Worth Fixing: Personalizing Maintenance Alertsfor Optimal Performance

Avraham Shvartzon1, Amos Azaria1, Sarit Kraus1, Claudia V. Goldman2,Joachim Meyer3 and Omer Tsimhoni2

1 Dept. of Computer Science, Bar-Ilan University, Ramat Gan 52900, Israel2 General Motors Advanced Technical Center, Herzliya 46725, Israel

3 Dept. of Industrial Engineering, Tel Aviv University, Ramat Aviv, Tel Aviv 69978,Israel

{shvarta,azariaa1,sarit}@cs.biu.ac.il, claudia.goldman, omer.tsimhoni@gm.com,jmeyer@tau.ac.il

Abstract. Preventive maintenance is essential for the smooth operationof any equipment. Still, people occasionally do not maintain their equip-ment adequately. Alert systems attempt to remind people to performmaintenance. However, most of these systems do not provide alerts atthe optimal timing, and nor do they take into account the time requiredfor maintenance or compute the optimal timing for a specific user. Inthis paper we model the problem of maintenance performance, assumingmaintenance is time consuming. We solve the optimal policy for the user,i.e., the optimal timing for a user to perform maintenance. This optimalstrategy depends on the user’s value of time, and thus it may vary fromuser to user and may change over time. Based on the solved optimalstrategy we present a personalized alert agent, which, depending on theuser’s value of time, alerts the user when she should perform mainte-nance. In an experiment using a spaceship computer game, we show thatreceiving alerts from the personalized alert agent significantly improvesuser performance.

1 Introduction

In our daily life we rely on various types of mechanical equipment and electricaldevices such as our computers, cars or bicycles, smartphones, washing machines,dryers, heating and air conditioning systems and so on. These devices are veryimportant to us, but they tend to malfunction occasionally, which can greatlydisrupt our lives. Most devices come with maintenance instructions, which, iffollowed, aim to decrease the probability and frequency of such malfunctions.Unfortunately, performing maintenance actions is both costly and time consum-ing. Therefore many people fail to perform these maintenance actions in a timelymanner, and consequently they suffer the consequences, when necessary devicessuddenly malfunction (occasionally when they are most needed).

This non-optimal behavior with regards to performing maintenance may beattributed to the following reasons:

1. Procrastination and forgetfulness: People are known to forget and procrasti-nate, especially in regard to tasks for which the consequences are not imme-diately evident [3, 21]. Therefore, when it is time to perform a maintenancetask (according to the user manual), people often either forget or procrasti-nate.

2. Non-optimal suggestions: Occasionally it is not optimal for the user to per-form all maintenance tasks as required by the manual. Performing main-tenance for all devices according to their manual may be tedious and notcost effective. Users may actually benefit, in terms of time and cost, fromperforming maintenance less often than requested by the manual.

3. Non-personalized suggestions: The instructions which appear in manuals arenot personalized and thus do not account for people who have differentvalues of time or different costs associated with performing maintenance andrepairs. Therefore performing maintenance tasks according to the manualmay not be the optimal behavior for a specific user.

In an attempt to increase people’s awareness to perform maintenance, andsolve the problem of procrastination and forgetfulness, many devices includealert systems or reminders to perform maintenance activities. For example, anair conditioning system may turn on a warning light when the filter needs to bereplaced. A car may have similar warning lights, which are set to go on whenan oil change or another periodic treatment is required. There are also softwareprograms which alert users when a computer system has not been backed-up forsome time. Reminders and alerts have been shown to have a positive impact onpeople’s tendency to perform a task [5].

We model the problem of maintenance performance, taking into account thefact that performing maintenance and repairing malfunctions are both wealthand time consuming. Inspired by the Bellman Equation, we solve the optimalpolicy for the user, i.e., the optimal timing for a user to perform maintenance.It is important to note that in order to accurately capture the cost of timeconsuming actions, the model must take into account the value of time for eachuser (or user performance). Therefore, our solution depends on this value of time,and thus the optimal performance time varies from user to user and may changeover time.

