Sampling Procedure for Performance-Based Road Maintenance Evaluations

Samling Procedure for Performance-Based Road Maintenance Evaluations Jesus M. de la Garza, Juan C. Piñero, and Mehmet E. Ozbek Maintaining the road infrastructure at a high level of condition with generally limited amounts of available funding is a challenge for many transortation agencies. To address this challenge, many road administrators worldwide have imlemented erformance-based maintenance contracts. In erformance-based maintenance contracts, road administrators define erformance measures (e.g., erformance-based secifications) that secify the minimum condition at which the asset items are to be maintained. To ensure that contractors maintain the asset items according to these measures, road administrators must design and imlement a comrehensive and reliable erformance monitoring rocess. One of the most imortant areas within the erformance monitoring rocess is insection conducted in the field. Defining a rocedure that guarantees the success of field insections is a challenge. When defining such a rocedure, road administrators must consider budget and time limitations, among others. Since erformance-based road maintenance contracts are relatively new, the availability of guidelines for such issues (with focus on erformance-based contracts) is limited. That need is addressed by resentation of a three-stage and seven-ste statistical samling rocedure develoed to ensure that findings from field insections will be reliable and reresentative with high confidence of the actual condition of asset items in the entire oulation. Also resented are three alternative aroaches for samling for the cases in which samling needs to be erformed not just once but multile times over the duration of a erformance-based road maintenance contract. The challenge of maintaining the road infrastructure at the best ossible condition by investing the minimum amount of money kees transortation agencies continually searching for innovative aroaches to eventually rovide otimum benefits to taxayers. According to road administrators worldwide, in the last two decades, one initiative that has roduced significant benefits is the imlementation of erformance-based contracts in maintenance of road infrastructure. In the United States, transortation agencies in Virginia, Florida, Texas, and District of Columbia have been active in imlementation of erformance-based road maintenance contracts. In the international arena, countries such as Argentina, Uruguay, Australia, New Zealand, Brazil, Chile, and Colombia are considered ioneers in imlementation of this initiative as art of their strategies to reserve the road J. M. de la Garza and M. E. Ozbek, Charles E. Via, Jr. Deartment of Civil and Environmental Engineering, 200 Patton Hall, 0105, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061. J. C. Piñero, NEX Cororation, 400 Calaf Street, Suite 225, San Juan, Puerto Rico 00918. Corresonding author: M. E. Ozbek, meozbek@vt.edu. Transortation Research Record: Journal of the Transortation Research Board, No. 2044, Transortation Research Board of the National Academies, Washington, D.C., 2008,. 11 18. DOI: 10.3141/2044-02 system (1, 2). This initiative calls for erformance-based work, in which a desired outcome is secified rather than materials or techniques to be used by the contractors to maintain the asset items. In erformance-based contracts, road administrators define erformance measures that secify the minimum accetable condition at which the asset items should be maintained. To ensure that contractors maintain the asset items according to these measures, road administrators must design and imlement a comrehensive and reliable erformance monitoring rocess. One of the most imortant areas in the erformance monitoring rocess is insections conducted in the field. Field insections require a significant amount of lanning and careful monitoring. Defining a rocedure that guarantees the success of field insections is a challenge. When defining such rocedure, road administrators must consider budget and time limitations, among others. These constraints influence the final techniques adoted that address issues such as the ortion of the oulation to be insected, frequency at which insections should be conducted, and methodology to be used to collect information. Since erformancebased road maintenance contracts are relatively new, the availability of guidelines that address such issues (with focus on erformancebased contracts) is limited (2). This aer resents a three-stage and seven-ste statistical samling rocedure develoed to ensure that findings from field insections will be reliable and reresentative with high confidence of the actual condition of asset items in the entire oulation. Also, this aer resents three alternative aroaches of samling for the cases when samling needs to be erformed not just once, but multile times over the duration of a erformance-based road maintenance