Calculation of Aggregate Pavement Condition Indices from Damage Data Using Factor Analysis

Transcription

1 214 TRANSPORTATION RESEARCH RECORD 1311 Cacuation of Aggregate Pavement Condition Indices from Damage Data Using Factor Anaysis RoHIT RAMASWAMY AND SuE McNEIL Aggregate pavement condition indices are used by many agencies in the United States and abroad to seect maintenance strategies and program network rehabiitation strategies. These indices are usuay cacuated as weighted sums of severa individua damage measurements such as ength of transverse cracks, rut depth, and roughness. Existing approaches to condition index caibration are reviewed and a statistica procedure for deveoping pavement condition indices from distress measurements using factor anaysis is described. This method is used to reestimate a condition index from the data coected in the AASHO Road Test for caibration of the present serviceabiity index (PSI). The new index is compared with the PSI. The measures used for evauating pavement condition differ depending on the perspective of the evauator. Different terms are used in the condition evauation iterature to refect these perspectives. For exampe, the broady defined terms "distress" or "damage" or an aggregate measure such as "condition" have been used to describe the surface quaity of the pavement and to schedue maintenance based on this quaity. Simiary, the term "serviceabiity" has been used to define the roughness or ride quaity characteristics of the pavement from a user's perspective. Terms ike "skid resistance" describe the pavement condition from a safety perspective. These aggregate evauations of pavement condition are often referred to as indices. Even though these different terms for pavement condition have been identified in the iterature, there has been a tendency to use them interchangeaby, and poicy decisions on pavement mainten mce have not adequatey refected the different characteristics measured by the different indices. However, there is an advantage in being abe to precisey tie a condition index to the specific characteristic of pavement deterioration measured by the index, because maintenance decisions can then be taken to correct that characteristic. For exampe, if a condition index can be defined as roughness reated, then this information can be used to pan strategies that improve the pavement ride quaity. It is therefore desirabe to deveop indices that can be defined in terms of their primary deterioration characteristics rather than in terms of broad and sometimes misunderstood terminoogy. By doing so, it is then possibe to identify the different dimension of deterioration of the pavement and to schedue maintenance R. Ramaswamy, AT&T Be Laboratories, Homde, N.J S. McNei, Department of Civi Engineering, Carnegie-Meon University, Pittsburgh, Pa to correct this deterioration. Factor anaysis techniques are used herein to estimate such indices. The indices are deveoped from the AASHO Road Test data that were used to caibrate the famiiar PSI equation. This procedure is for purposes of easy comparison with existing indices such as the PSI. Another reason for using factor anaysis as a technique is that it does away with the reiance of traditiona indices on inspector judgments for their caibration, if required. Athough experienced inspectors can provide vauabe information on the reative condition of different pavements, it is difficut to evauate the precision of these judgments. Modes deveoped using these evauations may not be as easiy transferabe to other ocations as modes deveoped from data coected through a standardized measurement scheme. The initia modes estimated ony use measured information for the cacuation of the condition index; subsequent modes use the inspector ratings as additiona information, but these can be omitted if there is reason to beieve that these ratings are inaccurate or biased. The factor anaysis modes are therefore not intrinsicay dependent on judgments for their estimation. The foowing section describes some common deterioration indices used in practice. Specificay, the caibration of the PSI equation from AASHO Road Test data and some of the probems associated with its use are discussed aong with some background on methodoogy. The foowing section, which is a mathematica specification of factor anaysis modes, describes estimation methods. Estimation