In this paper, we present the spaceship game, which allows us to evaluatepeople’s tendency to perform maintenance and repairs. In this game, a playercontrols a spaceship, which shoots asteroids (see Figure 1 for a screen-shot). Theplayer is required to perform maintenance actions on his or her spaceship. Occa-sionally, and depending on the frequency at which the player performs mainte-nance, the spaceship may suffer malfunctions which are repaired at a significantcost.

We present a personalized agent to provide malfunction alerts. This agenttries to overcome the three causes mentioned above for non-optimal human be-havior with respect to taking maintenance actions. Given the user’s performanceso far the agent predicts the user’s expected future performance, and, using ourgeneral solution, the agent identifies the optimal timing for a player to perform

Fig. 1. A screen-shot of the spaceship game in progress.

maintenance. We show in an experiment, that when subjects are presented withpersonalized optimal alerts, they significantly perform better than when theyare presented with non-personalized alerts (which are optimal only for averageperformance) and when they receive no alerts at all. This result may encouragealert systems designers to not only urge users to take maintenance actions, butto do so according to timing which is optimal for each specific user and his orher needs, which may change over time. Such personalized alert systems maysignificantly improve users’ overall performance.

2 Related Work

An empirical study that examined users’ tendency to perform preventive main-tenance actions with or without indications from an alert system that indicatedthe need for intervention was conducted in an abstract laboratory setting [6].The study showed that users do not optimally perform preventive actions, andthat they can be aided by an alert system, especially when the system is reliable.

Many applications exist to help equipment owners maintain equipment. In[9], the author describes several optimization models for maintenance, includingstochastic and deterministic models, which are distinguished by simplicity (witha single component) and complexity. Such an optimization model is deployed by[13]. Their optimal maintenance model is based on the expected lifecycle of agiven equipment, taking into account the costs of production, inspection, etc. A

list of car and house maintenance applications that provide reminders accordingto fixed times and fixed content strategies appears in [14], and a list dedicatedto car maintenance reminders in [8]. However, all the above mentioned applica-tions are not personalized and use the same strategies and same content for allpeople. So far, to the best of our knowledge, no studies exist that discuss andevaluate different reminder strategies for maintenance of cars or other equip-ment. Sherif and Smith [16] provide a review on optimal maintenance models,however, neither of the papers in the review account for the time required toperform maintenance, and thus there is no personalized model.

Many studies on reminder strategies exist in the field of medicine. For exam-ple, a survey by Vervloet et al. [20] examines the effectiveness of interventionsusing electronic reminders in improving patients’ adherence to chronic medica-tion. This review provides evidence for the effectiveness of electronic remindersin improving adherence by patients taking chronic medication. However, theystate that all 13 studies included in their review automatically sent electronicreminders, regardless of whether or not patients took their medication. This in-dicates that these works did not consider even the trivial personalization, of notsending a reminder after the medication was taken. They emphasize that fur-ther research is needed to investigate the influence of the frequency with whichreminders are sent on adherence. Moreover, they strongly recommend real timeadherence monitoring that offers the possibility of intervening only when patientsmiss a dose. The effectiveness of this non-automated type of electronic reminderfor adherence is currently being investigated [19]. Similarly, a survey by Tao etal. [18] supports these findings, affirming that the use of electronic remindersseems to be an effective way to improve medication adherence of patients withchronic conditions. They recommend that future research should aim to identifyoptimal strategies for the design and implementation of electronic reminders,with which the effectiveness of the reminders is likely to be augmented.

Several works have considered interruption management, questioning whenwould be the best time to interrupt the user [1, 4]. Shrot et al. [17] clusteredthe users into groups and then used collaborative filtering in order to determinewhich interaction method would work best with each type of user. This approachyields different policies for different users. However, in contrast to this paper,they did not try to change the user’s behavior, but convey information at thebest timing.

Several additional approaches use a form of personalization for maintenance.A model based on equipment personalization is discussed in [12]. This modelpredicts equipment failures, based on sensor measurements and warranty claims.Huang et al. [11] suggest a maintenance model, which indeed uses a form ofpersonalization, albeit the model does not attempt to optimize the maintenance,but rather utilizes collected data to inform the user about recommended tasksthat needed to be performed, based on the personalized usage history.