contract (e.g., once in every year to monitor a contractor working under the terms of a 5-year-long erformancebased road maintenance contract). Of note is that this aer does not discuss the oerational issues related to the condition assessment rocess, such as frequency of insections and insection techniques. Discussion of oints resented is limited to the samling asect of the condition assessment rocess. RANDOM INSPECTIONS In road maintenance evaluations, conducting a 100% insection may not be feasible because of time and cost constraints. The condition data for a number of asset items such as avement and shoulders can be collected by using road scanning vehicles at traveling seeds without necessarily deloying crews to erform manual assessments in the field. However, data collection with resect to many other asset items, such as ies, ditches, underdrains, and fences, requires a considerable amount of time to be sent by the crews in the field. It is not feasible to collect the condition information for such asset items for the whole oulation when such information cannot be collected at traveling seeds. When collecting information for the 11

12 Transortation Research Record 2044 whole oulation is not feasible, erforming random insections is considered a useful way to maximize the benefits of the data collection effort (3). The objective of random insections is to measure or survey only a ortion of the whole oulation of interest. Results obtained from the samled ortion are then generalized to the whole oulation at a certain confidence level. If the intent is to use samling in the data collection rocess, as is mostly the case for road administrations (because of budget and time constraints), then the rocess should secify a samling method. The selection of method and the comlexity of the samling rocess deend on characteristics of the oulation considered in the evaluation and the confidence at which the findings from the samled oulation need to be rojected to the entire oulation. When considering the use of samling in the evaluation rocess, it is imortant to understand any bias that may be inherent in the samled data. Samle bias refers to the likelihood that a measurement by a samle of the oulation does not accurately reflect the measurement of the whole oulation. Random insections and the collection of large samles are efficient ways to decrease samle bias. Moreover, this aroach can make significant contributions such as reducing the cost of data collection and data analysis, and decreasing the time needed to comlete an evaluation. However, one must consider that there are also some disadvantages associated with samling or random insection. One of the most significant disadvantages is that samling does not collect all cases and, although statistically unlikely, may result in misidentification of the general condition. Moreover, the situation of missing observations may lead to loss of unique ersectives, affecting the quality of data. Thus, attention must be aid when defining and imlementing samling techniques (2). With resect to the secific scenario, defining a methodology that addresses all the samling needs associated to erformance-based road maintenance evaluation is a challenge. The objective of this aer is to rovide a detailed descrition of the aroach used to define such rocedure. DEVELOPMENT OF SAMPLING PROCEDURE The samling rocedure resented in this aer was develoed in three stages, to do the following: 1. Perform a detailed analysis of the characteristics of erformancebased road maintenance evaluations, 2. Study otential samling techniques that can be used to imrove the effectiveness and efficiency of the samle selection rocess, and 3. Define a comrehensive methodology for the selection of samle units that will ensure with a high confidence level that the findings from the samled ortion of the oulation are reresentative of the entire oulation. A detailed descrition of each of these stages follows. Characteristics of Performance-Based Road Maintenance Evaluations The first ste when defining any samling alication is to comrehensively study the articular roerties of the oulation to be evaluated. This is Stage 1. With resect to erformance-based road maintenance evaluations, understanding the characteristics of factors such as overall oulation, samle units, asset items within each samle unit, and accetable quality levels for each asset item is crucial to guarantee the success of the samling rocedure to be defined. An evaluation of each one of these factors is resented as follows. Poulation The oulation normally considered for the road maintenance evaluations is defined by small road segments of a secific length. These segments are better known in samling theory as the samle units. Samle units can be considered indeendently on each direction (north and south, east and west). For examle, for a ortion of a road that is 10 mi long running north and south direction and that is divided in samle units of 0.1 mi