resuts are presented, and finay, concusions. PAVEMENT CONDITION INDICES: DESCRIPTION AND CALIBRATION The basic probem with the caibration of aggregate indices for pavement condition is that it is not possibe to directy measure the condition of a pavement. Athough natura measurements exist for the different components of pavement damage (e.g., area cracked, rut depth, and sope variance) pavement condition itsef is an unobservabe (or atent variabe) and as discussed in the previous section, can be defined in different ways depending on the evauator's perspective. Caibration of aggregate pavement indices is often performed by regressing a measure of serviceabiity or condition against a set of damage measurements. In order to obtain a quantitative measure for condition, experienced pavement inspectors are asked to rate the pavement on an arbitrary

2 Ramaswamy and McNei quantitative scae. The scae of measurements and the inspectors chosen may differ depending on the particuar deterioration characteristics (e.g., surface quaity, structura strength, or safety) that the index is intended to capture. The estimated parameters are the weights assigned to each damage measurement. After caibration, the fitted vaue of the index can be simpy cacuated from future damage me'asurements using the estimated weights. In order to iustrate the form and use of aggregate indices, four exampes are presented. The first and probaby the most widey used in the United States is the present serviceabiity index (PSI). It was deveoped by Carey and Irick (1) as a means of estabishing a faiure condition for the AASHO Road Test in terms of the users' response to pavement condition. It is an approximation to the present serviceabiity rating (PSR), which is the mean vaue of ratings assigned to a pavement on a discrete scae from 0 to 5 ( 5 is a new pavement and 0 represents compete deterioration) by a pane of experienced raters representing highway users. The origina definition is based on the foowing five assumptions: 1. Safe and smooth highways are desirabe; 2. Users' ratings of highways are subjective; 3. Weighted, measured pavement characteristics can be deveoped that reate to the users' subjective evauations; 4. Serviceabiity is the average of a users' evauations; and 5. Performance is the overa serviceabiity history. The third assumption is the basis for deveoping PSI as a mathematica combination of physica measurements of cracking, patching, rut depth, and sope variance to predict PSR. The PSI, on the basis of measured quantities, is both ess expensive to obtain than the PSR and intuitivey more appeaing to engineers. It is used to predict performance over time and is used by the Highway Performance Monitoring System (2) to provide an overa evauation of the U.S. highway system. The second exampe is the pavement condition index (PCI), which was deveoped by the U.S. Army Corps of Engineers at the Construction Engineering Research Laboratory. For fexibe pavements, the PCI is constructed from 19 different damage types and is an aggregate measure of pavement surface damage on a scae from 0 to 100. It is used in the PA VER pavement management system to identify maintenance and rehabiitation aternatives and to forecast pavement condition. This management system has been adopted by severa miitary bases, cities, and counties. The third exampe is a series of indices used in Canada. They are the visua condition index (VCI) or surface damage index, the roughness condition index (RCI), and the structura adequacy index (SAI). Each index is based on a weighted function of observations of pavement damage to give an index on a scae of 1 to 10 (3-5). They are aggregated into the pavement quaity index. They are aso used for street maintenance programming and network rehabiitation programming (6). The fina exampe is a simpe distress index used in Finand (7). It is a weighted, inear function of the area of aigator cracking, ength of ongitudina cracking, ength of transverse cracking, number of hoes, and area of worn surface. This index is then used to determine rehabiitation needs. As discussed in the previous section, athough trained inspectors are abe to make reativey accurate assessments of the aggregate pavement condition, the introduction of a judgmenta measure introduces an uncontroabe arbitrariness into the procedure for caibration. As a resut, these modes need