3 Formal Model

In this section we build a formal model of a maintenance game. This model hasthe following characteristics (which are motivated by real world maintenance set-tings): 1. A user must determine at which time (t) to perform maintenance. 2.Such maintenance actions impact the probability of faults (as will be explainedbelow). 3. If a malfunction occurs, the user must fix it in order to continue.4. Maintenance and repair actions are associated with a maintaining / repair-ing cost and maintaining / repairing time. While the equipment is being eithermaintained or repaired, it may not be used. We denote by cm the monetary costof maintenance and by cr the monetary cost of repair (usually cm ≤ cr). Weuse wm to denote the waiting time required (cost of time in seconds) once theplayer performs maintenance and wr to denote the waiting time of repairing amalfunction. 5. Future discounting. We assume that any future action is dis-counted, i.e., multiplied by an exponentially decreasing discounting factor (γ).Future discounting has justification from both psychology and economics [7] (al-though the exact function that should be used is often in dispute [15]). In ourdomain, a discount factor may be justified by a probability for a sudden break-down (which is unrelated to the maintenance-repair actions), such as a total lossin a car accident, the loss of a phone, sudden-death of the player etc.

In general we assume the following sampling method procedure for deter-mining when and whether a malfunction will occur: 1. At the beginning of thegame a time at which a malfunction may potentially occur is sampled using someprobability density function (pdf) (or a cumulative density function, CDF ). 2. Ifthe player performed maintenance before that time, this malfunction is removed.Once the maintenance ends, a new potential malfunction is sampled using thesame pdf , but from the current time. The player is associated with both themonetary and time costs of maintaining. 3. If the player has reached the timeat which a malfunction may potentially occur, a malfunction occurs and is fixed(and the player is associated with both the monetary and time costs of repairing).A new future potential malfunction is sampled similarly to the above.

The following two propositions relate to the properties of the optimal policy.We show that the optimal policy has the form of performing maintenance everyX seconds since the last maintenance or repair action has ended.

Proposition 1 From the sampling method we notice that once the player per-forms maintenance (and the maintenance cost is applied), or a malfunction oc-curs (and is fixed, along with it’s cost), the player faces the exact situation as int = 0.

Proposition 2 The optimal policy may be determined by some value t. Whenfollowing the optimal policy, the player performs maintenance once t time unitshave passed since the last time maintenance was performed or a malfunction hasoccurred.

Proof. Assume an optimal policy Π∗. Since this policy may be general, it maytake into account all previous actions and occurrences. Running Π∗ on a sam-pled game, and assuming no malfunction occurred from the beginning until the

first maintenance, denote by X the first time Π∗ implied a maintenance action.Clearly (since Π∗ must be deterministic), in any game, unless a malfunctionoccurs before t, t is fixed. Once a maintenance action is performed or a malfunc-tion occurs (resulting in a repair action) at time t1, according to Proposition 1,the game becomes identical to the starting position and thus the optimal policyis identical and, unless a malfunction occurs, the next maintenance should beperformed at t1 + t.

A corollary of Proposition 2 is that the domain of policies in which we aresearching may be determined by a single parameter t. Thus, we denote by Π(t)a policy in which maintenance is performed after t seconds.

Due to the complexity of our solution, we begin by presenting a simplermodel in which there is no time cost associated with performing maintenanceor repairing a malfunction, i.e., there are only monetary costs associated withmaintenance and repairing malfunctions.

3.1 Actions Have Monetary Cost Only

In this section we assume that there is no time cost associated with performingmaintenance or repairing a malfunction. This simplifies the model and makes iteasier to identify the optimal strategy for maintenance. In this section we willcompute the policy which brings to minimum the expected cost of maintenance/ repair actions, over time.