long, then the total oulation size will be 200 samle units (10 mi 2 directions 10 segments). Another imortant characteristic of the oulation is that ortions of the road (oulation) can be exosed to very different conditions. In most cases, as in this one, it is of interest to evaluate areas with different characteristics searately. To address this need, it is recommended to divide the oulation in grous exosed to similar conditions, such as same geograhical location, weather variation, urban and rural settings, traffic volumes, and tye of asset items. For examle, suose that the first 5 mi of the 10 mi of road in the revious examle are located in urban areas and the other 5 mi are located in rural areas, then the 200 samle units will be divided in two oulations with 100 samle units each. This concet of dividing the oulation in grous with similar characteristics is better known in samling theory as stratification of the oulation. Samle Units One imortant characteristic of each tyical samle unit considered is that each contains more than one element to be evaluated. Such elements are named asset items. Each samle unit may have different number of asset items. Considering once again the examle of the 10 mi of road ortion, let us say that there is a total of five asset items that can be resent on a given samle unit (0.1-mi long road segment). Obviously, not all samle units contain similar asset items. For examle, 3 of 5 asset items can be resent in one samle unit and 2 of 5 asset items can be resent in another samle unit. This articular characteristic of each samle unit makes the develoment of an aroriate samle selection rocess comlex. The challenge is to sufficiently insect each asset item to guarantee the findings from the samled oulation are reresentative, with high confidence, of the condition of the asset items in the entire oulation. Performance Targets Since the methodologies resented in this aer focus on erformancebased evaluations, accetable quality levels, better known as erformance targets, must be considered in the develoment of the samling rocedure. Performance targets are generally different for each asset item. For examle, a erformance target can state that it will be considered accetable when 90% of the ies in a oulation are in good condition, where good condition is defined according to secific erformance criteria (e.g., greater than 80% of the ie s diameter should be oen), whereas the erformance target for traffic signs can be 95%. The variability in erformance targets among asset items is an imortant characteristic that can make a significant difference when determining the minimum number of samles required for each asset item.

de la Garza, Piñero, and Ozbek 13 Samling Concets and Techniques Now that the characteristics and roerties of the oulation under consideration are known, a review of samling concets is resented. This is Stage 2. The objective is identifying otential techniques that can serve as a latform to define the methodology that will better address samling needs. The review of samling theory focuses on the following three areas: (a) samling mechanism for drawing samles from the oulation, (b) basic samling concets, and (c) formulas for samle size determination. Samling Mechanism The roosed rocedure entails three different samling mechanisms to be used as discussed herein (2). As reviously mentioned, one need is to erform an indeendent evaluation of ortions of the roadway system that are exosed to different conditions. For this reason, stratified samling is used to be able to divide the oulation into suboulations or strata. Once stratification is erformed, then samle size for each asset item is calculated using the simle random samling equations, as will be resented later in this aer. For the actual rocess of random samling, a samling mechanism known as samling roortional to size is alied. In this samling mechanism, instead of assigning equal robability (equal chance of being selected) to each samle unit, unequal robabilities are assigned to each samle unit based on the number of existing asset items in such samle unit. The objective of assigning unequal robabilities is to give more chance to the samle units that contain more asset items of being selected comared with the samle units containing less number of asset items. This aroach is more cost-effective because field insections can be accomlished by visiting a minimal number of samle units with many asset items, as oosed to a large number of units with a few asset items. Basic Samling Concets This section reviews the basic samling concets that will be used in the samling rocedure roosed by this aer (4, 5): 1. Poulation. Poulation is defined as the collection of N samle units denoted by Y 1,..., Y N. Each samle unit is associated with a unit size a i. In the scenario, the unit size is determined according to the number of asset items. Each samle unit is associated with a quantitative resonse measurement, denoted as x i, that