to be used with caution, especiay in ocations different from they were originay estimated. Carey and Irick (1) point this out in their discussion about the PSI concept, and the warning is subsequenty reiterated by Haas and Hudson (5). However, because of the expense and effort of caibrating a new mode for each appication, these imitations have been argey ignored. The probem of transferabiity is magnified in this particuar instance because the sope variance is now measured with a device that is caibrated differenty from the type used in the AASHO Road Test (5). Another probem reates to the ack of statistica information reported with the modes. Because typicay somewhat ad hoc measures have been used to measure and caibrate the modes, information on t-statistics or goodness-of-fit is rarey found in the iterature. Therefore, future users of the mode have no knowedge of how we the mode fits the data, or even if the mode was propery specified. This makes the transferabiity of these modes uncertain as we. In order to iustrate this point, a reestimation of the basic PSI equation for fexibe parameters was conducted to obtain the statistics not reported in the origina iterature. The data, comprising ratings and damage measurements from 74 sections in Iinois, Minnesota, and Indiana, was provided by Carey and Irick (1). The functiona form of the PSI equation was based on transformations of the measurement of sope variance, mean rut depth, and area of cracking and patching deveoped through pots of the data against PSR. The resuts from the reestimation using ordinary east-squared regression are as foows: PSI = S (C + P) RD og 10 (1 + SV) (1) (C + P) = RD 2 og 10 (1 + SV) 215 area of aigator and inear cracking and patching ( ft 2 ); square of rut depth (in. 2 ); and og of sope variance to base 10 ( x 10 6 ). The t-statistics for the coefficients are , , -3.88, and and the R 2 vaue is The coefficients in Equation 1 are the same as those deveoped by Carey and Irick (1) except for the second decima pace. The differences are probaby caused by rounding errors. Athough the fit is good, the I-statistics indicate that the cracking and patching term is not significant. As aso noted (8,9), the main emphasis is on roughness measured in terms of sope variance. However, despite the ack of significance of some of the dependent variabes, this mode has been widey used. The factor anaysis methodoogy, described in detai in the foowing section, seeks to address some of the issues mentioned in this section. The procedure, as mentioned before, does not need inspector ratings for caibration, though this can be incuded as additiona information. Aso, the goodnessof-the-information is used to determine the extent to which

3 216 each measurement contributes to the caibration of the performance index. This provides an anaytica basis for distinguishing between different indices. FACTOR ANALYSIS: AN OVERVIEW A factor anaysis mode describes the covariance reationships among many variabes in terms of a few underying, but unobservabe random quantities caed factors (10). Factor anaysis modes have been widey used in psychometrics for extracting unobservabe measures of quantities such as verba or anaytica abiity from standardized test scores. More recenty, it has been used in engineering appications for identifying uncorreated pavement distress categories for pavement design and ong-range panning (11), and to determine true distress from measurements made by a set of different inspection technoogies (12). Suppose there exist some observed variabes that are grouped by their correations. Then a variabes that are highy correated with each other but are not highy correated with members of other groups can be thought of as measuring a singe underying variabe. A factor anaysis mode is a parametric construct of this concept, and the parameter estimates indicate the extent to which the measured variabes represent the unobserved factors. From the earier discussion, it is cear that the probem of extracting a performance index from severa damage measures can be modeed using the factor anaysis approach. The performance index is the underying unobserved factor, and can be represented by a group of damage measurements. The forma specification is now presented. Specification of a Factor Anaysis Mode for Highway Pavements For purposes of iustration, a singe atent factor S