According to Proposition 2, finding the optimal policy is equivalent to deter-mining t such that the overall expected cost under a policy Π(t) is minimized.We use C(t) to denote the expected cost of maintenance and repairs under a pol-icy in which maintenance is performed after t seconds. Thus the optimal policy,Π∗ is Π(t) such that: t = arg mint C(t).

Unfortunately, calculating C(t) is not simple. In order to calculate C(t) wewill first calculate C(t) given no malfunction occurs the first time, i.e., the firstmalfunction is sampled after t. Denote the first malfunction sampling time astm1. We are therefore interested in C(t | tm1 > t). The next lemma will showthat C(t | tm1 > t) has a form similar to that of a Bellman Equation, i.e., theexpected cost appears on the right side of the formula multiplied by the discountfactor.

Lemma 1 C(t | tm1 > t) has the following property:

C(t | tm1 > t) = γt(cm + C(t))

Proof. Since no malfunction occurs, at time t, according to the policy, the userperforms maintenance at a cost of cm. This cost is discounted by γt (since itoccurs at time t). As claimed in Proposition 1, once a maintenance is performed,the player faces the same situation as in t = 0 and thus the expected cost is C(t)(multiplied by the discount factor).

Denote pr(·) as the probability for an event. We now calculate C(t | tm1 <t) · pr(tm1 < t), the expected cost given that the malfunction actually occursin the first time, i.e. the malfunction is sampled before t, multiplied by theprobability that the malfunction actually occurs before time t.

Lemma 2 C(t | tm1 < t) · pr(tm1 < t) has the following property: C(t | tm1 <

t) · pr(tm1 < t) =∫ t0pdf(x)γx(cr + C(t))dx

Proof. Once a malfunction occurs, the player encountered cost cr and returnsto the starting position C(t). Assuming this malfunction occurred at time x,this cost and the starting position are multiplied by γx. Given an infinitesimallysmall time x, the probability that the malfunction occurs at this time is pdf(x)dx.Therefore, the portion of the expected cost when the malfunction actually occursbefore t is

∫ t0pdf(x)γx(cr + C(t))dx.

Finally we define an equation which helps calculate C(t):

Theorem 1 The expected cost follows:

C(t) =

∫ t

0

pdf(x)γx(cr + C(t))dx+

(1− CDF (t))γt(cm + C(t)) (1)

Proof. According to the law of total probability: C(t) = C(t | tm1 < t) · pr(tm1 <

t)+C(t | tm1 > t)·pr(tm1 > t) By Lemmas 1 and 2: C(t) =∫ t0pdf(x)γx(cr + C(t))dx+

γt(cm + C(t)) · pr(tm1 > t). The probability for a single malfunction to be sam-pled after t, pr(tm1 > t), is (1 − CDF (t)), since by definition, CDF (x) is theprobability that X ≤ x.

3.2 Time consuming actions

In this subsection we take into account the fact that performing maintenance orrepair may be time consuming. As we will show, this solution implies that theplayer’s optimal time to perform maintenance actually depends on the player’sperformance.

In order to account for the value of time and thus model the loss which theplayer will encounter by waiting, we need to consider the performance of theplayer, i.e., the points of value the player obtains per unit of time (excludingany maintenance or repair costs). This value will be denoted p. Note, that inSection 3.1 we did not need to consider this performance value. Since the playeris assumed to have some value of time, we now denote Up(t) as the expectedutility for a player with performance p using a policy that performs maintenanceevery t seconds, and our problem becomes a maximization problem. The optimalpolicy Π∗ is now Π(t) such that: t = arg maxt Up(t).

Calculating the expected utility must take into account the player’s per-formance and the time cost of both maintenance actions and malfunctions (orrepair). We first calculate the utility of Up(t) given no malfunction occurs thefirst time, i.e., the first malfunction is sampled after t (tm1 > t).

Lemma 3 Up(t | tm1 > t) has the following property: Up(t | tm1 > t) = γt(−

cm + γwmUp(t))

+∫ t0pγydy

Proof. Since no malfunction occurs, at time t, according to the policy, the userperforms maintenance at a cost of cm (discounted by γt). After waiting the timecost of maintenance, wm, and thus applying an additional discounting factor ofγwm , the player faces the same situation as in t = 0. Since the player playeduntil time t performing no maintenance, and no malfunction occurs, the utilityfrom performance alone upto time t is given by:

∫ t0pγydy.