can be observed only if it is drawn and included in the samle. When the resonse measurement can only take two values (for convenience, x i = 0 or 1) the oulation is classified as a binary oulation. For instance, the scenario has a binary oulation because an asset item within a samle unit either meets the erformance criteria (x i = 1) or it does not (x i = 0). The samling concets resented in this aer focus on a binary oulation, because one is dealing with such a oulation tye. 2. Poulation roortion for each asset item. The objective of most samling rocedures is to make inferences about the oulation roortion, denoted by and defined by the following: = # assing in the oulation total count in the oulation Because the entire oulation is never observed, the oulation roortion cannot be known exactly. Instead, inferences about are to be derived from the observed samle. () 1 3. Samle roortion for each asset item. Inferences about the oulation are made through the use of samle roortion, denoted by ˆ and defined by the following: ˆ = 4. Confidence interval. A detailed assessment of uncertainty is available in the form of an interval estimate, which is meant to reresent a region of high confidence, where the oulation roortion is thought to lie. Such interval, known as confidence interval, is stated with a numerical level of confidence, usually a high ercentage such as 90%, 95%, and even 99% in some cases. In the case used here, the confidence interval for the oulation roortion is where e is the desired (secified) recision rate, which will be discussed in detail later. Formulas for Samle Size Determination To determine the samle size for erformance-based road maintenance evaluations, the following equations are used (6, 7): zα 2S n = 2 2 e + z S 2 # assing in the samle total count in thesamle [ ] 3 ˆ e, ˆ + e () 2 2 α 2 S N ( 4) 2 N = 1 5 N 1 ( ) () where e = desired recision rate that should be secified by road administrators, z α /2 = confidence level coefficient, N = oulation size, and = oulation roortion. For simlicity, the factor N / N 1 can be set to 1, which is a fair assumtion for large oulations the case investigated in this aer (2). In the roosed methodology, it is recommended to assign the value of as the minimum of the following two: the historical erformance rate or the erformance target. This definition results in taking any value such that 0 1. However, can not be chosen to be equal to 0 or 1. In such cases, the equations defined to determine the samle size are considered invalid as they yield to a samle size that is equal to 0. In addition to this restriction, must be at least 0.5, which is the value to obtain the maximum samle size (2). Proosed Samling Procedure This section, Stage 3, rovides a detailed descrition of the stes required to imlement the roosed samling rocedure for conducting erformance-based road maintenance evaluations. The methodology is summarized in seven stes in which the samling theories and concets introduced in revious sections are combined. They rovide comrehensive guidance on how to determine the aroriate ( 2)

14 Transortation Research Record 2044 samle size and then select samle units for evaluation. A descrition of each ste follows. Stratifying the Poulation The oulation is stratified into different areas of interest, with the number of strata deending on the information needed and the different arameters to be incororated in the analysis. Some of the criteria that can be considered to stratify the oulation were reviously discussed (e.g., rural versus urban areas). Defining the Samle Units Once the strata are identified, the next ste is to divide each stratum into samle units. It is suggested that one secifies the same samle length to all units. For instance, in the scenario, one can secify a samle unit length of 0.1-mi long, which divides each mile into 10 equal samle units in one direction and 10 in the other direction (if two directions are considered searately). Identifying Asset Items on Each Samle Unit via Asset Density Database Once the samle units have been defined, a density of all the asset items located within each samle unit needs to be created. What must be recorded in this asset density is not the exact quantity of a articular asset item on a given samle unit, whereby to establish if the asset item exists or not. For instance, a given samle unit may have 10 ies. Information that needs to be recorded in the asset density database is only that ies exist on that articular samle unit as oosed to secifying the exact quantity (in this case 10). Thus, the asset density can easily (and by sending a minimal amount of resources) be obtained by erforming windshield insections along with making use of the construction lans. The only required information is whether an asset item is resent in a given samle unit and not the count, condition, or hysical characteristics of such asset item. Table 1 resents an examle of the kind of information needed in the asset density to