is assumed to be represented by three measurements of damage, Ii, I 2, and I 3 Ceary, it is possibe to have more than one unobserved factor represented by the same set of measurements. The specification assumes that each observed variabe can be expressed as a inear function of the atent factor pus an error term. In agebraic terms, this can be written as I 1, I 2, and I 3 = measurements of damage, S = unknown factor, Ai. A 2, and A 3 = factor oadings, and e 1, e 2, and e 3 = error terms. (2a) (2b) (2c) The factor oadings refect the extent to which each measured variabe represents the atent factor. This can be seen TRANSPORTATION RESEARCH RECORD 1311 by examining the variance of the observed variabes of Equation 2. Considering the first of the three equations, for exampe, Equation 3 partitions the variance of the observed measurement into two parts: the variance of the atent factor mutipied by Af and the variance of the error term. Anaogous to a regression equation, a goodness of fit statistic for Equation 3 is the ratio of expained variance [that is, Af Var (S)] to the variance of Ii. As Ai increases in magnitude, the expained variance term increases and the corresponding measurement pays a greater part in expaining the atent factor. Estimation of the Parameters of the Factor Anaysis Mode The parameters A 1, A2, and A 3 of Equation 2 are estimated by comparing the observed covariance matrix of the measured variabes with a cacuated covariance matrix expressed as a function of the parameters. To iustrate this, consider Equations 2a and 2b. Assuming S and e are independent, the covariance between Ii and 1 2 can be cacuated as foows : Cov [(>.. 1 S + Ei)(A2S+ Ez)] (3) A 1 A 2 Var (S) + Cov (E 1, E 2 ) (4) If the variance of the atent factor is denoted by iii, and the error term covariance by 0 12, then Equation 4 can be written as Comparing Equation S with the observed covariance between 1 1 and 1 2 cacuated from the sampe data provides an equation in terms of A 1, A 2, iii, and 0. Simiar equations can be written for six observed variances and covariances between Ii, I 2, and I 3 Obviousy, ony six parameters can be estimated from these equations; the others have to be set to zero. The choice of which variabes to set to zero depends on the assumptions made from a priori knowedge about the independence of error terms in the mode specification; for exampe, in Equation S, if there is no reason to beieve that the measurement errors of 1 1 and I 2 are correated, then 0 12 can be set to zero. In addition to setting a but six parameters to zero, one parameter for each factor has to be fixed to set the scae of the mode. From Equation S, it can be seen that for any nonzero constant M, AiM and A 2 M wi satisfy the equation as we as A 1 and A 2 There are therefore infinite soutions to the factor anaysis probem uness one of the parameters is fixed. Typicay, one of the AS (for exampe, A 1 ) is set to a fixed vaue of 1. The other parameters are then cacuated reative to this vaue. In practice, the parameters are estimated by an iterative east-squares-ike procedure that minimizes the weighted squared distance between the observed and cacuated covariance matrices. If the observed covariance matrix is denoted (S)

4 Ramaswamy and McNei by V and the cacuated covariance matrix by, then the objective function F to be minimized is given by F = [(v - : )' w- 1 cv -!)J V = observed covariance matrix of the parameters, : = cacuated covariance matrix, and W = a matrix of weights. The estimator is caed the "asymptotic distribution free" (ADF) estimator and produces consistent estimates irrespective of the samping distribution of /. If W is set to be an estimate of the covariance matrix of V (that is, products of second and fourth order terms in/), then the estimates produced are aso best in the sense of having minimum variance. Further detais on factor anaysis modes and the estimation procedure have been provided ese (10,13,14). Extraction of Factor Scores Estimation of the parameters of Equation 2 does not produce a vaue for the atent factor S. This vaue is obtained by an ad hoc regression-ike procedure after the parameters have been estimated. In order to compare the factor anaysis procedure with an existing mode such as the PSI mode, it is necessary to express the factor S in terms of its associated measurements I. Such a mode can be specified