can be computed as follows:

    kð z Þ ¼  z k   for 0 6  z 6 N ;   lð y; mÞ ¼ ½Minð y; mÞl

    for 0 6  y 6 S  þ N    ð2Þ

    4. The Markov model

    Based on the above assumptions, the corresponding Markov

    model is developed representing the state space ( x). There are

    two events that change the state of the system: (1) a component

    fails and the supplier replaces the failed component with aready-to-use one from the warehouse (sending the failed compo-

    nent to the repair facility); (2) a repaired component arrives at

    the warehouse from the repair system. The transition diagram of 

    the system is shown in Fig. 2.

    Let p x be the steady-state probability of inventory level ‘ x’ at thewarehouse. The flow balance equations are laid out next in follow-

    ing equation.

    p x   z k þ ½Minð y; mÞlð Þ ¼ ðDÞ p x1ð½Minð y þ 1; mÞlÞ þ ðF Þ

    p xþ1ð½Minð z  þ 1; N ÞkÞ

    for  N 6  x 6 S    ð3Þ

    D ¼

      1 if     N  þ 1 6  x 6 S 

    0 otherwise

      F  ¼

      1 if     N 6  x 6 S   1

    0 otherwise

     ( z)

     µ ( y , m) Repair FacilityWarehouse

    S ......

    Systems

    Fig. 1.  Closed-loop inventory system.

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    The left side of Eq. (3) represents the average rate of transition

    out of state ( x). The terms inside the parenthesis indicate the tran-

    sition due to a failed component, which depends on the number of 

    working systems ( z ), and the replenishment rate from repair facil-

    ity to the warehouse, which itself is a function of the on-order

    inventory ( y) and the number of servers at the repair facility (m).

    The right side of Eq. (3) represents the average rate of transition

    into state ( x). The terms determine the rate at which the replenish-

    ment components arrive at the warehouse and the transition to

    satisfy the demand when a component fails, respectively. Binary

    variables D  and  F   denote whether the number of backorders is  N 

    and the inventory level at the warehouse is   S , respectively. We

    solve the balance Eq.   (3)   and the normalizing constraint   (4)   to

    determine p x.

    XS  x¼N 

    p x ¼  1   ð4Þ

    5. System performance and the metrics

    The supplier can improve the system performance (e.g. theavailability of the system) by managing three parameters: (1) base

    stock level at the warehouse, (2) component reliability, and (3) effi-

    ciency of the repair facility. We model the last two metrics in Eq.

    (5).

    MTBF  ¼  E ½1=kð z Þ   0 6  z 6 N ;

    MTTRe ¼  E ½1=lð y; mÞ   0 6  y 6 S  þ N    ð5Þ

    The first term of Eq.  (5)  represents the  Mean Time between Fail-

    ures   and the second one represents the   Mean Time to Replace.

    The  MTBF  and  MTTRe  are represented as a function of the steady-

    state probabilities next.

    MTBF  ¼ XS 

     x¼0

    ½1=kðN Þp x þ X1

     x¼N 

    ½1=kðN  þ xÞp x;

    MTTRe ¼XS 

     x¼N 

    ½1=lðMin m; ðS   xÞf gÞp x   ð6Þ

    Given the steady-state probabilities, the average number of backor-

    ders can be computed as follows:

    E ðBÞ ¼X1

     x¼N 

     xp x

    ð7Þ

    We use the operational availability to measure the performance

    of the system. Following  Kim et al. (2007a), and assuming each

    backordered component results in an un-operational system we

    define the availability of the entire set of systems as:

     A ¼  1  E ðBÞ=N    ð8Þ

    6. Numerical study 

    An Unmanned Aerial Vehicle (UAV) system consists of four air

    vehicles (AV’s), two ground-control stations (GCSs), modular mis-

    sion payloads (MMPs), data links, remote data terminals (RDTs)

    and an automatic landing system. The AV flying hours are esti-

    mated at 120 h per month, per vehicle. We consider the critical

    components of AV (engine, propeller, avionics computer) to sup-

    port 10 UAV systems with 40 air vehicles for one year (Kang

    et al., 2005). The parameters of the system are tabulated in Table 1.

    As mentioned earlier, the repair lead time of each server (l)1

    includes the repair time and the transportation delay. For example,

    when an engine fails, it incurs 4.5 days (2.25 days each way) of 

    transportation delay, along with 15 h of repair time, on average.

    Similarly, the repair lead time calculations of propeller and avion-

    ics computer are shown in  Table 1. The mean time between fail-

    ures of an engine, propeller and avionics computer is expected to

    be 750, 500 and 1000 h, respectively. By considering the AV flying

    hours per year (12 120), the annual failure rate of each engine,

    propeller and avionics computer is 1.92(1440/750), 2.88 (1440/

    500) and 1.44(1440/1000), respectively.

    Above example is modeled by the proposed queuing model

    (Eqs. (3)–(8)) which is then coded in MATLAB software. The result-

    ing metrics (MTBF ,   MTTRe) and the performance of the system

    (Availability) are shown in Table 2.