roerly imlement the roosed rocedure. As deicted, the oulation in Table 1 contains N = 95 samle units (Column 1) for which the existing asset items have been identified (Columns 2 through 5). The total of existing asset items in each sam- le unit is added in Column 6. Note that in addition to the column with the total number of asset items on each samle unit, an additional column (Column 7) with the cumulative number of asset items is included. The urose of having the cumulative number of asset items is to use them to define the intervals (Column 8) that will be used to determine the sites selected for insection. This rocedure is detailed in Ste 7. Creating the Database with the Samle Units Containing Each Asset Item Before erforming the calculations to determine the samle size for each asset item, comlementary databases identifying the samle units containing each asset item within each stratum should be created. These databases are essential to guarantee the success of the random selection rocess discussed in Ste 7. The information needed to create these databases can be derived from the asset density study conducted in Ste 3. Table 2 rovides an examle of what these databases look like, based on the information rovided in Table 1. For instance, note in column 3 that database number 1 (for sloes) only contains samle units 1, 3,..., and 95. Samle unit number 2 is not included in database 1 because according to the information in Table 1, that segment does not have sloes that is, they do not exist. Defining the Values of Parameters to Be Used in Samle Size Formulas The next ste is to define the values for arameters to be used in the formulas to determine the samle size. According to Equations 4 and 5, the arameters that need to be defined for each asset item are oulation size (N), standard normal deviate (Z α/2 ), oulation roortion ( ), and desired (secified) recision rate (e). As shown in Ste 3, the value of N for each asset item is already calculated. The standard normal deviate Z α/2 value deends on the desired confidence level (CL). This value can be obtained from statistics tables. Among the most commonly used values for Z α/2 are 1.96 for a 95% CL (α =0.05) and 1.65 for a 90% CL (α =0.10). It is recalled that the value of must be assigned as the minimum of the historical erformance rate or the erformance target (but not lower than 0.5). Finally, the desired recision rate e, as the name imlies, must be defined by the road administrators according to the accetable range within the confidence interval. TABLE 1 Examle of Density of Asset Items in Each Samle Unit Asset Items That Exist at Each Site (E = exists, NE = does not exist) Samle Unit (1) Sloes (2) Signals (3) Guardrail (4) Sidewalk (5) Total (N) (6) Cum. (ΣN) (7) Interval (8) 1 E E E E 4 4 0 4 2 NE E NE E 2 6 5 6 3 E NE E NE 2 8 7 8........................ 95 E NE E E 3 Σ E 95 Σ E 94 + 1 ΣE 95 Total Σ E s Σ E s Σ E s Σ E s Σ E s

de la Garza, Piñero, and Ozbek 15 TABLE 2 Databases for Each Asset Item Performing Random Selection of Samle Units Database (1) Main Asset Included (2) Sites Included in Database (3) 1 Sloes 1, 3,..., 95 2 Signals 1, 2,..., 95 3 Guardrail 1, 3,..., 95 4 Sidewalks 1, 2,..., 95 Comuting the Required Samle Size for Each Asset Item The samle sizes determined for each asset item need to guarantee with high confidence that findings from the samled ortion of the oulation are reresentative of the general condition of the different asset items in the entire oulation. To identify the samle size for each asset item, Equations 4 and 5, which corresond to simle random samling on a binary oulation, should be used. For examle, let us assume that, as identified through the asset density database, a total of 91 samle units contain sloes. This value reresents the total oulation for the sloes asset item (N = 91). Assuming that the values of Z α/2,, and e have been defined, one can comute the required samle size n for sloes by using Equations 4 and 5. This rocedure must be reeated for each asset item within each stratum. Once that is done, the actual random selection of samle units can be erformed. The first ste in selecting sites for insection is to generate random numbers. This random number must be generated from an interval of 1 through the total number of asset items on each stratum. The urose of using this interval is to introduce the concet of samling roortional to the samle size to the random selection rocess. Deending on the interval (Column 8 of Table 1) in which the random number is located, the samle unit associated with that articular interval will be selected. For examle, according to Table 1, if a value of 5 is randomly generated, then the samle unit that will be selected for insection is unit 2. The remaining stes of the rocedure to be followed, once a samle unit is selected, are illustrated in Table 3. As shown in Table 3, samle units will be randomly selected from all the databases created in Ste 4 until a articular asset