We now calculate Up(t | tm1 < t) · pr(midtm1 < t), the expected utility ofthe player given that the malfunction is sampled before t and multiplied by theprobability that the malfunction actually occurs before time t.

Lemma 4 Up(t | tm1 < t) · pr(midtm1 < t) has the following property: Up2(t) =∫ t

0pdf(x)

(γx(− cr + γwrUp(t)

)+∫ x0pγydy

)dx

Proof. Until the malfunction occurs (at time x), the player gains a utility of∫ x0pγydy. Once the malfunction occurs, the player encountered cost cr and re-

turns to the starting position Up(t) After waiting the time cost of repairing, wr,thus an additional factor of γwr . All other factors are identical to Lemma 2.

Finally we define an equation which helps calculate Up(t):

Theorem 2 The expected utility of a policy Π(t) performing maintenance everyt time units since previous malfunction or maintenance, and assuming perfor-mance p follows the following equation:

Up(t) =

∫ t

0

pdf(x)(γx(− cr + γwrUp(t)

)+

∫ x

0

pγydy)dx+

(1− CDF (t)

)(γt(− cm + γwmUp(t)

)+

∫ t

0

pγydy)

(2)

Proof. According to the law of total probability: Up(t) = Up(t | tm1 < t)·pr(tm1 <t) + Up(t | tm1 > t) · pr(tm1 > t). The rest follows from Lemmas 3 and 4:

Equation 2 can be written as:

Up(t) =(−cr + p

ln(γ) )∫ t0pdf(x)γxdx− p

ln(γ)

∫ t0pdf(x)dx

1− (1− CDF (t))γ(t+wm) −∫ t0pdf(x)γ(x+wr)dx

+

(1− CDF (t))(γt(− cm + p

ln(γ)

)− p

ln(γ)

)1− (1− CDF (t))γ(t+wm) −

∫ t0pdf(x)γ(x+wr)dx

(3)

In order to find the optimal policy, we must derive Equation 3 with respectto t and solve U ′p(t) = 0 (and test the two extreme cases of t = 0 and t =∞).

4 The Spaceship Game

The spaceship game is an instance of the formal model described in Section 3.In the spaceship game the player controls a spaceship (see Figure 1) for a

fixed amount of time. Throughout the flight the spaceship should shoot downmeteors which fly in space. Every time a meteor is shot down, the player gainsmoney (points). The player must also avoid getting hit by the meteors, and heloses money if he is hit by them. As the players achieve points, they obtainadditional cannons.

In order to reduce the probability of malfunctions, the spaceship needs tooccasionally carry out maintenance actions. Each of these actions is both timeconsuming and incurs a monetary cost. While performing a maintenance action(which lasts several seconds), the spaceship ’freezes’ and the player cannot shootdown any asteroids and thus is unable to gain any points (but at the same timecannot lose points either). If a malfunction occurs it is repaired. This repair isassociated with both a score and time cost (i.e. the spaceship freezes during therepair time). In this paper we study how an agent providing maintenance alertsmay improve a player’s performance in the spaceship game.

We use a simple form of the beta distribution with α = 2 and β = 1, spreadover T seconds. That is, we calibrate the beta distribution over a time-line of Tseconds, i.e., pdf(t) = 2

T 2 t and CDF (t) = ( tT )2. This function has the followingcrucial property related to repairing and maintenance: the more time that haspassed since the latest maintenance, the more likely it is that a malfunction willoccur at each moment.