as foows: S =a + v (7) a is a vector of parameters, and v is an error term. Equation 7 ooks ike a regression mode, and so an expression for a can be written anaogous to a traditiona east squares estimator as foows: a = Var (I)- 1 Cov (I,S) (8) For each observation (or pavement section), given a vector of damage I, the vaue of Scan now be cacuated from Equation 7. This is the vaue of the atent pavement condition for that section. The variance and covariance terms of Equation 2 can be cacuated after the parameters have been estimated from equations such as Equation 5. Further detai on the extraction procedure has been provided ese (15). MODEL RESULTS In order to compare the factor anaysis mode resuts with the PSI equation, the first specification given by Equation 1 (referred to as MODEL) uses the same measurements as the PSI [that is, (C + P) 112, RD 2 and og 10 (1 + SY)] as determinants of the unknown factor S 1 Comparison of this mode with the PSI indicates that the factor S 1 is in fact sighty different from the PSI. The second specification given in Equation 13 and referred to as MODEL2, is an attempt to produce a PSI-ike factor; this is done by adding the PSR as an additiona measurement to the specification of MODEL. (6) The factor S 2 produced from this mode is highy correated with the PSI. The fact that two different factors, S 1 and S 2, can be extracted from the data indicates that a two-factor specification is a more appropriate mode. This specification, caed MODEL3, is given in Equation 15. MODEL: Factor Anaysis Mode with PSI Measurements The specification of MODEL is as foows : cp, /RD sv = measurements for (C + P) 112, RD 2 and og 10 (1 + SV), respectivey; S 1 = unknown factor; Acp, ARD and Asv = parameters to be estimated, and Ecp, ERo and Esv = error terms. Computationa requirements necessitate a transformation of the measurements so that the diagona eements of the observed covariance matrix V are a of the same magnitude. The foowing transformations are used in this specification of MODEL: og 10 (1 + SV) (10.0) 112 RD 2 * (9) ( C + P) 0 5/10.0 (10) The parameter estimates are presented in Tabe 1. As discussed in the previous section, one of the parameters needs to be fixed to set the scae for the mode. In Tabe 1, Asv is set to 1, and the other parameters are estimated reative to this fixed vaue. There is no singe standard method that can be used to interpret the parameter estimates of Tabe 1. The magnitudes of the parameters are not meaningfu because they are dependent on the scae of the individua measurements. Simiary, the reported t-statistic can ony be used as a broad guideine for statistica significance if the data come from a distribution that is Kurtose, because the distribution of the parameter estimates is unknown in this case (14). The signs of the parameter estimates and the fit of each equation, reported in TABLE 1 PARAMETER ESTIMATES FOR MODEL Parameter Estimate (t-statistic R2 Asv 1.00 (-) 0.58 ),.RD (-0.51) Acp 0.70 (0.97) 0.72

5 218 Tabe 1 as the R 2 vaue, provide insight into the nature of the unknown factor S 1 The sign of the rut depth parameter is negative, indicating that the pavement improves in the dimension of S 1 as the rut depth increases. However, the ow I-statistic and negigibe fit impy no contribution of the rut depth measurement to S,. The best fit is obtained for the cracking equation, indicating that the factor S 1 probaby describes some underying index that is a mixture of cracking and sope variance with an emphasis on cracking. In this way, it differs from the PSI, which paces emphasis on the sope variance. This difference between S, and the PSI can aso be seen when the factor is expressed as a function of the damage components in an equation simiar to the PSI reationship using the extraction method described in Section 3. The positive signs of Xcr and Xsv impy that as the measurements fer and sv increase, the vaue of S, increases. In other words, increasing vaues of S 1 refect decreasing condition of the pavement. Because this is opposite to the direction of the PSI, the negative PSI (referred to as - PSI) is used for comparison. The PSI equation (Equation 1) aso needs to be transformed so that the variabes in both the PSI and the factor equation have the same scae. When this is done, the foowing equations are obtained: - PSI = sv /RD + O. cp (11) S 1 = sv /Ro cr (12) - PSI and S, represent the fitted vaues and the other variabes have been defined before. As is evident from these equations, the ratio of the sope variance coefficient to the cracking coefficient is approximatey 10 in Equation 11 and is 0.3 in Equation 12. This indicates that the PSI equation paces a greater reative importance on the sope variance measurement than the atent factor equation. This difference is aso shown in Figure 1, which is a scatter pot of - PSI against S 1 For good-condition pavements, there is reativey cose correation, probaby because pavements in good condition have ow cracking and ow roughness. For more deteriorated pavements, a higher degree of scatter is observed. Factor anaysis of the PSI measurements therefore produce a factor refecting different underying characteristics than the PSI. S 1 has more to do with the structura strength of the pavement than with the ride quaity. In order to estimate a roughness-reated factor, the pavement rating, PSR, is incuded in the mode as an additiona measurement. This specification, caed MODEL2, is now described. MODEL2: Factor Anaysis Mode Incuding PSR The use of rating information such as PSR is vauabe as it refects engineering judgment and fied experience. This information has been integrated into the second mode. The specification of MODEL2 is simiar to that of MODEL, except for an additiona measurement equation for the PSR. The compete specification can be written as foows: TRANSPORTATION RESEARCH RECORD 1311 (13) IrsR = measurements for PSR, S 2 = unknown factor, Acr XRD Asv. and ApsR = parameters to be estimated, and Ecp, erd e 5 v, and ersr = error terms. The parameter estimates obtained for this mode are presented in Tabe 2. From Tabe 2, it can be seen that the factor S 2 paces an emphasis on the roughness-reated measurements. This is evident from the fit of the sope variance and PSR equations. Rut depth has no effect on S 2 as the cracking and patching has a smaer, ess significant effect. S 2 can therefore be referred to as a ride-quaity-reated factor. S 2 can be expressed as a function of its constituent measurements. S 2 = sv Ro cp rsR (14) It is evident from this equation that the rut depth and cracking terms are ess signifisant than the roughness terms (compare with Equation 12). S 2 is more simiar to the PSI (compare with Equation 11) than S,. This simiarity can aso be seen from the scatter pot of Figure 2 that pots the fitted vaue of PSI against S 2 Compared with Figure 1, Figure 2 shows a much tighter reationship. MODEL and MODEL2 have identified the presence of two underying factors: (a) a structure-reated factor that is measured argey by the extent of cracking, and (b) a ridequaity-reated factor that is measured by the extent of pavement roughness. Even though the two factors have different emphases, they are highy correated with a correation coefficient of The high correation is understandabe, because in genera poor ride quaity (or high roughness) is accompanied by a high eve of cracking and vice versa. In order to make the factor from MODEL2 more comparabe to the PSI, the PSR term in Equation 14 was dropped and a modified factor was cacuated that used the same measurements as the PSI: S2x = fsv TRD fcp (15) Figure 3 is a scatter pot of the modified factor Six and the fitted vaue of - PSI. Simiar to Figure 2, the pot shows a much smaer degree of scatter than Figure 1. The atent variabe of MODEL2 is therefore much coser to the deterioration characteristic represented by the PSI. The anaysis of MODEL and MODEL2 indicates that a more reaistic specification shoud incude both factors in the same mode. This eads to a specification of a two-factor mode, MODEL3, which is described in the foowing section.