item is sufficiently insected. Then the list of databases used for the selection of samles is narrowed to only those databases containing the asset items that have not reached sufficiency (i.e., samle size determined in Ste 6). A closer look at Table 3 illustrates this rocess. For the first 35 samle units selected for insection (order of selection 35), all databases were considered. However, after 35 samle units have been selected, the signals asset item met sufficiency (according to Column 6, which indicates that 22 sites were needed and 22 sites were selected). Nonetheless, since the cumulative number of selected samle units (n A ) containing sloes, guardrails, and sidewalks is lower than the number of samle units required (n R ) for such asset items, more samle units need to be selected for insection. After the selection TABLE 3 Selection of Sites Statistics of Asset Insected Sloes Signals Guardrail Sidewalks Order of Unit Database (5) (6) (7) (8) Route Selection a Selected Used (1) (2) (3) (4) b n R c n A b n R c n A b n R c n A b n R c n A A 1 3 1,2,3,4 70 1 22 0 66 1 14 0 35 67 1,2,3,4 70 35 22 22 66 35 14 9 50 5 1,3,4 70 48 22 22 66 50 14 14 71 23 1,3 70 67 22 22 66 66 14 14 74 10 1 70 70 22 22 66 66 14 14 NOTE: reresents the asset items that met sufficiency. a Reresents the cumulative number of sites selected for insection. b Reresents the minimum number of sites required for insection in order to meet sufficiency. c Reresents the actual number of asset items selected for insection.

16 Transortation Research Record 2044 of the 35th samle unit at which sufficiency is met for the signals asset item, only databases 1, 3, and 4 are used for the selection of the next samle units. Note that after 50 sites were selected, the sidewalks asset item met sufficiency, which required another reduction in the databases considered for selection of the next samle units (only databases 1 and 3 are used after that oint). This rocess is reeated until the sufficiency is met for all of the different asset items as shown in the last row in Table 3 (74 sites were required to sufficiently insect all asset items). Note in Table 3 that every time sufficiency is met for a given asset item, the cumulative number of such asset item selected for insection, n A, remains the same as the number of such asset item required to be insected, n R, even though the samling continues to take lace. This means that only the asset items that have not met sufficiency yet will be considered for insection in the subsequent samle units selected. For examle, let us consider in Table 3 the order of selection number 50, which corresonds to the selection of unit number 5. At this stage, two of the four asset items have met sufficiency (signals and sidewalks). However, one of these asset items, signals, had already met sufficiency in selection order number 35. If any samle unit selected for insection after the signals asset item had met sufficiency (which occurs at selection order number 35) contains such asset item, then such asset item would not be selected to be insected in those samle units, even though it exists. This aroach makes the rocess more cost-effective since only the asset items within each samle unit that make a contribution to the sufficiency of asset items are selected to be insected. SAMPLING MULTIPLE TIMES OVER THE COURSE OF A PERIOD Performance-based road maintenance contracts tend to last for long terms. Field insections should be erformed a number of times over the course of the contract to ensure continuous monitoring of the contractor s erformance. Deending on the resources allocated by the transortation agency, the frequency of such insections may range from four times a year to cature the seasonal effects on the asset items to once a year. Presented in this section are three alternative aroaches of alying the samling rocedure discussed in the revious section for cases in which samling needs to be erformed not just once, but multile times over the course of the erformance-based contract duration. Keeing Desired Precision Rate e Constant As discussed earlier, the value of in Equation 5 must be assigned as the minimum of the historical erformance rate or the erformance target. In the absence of historical erformance data, the erformance targets as secified by the contract should be used in the samling equations to determine the samle size. This is usually the case for the first samling rocess (i.e., to evaluate the contractor s erformance for the first time) for which no historical data are available. In Aroach 1, starting with the second evaluation, is chosen according to the aforementioned criterion. This means that, as a result of the first insections, if the erformance of the contractor is found to be less than the erformance target for a given asset item, then the used in the samling rocedure erformed for the second insections will be based on such erformance. Consequently, in the second insections, the determined samle