5 Optimal Maintenance Timing in the Spaceship Game

We use our results from Theorem 2 to solve the optimal maintenance timing inthe spaceship game. Plugging the beta distribution used in the spaceship gameinto Equation 3 we get:

Up(t) = −p t2

T 2 ln(γ) −(t2

T 2 − 1) (

pln(γ) + γt

(cm − p

ln(γ)

))γt+wm

(t2

T 2 − 1)− 2 γwr (γt t ln(γ)−γt+1)

T 2 ln(γ)2+ 1

+

2 (cr− pln(γ) ) (γt t ln(γ)−γt+1)

T 2 ln(γ)2

γt+wm(t2

T 2 − 1)− 2 γwr (γt t ln(γ)−γt+1)

T 2 ln(γ)2+ 1

(4)

Equation 4 is clearly derivable, however, due to its length we omit its deriva-tive from this paper. The agents described in the next section, use the derivativeof Equation 4. As for the discount factor γ; given the total length of the game,ttot, we use: γ = 1

1−ttot to determine the discount factor. Assuming the discountfactor is viewed as a way to model the probability that the game will suddenlyend, the above formula ensures that the expected length of such a game whenusing the discount factor will be ttot.

6 Alert Agents

We considered two alert agents. The first, is a non-personalized agent (NPA)that only uses the average human performance when providing maintenancealerts. This agent, calculates the optimal time to perform maintenance, using theformulas developed in Section 3) and assuming the performance of an averageplayer.

The second is our Fully Personalized Agent (FPA). This agent predicts theexpected performance of the current player, and, using this information, theFPA calculates the optimal time to perform maintenance (using the formulasdeveloped in Section 3). We considered four different methods to compute theexpected performance, based on the previous data of the current player. Thefirst method is simply to use the performance in the previous second to predictthe performance in the current second. The second method is to use the averageperformance of the current player from the beginning of the (current) game. Thethird method, the moving window method, requires a parameter x. This methoduses the average performance of the past x seconds to predict the current per-formance. The fourth method, known as exponential smoothing ([10]) predictscurrent performance by multiplying the previous expected performance by somediscount factor, δ, and the performance of the previous second by 1−δ. Both theexponential smoothing and moving window methods require some initial value,which is also a parameter that must be determined.

In order to determine the average performance for NPA and the method tobe used to predict the user performance along with its parameters for FPA,we collected training data from 20 subjects. Table 1 presents the mean squarederror (MSE) of the prediction methods employing a tenfold-cross-validation onthe training data (lower values indicate a better fit). As shown, the exponentialsmoothing method exhibited a higher fit-to-data than all other performanceprediction methods. Therefore the exponential smoothing method was selectedto be implemented in the FPA.

Method MSE

Previous second 1393Full average 766.5

Moving window 767.1Exponential smoothing 649.5

Table 1. Prediction methods and their mean squared error (MSE) on training data.

7 Evaluation

7.1 Experimental Setup

In order to evaluate our agent, we recruited a total of 56 subjects to playthe spaceship game. We conducted our experiments using Amazon’s Mechan-ical Turk (AMT) [2], a crowd sourcing web service that coordinates the supplyand demand of tasks which require human intelligence to complete. The set ofsubjects consisted of 57% males and 43% females. Subjects’ ages ranged from 18to 51, with a mean of 32. All subjects were residents of the USA. The subjectswere paid 20 cents to participate in the experiment, and, depending on theirperformance, could achieve an additional payment of up to $2.00.

Before starting to play, the subjects had to fill out a short demographicquestionnaire. Then they were presented a tutorial of the game and started byplaying a training game to help them understand the game rules. The subjectsthen played a two minute practice game. Each subject played 3 actual gameswhich lasted 4 minutes each. In these three games the subjects either receivedalerts from FPA, NPA or received no alerts and were simply told that theyshould perform maintenance every 20 seconds (which is optimal for a playerwith average performance). The order of these different games was controlled.In order to increase compliance, when presenting a maintenance alert both alertagents also made the whole screen flash for a second and played a tone. Thealerts were presented one second in advance. Table 2 presents the settings weused for the spaceship game. After playing all games, the subjects filled out aconcluding questionnaire. Unfortunately, since the experiment turned out to be

Action Score ($) Time cost(spaceship frozen)

Maintenance −$5 8 secsRepair −$500 3 secs

Hit by meteor −$10 N/AHit a meteor +$30 N/A

Table 2. Settings used in the spaceship game

too long for some subjects, some subjects did not play seriously in some of thegames (this was also supported by some of the subjects’ comments). Therefore,we removed 20 subjects which had a negative score in any of the three games.