6 Ramaswamy and McNei DI ""'4.a ID. ID c: DI ID.J J DI LL :.-- ;._;...,, j : i i! i I I i I,, i I : I t i i! I I I r- - 1 :_,:_.. H - u -... t :.: i I : _;! '".o u o o o o "''' ' ''''''i ' ' '''''' ' '' '' ' '''' ' '''""'''''''""'''' ' '!" :...,,,,,,,.,,..,_., ''"' "!"'"'"'"'''''''''''''''''"'''''"'"'' i.! :!.. ::-:.. ::.. 1 : ' - -j ;- u.. ;" FIGURE I A -PSI o A Scatter pot of S 1 versus - PSI for cracking-reated factor. TABLE 2 PARAMETER ESTIMATES FOR MODE1-2 Parameter Estimate (t statistc) R2 Asv 1.00 ( ) 0.98 D ( 0.62) 0,01 >.cp 0.36 (6.01) 0.36 A.psR 0.67 (9.61) 0.85 MODEL3: The Two-Factor Mode The specification of the two-factor mode differs sighty from the specification of the one-factor modes described in the previous sections. In addition to the difference in specification, this mode is not directy comparabe to the PSI or the atent variabes S 1 and S 2 because the measurements are different as we. Because the rut depth measurement did not contribute to either atent variabe, it was dropped from consideration. Instead, the rut depth variance, which is a measurement avaiabe in the origina road test data set, was used. The rut depth variance divided by is referred to as I Rv In the two-factor mode, a roughness-reated factor S 31 and a cracking-reated factor S 32 are specified. The sope variance and PSR are assumed to be measurements for S 31 and the rut depth variance and cracking and patching are assumed to be the measurements for S 32 The specification is as foows : sv = As v1s31 + Esv /RV= ARv1S32 + ERv cp = Ac p2s32 + Ec p /PSR = ApsR1S31 + EpSR (16) In Equation 16, it is assumed that the cracking and rut depth measurements ony affect the cracking-reated atent variabe, as the sope variance and PSR measurements affect ony the roughness-reated atent variabe. However, the two atent variabes themseves may not be independent,

7 220 - df), m f.d 111 L. 111 :::>.µ c m.µ 111..J "D m.µ.µ u. 4 2 e -2-4 TRANSPORTATION RESEARCH RECORD !..,.. 1. r I... : 1 : t O&O O<OOOOOo o OO-OOOO... j..,.+oooo O H "'' Hoooo n H o o ooo OO oo- O... -! oo. ; : :! :! i : I i.. : c I <!. : :. :...;.... _.. :j...!.... '! ; i ; i ::"": r ;-...-._.... ; : ;! : 1! i ; r !. 1 1! H... r! -4-2 e 2 4 /\ -PSI FIGURE 2 Scatter pot of S 2 versus -PSI for roughness-reated factor. because the onset of cracking affects the pavement ride quaity. It is therefore assumed that correations exist between S 3 J and S 32 The measurements of sope variance, cracking, and rut depth are made by different instruments, so the measurement error terms are assumed to be uncorreated. In order to set the mode scae, Asvi and AcP2 are set to 1. The mode resuts are presented in Tabe 3. Obviousy, other assumptions about the mode structure give rise to other specifications. Severa aternate mode specifications of MODEL3 were tested as part of this study. For the purposes of iustration, ony the simpest meaningfu specification has been presented here. A the estimates in Tabe 3 have the expected sign and are significant. The fit of the two roughness measurement equations is high and the fit of the cracking and rut depth equations is moderate, but higher than the vaues obtained in MODEL2. These resuts indicate that the two-factor mode describes the Road Test data better than either of the one-factor modes. Impications for Setting Maintenance Priorities A practica est fur the difference between the PSI and the atent variabes of MODEL and MODEL2 is to study how these indices differ in the assignment of priority ists for maintenance. This can be measured by ranking each of the indices and testing whether the ranking sequence is the same under a the indices. The Spearman's rank order correation coefficient is a statistic that measures the coseness between two ranked ists. A vaue of 1.0 indicates that the ranking is identica; vaues coser to 0 indicate increasing, rando1!1ness. The rank order correation between - PSI and SJ was 0.88, as that between - PSI and S 2 was This indicates that S 2 and the PSI produce amost identica rankings, and SJ is fairy cose as we. The picture changes somewhat when ony the poorer pavements are considered. For pavements with - PSI greater than 0 (see Figure 1) Lhe correaiun wih S 1 dropped to 0.67, as the correation with S 2 was This indicates that as the pavement condition decreases, ranking pavements for maintenance by different criteria may give rise to different maintenance priorities. It is important to consider this whie making maintenance decisions. CONCLUSION The traditiona PSI equation, of the form presented in Equation 1, has been in use for 30 years. Aternate methods for