size will be different from the one determined for the first insections. This is mainly because, keeing every other arameter in Equations 4 and 5 (i.e., Z α/2, e, and N) constant, samle size n changes when changes. Therefore, if desired recision rate e is ket constant in multile samlings, then the samle sizes resulting from such samlings will be different. Figure 1 deicts the relationshi of and n for an asset item with N = 785, Z α/2 = 1.96, and e = 0.04. Using Aroach 1 for multile samlings may result in considerable changes in the samle size from one evaluation to another. Using the case deicted by Figure 1 as an examle, if a of 0.95 is used to determine the samle size (for a given asset item) for the first evaluation of the contractor, resulting samle size is 100. Let us assume that as a result of the first insections, the erformance of the contractor (i.e., historical erformance) is found to be at 0.80. Then, such should be used as the value of for the samling erformed for second evaluations. That would result in a samle size of 258, which is a substantial increase from the first evaluations. Stating Desired Precision Rate e Relative to Poulation Coefficient of Variation One aroach to deal with the issue of substantial changes in the samle size from one evaluation to another (as shown in Aroach 1) is to state the desired recision rate e in the second and subsequent n 400 350 300 250 200 150 100 50 0 0.5 0.65 =0.80 n=258 N=785 CL=95% (z /2=1.96) e=0.04 (constant) =0.95 n=100 0.55 0.6 0.7 0.75 0.8 0.85 0.9 0.95 1 FIGURE 1 Relationshi between and n when e is constant.

de la Garza, Piñero, and Ozbek 17 evaluations relative to the oulation s coefficient of variation (COV) as follows (4): e = e initial COV = where e initial is the value of e used in the first evaluations, and initial is the value of used in the first evaluations. To better illustrate how this aroach works, let us consider the following examle: Suose in lanning a binary samling exeriment it is determined that a suitable e initial = 0.04 when initial = 0.95. However, the interest is in estimating the value of e when = 0.90. By substituting the known values into Equations 6 and 7, e can be calculated as follows: e = 004. 1 1 COV initial initial 1 0. 90 090. = 006. 1 0. 95 095. () 6 ( 7) Therefore, if this aroach is used for the multile samling scenario, then the desired recision rates in different evaluations will be adjusted according to the. This ensures that the samle size from one evaluation to another remains in the same order of magnitude. Figure 2 deicts the relationshi of and n when this aroach is used for an asset item with N = 785, Z α/2 = 1.96, e initial = 0.04, and initial = 0.95. As can be seen, with this aroach, when changes from 0.95 to 0.80, the samle size goes from 100 to 73. This is an insignificant change when comared with the change from 100 to 258, which was the case for Aroach 1. However, concurrently (when changes from 0.95 to 0.80) the desired recision rate e goes from 0.04 to 0.09, which may be too large for an accetable recision rate. Keeing the Samle Size Constant Using Aroach 2 for multile samlings, while keeing the samle sizes close to each other, may result in considerable changes in the desired recision rate, as mentioned. It is ossible to kee e in an accetable range while not changing the samle size from one evaluation to another. In this aroach, samle size is calculated for the first evaluations. In subsequent evaluations, the same samle size is used. Deending on the value of that is used in such evaluations, e changes from one evaluation to another. Nonetheless, such change is less than what is encountered when Aroach 2 is used. Figure 3 deicts the relationshi of and e when this aroach is used for an asset item with N = 785, Z α/2 = 1.96, and n = 100. As can be seen, with this aroach, when changes from 0.95 to 0.80, e goes from 0.04 to 0.07. This is much less of a change when comared with the case for Aroach 2 in which the change was from 0.04 to 0.09. CONCLUDING REMARKS This aer resented a samling rocedure that is develoed to address the need of monitoring, effectively and efficiently, the contractors working under the terms of erformance-based road maintenance contracts. The develoed rocedure is effective, for it ensures that the findings from the field insections will be reliable and reresentative with high confidence of the actual condition of asset items in the entire oulation. Also, the develoed rocedure is efficient because field insections can be accomlished by visiting a minimal number of samle units with many asset items rather than a large number of samle units with a few asset items. The result is substantial savings in cost and time in erforming such insections. 120 N=785 CL=95% (z /2=1.96) e initial =0.04 initial =0.95 100 n 80 60 40 =0.80 n=73 =0.95 n=100 e=0.04 20 e=0.09 0 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 FIGURE 2 Relationshi between and n when e changes relative to COV.