7.2 Results

The fully personalized agent (FPA) accounted for an improvement of between17% and 18% over the non-personalized agent (NPA) and the no alert condition(5637 vs. 4756 and 4833). We ran an ANOVA test with repeated measurementson the subject score and set the agent type as our dependent variable and the

3000

3500

4000

4500

5000

5500

6000

6500

7000

FPA NPA No alert

Sco

re

Fig. 2. Average performance of subjects in FPA, NPA and no alert games.

game order as a controlled variable. The impact that the agent type had onthe subject’s score was statistically significant (F (2, 30) = 3.467, p < 0.05). Inpairwise comparisons FPA significantly outperformed both the non-personalizedagent NPA and no alerts (with Bonferroni adjustment for multiple comparisons,single tailed, p < 0.05). Any differences between NPA and no alert were mi-nor and not significant. Figure 2 illustrates these results (error bars representconfidence interval).

The average standard deviation of the scores within each of the groups was3573, which is in fact 70% of the average score. This is clearly a very large stan-dard deviation, emphasizing the need for a personalized agent which is mostrequired when people differ from one another. Interestingly, the subjects per-formed more maintenance actions when presented with alerts from the NPA (7.8per game), than with the FPA (6.2 per game) and when they received no alertsat all (6.2 per game). This indicates that the failure of the NPA was not due tothe subjects not following its alerts but due to the fact that these alerts werenot presented at the optimal timing according to the individuals’ performance.

The subjects seemed to enjoy the game, giving it an average of 7.7 on a 1to 10 scale. Quite surprisingly, we found little correlation between the averagescore of a player and the answer to this question (0.29), and the player’s age andthe answer to this question (0.06).

7.3 Discussion

Clearly, in the spaceship game, any alert agent is limited in the ability to increasethe overall performance of the user, due to the fact that the major contributor

to the user’s score is actually the ability of the player to shoot down asteroidsand avoid being hit by them, and we assume that the alert agent has no impacton such abilities. Therefore, we believe that our results, which show that FPAincreases the average performance of the players by 17% is a very significantresult. Most alert systems do not account for the value of time of the user. Inour spaceship game, an agent not accounting for the value of time would alertthe user to perform maintenance every few seconds throughout the whole game,which would clearly result in a very low score.

In order to deploy FPA in any type of equipment, the agent must be ableto have access to the value of time for the user. For this information one mayconsider the earning wage, i.e. the amount the person earns a month or yeardivided by the number of working hours. Another option is to ask the user,either directly (how much would you be willing to spend in order to save an hourof your time?), or indirectly, using a questionnaire with several questions (Howmuch time would you be willing to spend to save $50 on your groceries?). Thecost (both in time and in money) of maintenance and repairing is often available.The probability density function may be trickier to obtain. In order to learn areasonable approximation for it, one needs to collect enough data. However, inthe field of car maintenance, for instance, most new cars have logs stating wheneach treatment was performed and when each malfunction appeared, etc. Thisinformation, if gathered from enough cars, may be a valid source for computingthe probability density function.

8 Conclusions

In this paper we study to what extent a maintenance alert system can be bene-ficial to a user. We present the spaceship game, which is a game wherein a usercontrols a spaceship that requires maintenance to avoid malfunctions. This gameallows the quantification and scoring of the user’s performance and enables us tomeasure to what extent alerts affect her behavior and performance. In contrastto most work discussing maintenance and alerts, which does not try to person-alize the alerts provided to users, in this paper we test the effectiveness of apersonalized maintenance alert agent. When interacting with a user, the agentpredicts the expected performance of that user. Based on this prediction and ouranalytically derived solution, the agent alerts the user to perform maintenanceat the optimal maintenance timing. To the best of our knowledge, this is thefirst paper that attempts to solve the optimal time for performing maintenance,when taking into account the value of time for the individual users and thusresulting in personalized alerts.

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