    7. Parametric analysis

    We conduct a parametric analysis to study the effect of varying

    component failure rate, server repair rate, number of servers and

    the base stock level on the availability of the air vehicles. The min-

    imum and maximum possible values of parameters of the compo-

    nents are tabulated in Table 3.

    Figs. 3–6 illustrate the computational results of the analysis. We

    used different values of the parameters, which range from mini-mum to maximum values with steps of 100, 15, 1 and 2 for mean

    time between failure, mean time to repair, number of servers and

    the base stock level, respectively.

    As can be seen in  Figs. 3, 5 and 6   decreasing the failure rate,

    increasing the server repair rate and the number of servers in-

    creases the availability of all the components. Fig. 4 indicates that

    the base stock level of the components has negligible effect on the

    Fig. 2.  The transition diagram of the inventory system.

     Table 1

    Basic parameters of the system.

    Component   k (per year) (l)1 h   S 

    Engine 1.92 123 (=15 + 108) 6

    Propeller 2.88 89 (=5 + 84) 8

    Avionics 1.44 135 (=15 + 120) 4

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    AV’s availability. Thus, for increasing AV’s availability the supplier

    must invest in improving the component reliability and the effi-

    ciency of the repair system rather than increasing the base stock

    level. We define   MTBF   for controlling the component reliabilityand MTTRe for monitoring the efficiency of repair facility. The  MTBF 

    measure based on our model is more accurate than the previous

    models, because it considers the dependency of subsystems failure

    rate to the number of operational units. Also, the proposed model

    measures  MTTRe  instead of  MTTR which considers the repair time

    and transportation delay, simultaneously. It is easier for the cus-

    tomer to monitor the warehouse replacement rate rather thanthe repair rate. This issue becomes more important under PBL con-

    tracts where the supplier may be hesitant in offering detailed

    information such as the facility repair rate during the contract’s

    lifetime.

    8. Conclusions

    In this paper we propose an enriched inventory model for

    repairable spare parts to illustrate the interaction between key

    parameters of such systems under the PBL contract, an increasingly

    popular strategy in the defense industry. Relaxing some unrealistic

    assumptions in the classical repairable spare parts inventory mod-

    els such as fixed failure rate, fixed repair rate and infinite repair

    facility capacity makes the model more robust. In addition, ourmodel provides the appropriate levers to the supplier and the

     Table 2

    System performance and the metrics.

    Component   MTBF MTTRe   Availability

    Engine 130 118.5 0.89

    Propeller 92.3 88.1 0.84

    Avionics 159.5 114.9 0.96

     Table 3

    Parameter range.

    Component (k)1 h (l)1 h   m S 

    Min Max Min Max Min Max Min Max

    Engine 550 950 105 165 1 3 0 12

    Propeller 300 700 70 130 1 3 0 12

    Avionics 800 1200 125 185 1 3 0 12

    50 60 70 80 90 100 110 120

    0.5

    0.55

    0.6

    0.65

    0.7

    0.75

    0.8

    0.85

    0.9

    0.95

    1

    Server Repair Rate (per year)

         A    v    a     i     l    a     b     i     l     i     t    y

     

    Engine

    Propeller 

     Avionics

    Fig. 3.   Impact of repair rate on availability.

    0 2 4 6 8 10 12

    0.5

    0.55

    0.6

    0.65

    0.7

    0.75

    0.8

    0.85

    0.9

    0.95

    1

    Base Stock Level

         A    v    a     i     l    a     b     i     l     i     t    y

     

    Engine

    Propeller 

     Avionics

    Fig. 4.   Impact of base stock on availability.

    1.5 2 2.5 3 3.5 4 4.5

    0.5

    0.55

    0.6

    0.65

    0.7

    0.75

    0.8

    0.85

    0.9

    0.95

    1

    Failure Rate (per year)

         A    v    a     i     l    a     b     i     l     i     t    y

     

    Engine

    Propeller 

     Avionics

    Fig. 5.   Impact of failure rate on availability.

     

    1 2 30.5

    0.55

    0.6

    0.65

    0.7

    0.75

    0.8

    0.85

    0.9

    0.95

    1

    Number of Servers

         A    v    a     i     l    a     b     i     l     i     t    y

     

    Engine

    Propeller 

     Avionics

    Fig. 6.  Impact of server number on availability.

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    customer, as the two main parties in the PBL contract who can

    manipulate them and guide the system availability towards the

    target, which is one of the ultimate goals of defense companies.

    A study of barriers to PBL implementation indicates a lack of 

    effective metrics that allow the customer to monitor the supplier’s

    real performance during the contract’s tenure. We formulated two

    metrics that facilitate monitoring (and control) of the supplier’s ac-

    tual performance. We also evaluated the effect of key parametersthat affect the system availability. The results show that the base

    stock level does not have any significant effect on the availability

    of the system, in comparison to other parameters, such as repair

    rate and failure rate. Furthermore, our model recommends concen-

    trating on the component reliability and repair system efficiency to

    improve the availability of the system with repairable spare parts.

    Optimizing the cost for a repairable inventory system in order to

    find the optimal failure rate, server repair rate and the number of 

    servers is a potential area for future research. Modeling such a sys-

    tem would be easier if the base stock were fixed at a constant va-

    lue, as it does not seem to have an effect on system availability.

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