18 Transortation Research Record 2044 e 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 =0.80 e=0.07 N=785 CL: 95% (z /2=1.96) n=100 (constant) =0.95 e=0.04 0.00 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 FIGURE 3 Relationshi between and e when n is constant. Presentation of the develoed rocedure and aroaches is in a stage-by-stage and ste-by-ste manner to hel interested transortation agencies easily comrehend the concets and imlement the develoed rocedure. The develoed rocedure has been imlemented since 2002 to assist the Virginia Deartment of Transortation (DOT) in monitoring the erformance of two searate contractors working under terms of erformance-based road maintenance contracts. Both contracts are long term, necessitating develoment of the three alternative aroaches of samling for cases in which samling needs to be erformed not just once, but multile times over the course of the contract duration, as resented in this aer. Of note is that such imlementations used sohisticated comuter rogramming aroaches during samling. Also, tablet comuters with built-in intelligent forms were used in data collection to ensure that monitoring of the contractors from incetion to finalization ran smoothly and was error free. Within all imlementations that included a number of different scenarios (i.e., number of asset items in a given samle unit), the samling rocedure was found successful in obtaining the required confidence levels. As stated, this aer does not discuss oerational issues related to the condition assessment rocess, such as frequency of insections and insection techniques. Nevertheless, it is suggested that insections be erformed multile times in a year to cature seasonal effects (resulting in climate and traffic changes) on the deterioration of asset items. Furthermore, in addition to erforming condition assessment of the samles generated by the methodology described, it is suggested that continuous and comrehensive monitoring be erformed of the whole oulation with resect to certain asset items, to cature conditions (such as large otholes and nonfunctioning signals) requiring emergency maintenance actions due to safety reasons. ACKNOWLEDGMENT The research work described in this aer has been funded by Virginia DOT. REFERENCES 1. Zietlow, G. Cutting Costs and Imroving Quality Through Performance- Based Road Management and Maintenance Contracts. University of Birmingham/Transit New Zealand Senior Road Executive Courses: Innovations in Road Management. Birmingham, United Kingdom, 2002. 2. Piñero, J. C. A Framework for Monitoring Performance-Based Road Maintenance. PhD dissertation. Virginia Polytechnic Institute and State University, Blacksburg, 2003. 3. Thomson, S. K., and G. A. F. Seber. Adative Samling. John Wiley and Sons, New York, 1996. 4. Scheaffer, R. L., W. Mendenhall, and R. L. Ott. Elementary Survey Samling, 5th ed. Duxbury Press (Wadsworth/ITP), Belmont, Calif., 1995. 5. Ott, R. L., and M. Longnecker. An Introduction to Statistical Methods and Data Analysis, 5th ed. Duxbury, Pacific Grove, Calif., 2000. 6. Schmitt, R. L., S. Owusu-Ababio, R. M. Weed, and E. V. Nordheim. Understanding Statistics in Maintenance Quality Assurance Programs. In Transortation Research Record: Journal of the Transortation Research Board, No. 1948, Transortation Research Board of the National Academies, Washington, D.C., 2006,. 17 25. 7. Kardian, R. D., and W. W. Woodward, Jr. Virginia Deartment of Transortation s Maintenance Quality Evaluation Program. In Transortation Research Record 1276, TRB, National Research Council, Washington, D.C., 1990,. 90 96. The oinions and findings are those of the authors and do not necessarily reresent the views of Virginia DOT. The Maintenance and Oerations Management Committee sonsored ublication of this aer.