8 Ramaswamy and McNei 221 OJ..D QI L QI :> c: OJ QI...J 1J OJ L r r... T ;! I i! I.. I =! r :.' !- :: -, 1... I :-.... r '......;-., I,, I I... I : - : '.1 r ' i i :. I 1 ;. :! n - --.,.. H H... +<.. I I " -PSI FIGURE 3 Scatter pot of S 2 x versus - PSI for S 2 without PSR measurement. TABLE 3 ESTIMATION RESULTS FOR MODEL3 Parameter Estimate (I-statistic) R2 Asv (-) 0.88 ARD2 1.16(3.88) 0.54 P ( ) 0.41 ApSR (17.95) 0.92 anayzing the data can be used to caibrate the PSI equation. Rather than specifying an a priori mode inking the PSR to the damage components, the factor anaysis method examines the correations between the measured damage components. From this kind of anaysis, it appears that these measurements by themseves are more highy correated with a cracking-type performance variabe rather than with a roughness-type index such as the PSI. In order to produce a PSI-ike index, the PSR data were incuded in the measurement set. The existence of two different underying deterioration characteristics indicates that merey substituting measured vaues of damage into the traditiona PSI equation and using the PSI as the soe determinant of pavement condition for scheduing maintenance activities may not be accurate. This is not to say that the PSI equation is incorrect and shoud not be used. The roughness-reated factors of MODEL and MODEL2 are highy correated with the PSI, and so the PSI is a good measure of the ride quaity characteristics of the pavement. However, other factors reated to cracking or structura strength can aso be identified in the data, and maintenance activities need to be performed to correct these aspects of deterioration as we, especiay for pavements in worse condition. It has been

9 222 reported before in the pavement deterioration iterature that it is necessary to use mutipe performance indices to capture a aspects of deterioration, but since the different indices were caibrated differenty, often with different data, there was no anaytica basis for determining exacty which indices address which deterioration characteristics, and consequenty how many indices form a sufficient set. The methodoogy presented aows for this determination. Some additiona research is required in severa areas. First, in the area of mutipe factor modes other specifications shoud be expored. Aso, if an index of this type is adopted, additiona research is required to reate the vaue of the index to maintenance and rehabiitation activities. However, it appears that the use of the factor anaysis methodoogy has the potentia for producing condition indices that provide vauabe information to practitioners in the fied. REFERENCES I. W. N. Carey and P. E. Irick. The Pavement Serviceabiity Performance Concept. Buetin 250, HRB, Nationa Research Counci, Washington, D.C., The Status of the Nation's Highways and Bridges: Conditions and Performance and Highway Bridge Repacement and Rehabiitation Program. Technica Report, FHWA, U.S. Department of Transportation, Washington, D.C., K. Anderson. Pavement Surface Condition Rating Systems. Technica Report, Roads and Transport Association of Canada, Ottawa, R. Haas. Notes for Short Course on Pavement Management for Municipa and Highway Engineers. Cass Notes, Canadian Society for Civi Engineers, Montrea, May TRANSPORTATION RESEARCH RECORD R. Haas and W. R. Hudson. Pavement Management Systems. McGraw-Hi, New York, B. Marcotte, A. Cheetham, M. A. Karan and R. Haas. Aberta's Municipa Pavement Management System, In R. Kher (ed.), Second North American Conference on Managing Pavements, Ministry of Transportation, Ontario, Canada, Nov. 1987, pp H. Jamsa. Pavement Management System at District Leve. In R. Kher (ed.), Second North American Conference on Managing Pavements, Ministry of Transportation, Ontario, Canada, Nov. 1987, pp E. J. Yoder and M. W. Witczak. Principes of Pavement Design. Wiey, New York, F. L. Mannering and W. P. Kiareski. Principes of Highway Engineering and Traffic Anaysis. Wiey, New York, R. A. Johnson and D. W. Wichern. Appied Mutivariate Statistica Anaysis. Prentice-Ha, Engewood Ciffs, N.J., J. J. Hajek and R. C. G. Haas. Factor Anaysis of Pavement Distresses for Surface Condition Predictions. In Transportation Research Record 1117, TRB, Nationa Research Counci, Washington, D.C., 1988, pp F. Humpick. Theory and Methods of Anayzing Infrastructure Inspection Output: Appication to Highway Surface Condition Evauation. Ph.D. dissertation, Department of Civi Engineering, Massachusetts Institute of Technoogy, Cambridge, Aug B. S. Everitt. An Introduction to Latent Variabe Modes. Chapman and Ha, London, Engand, M. W. Browne. Asymptoticay Distribution Free Estimates for the Anaysis of Covariance Structures. British Journa of Mathematica and Statistica Psychoogy, Vo. 37, 1984, pp R. Ramaswamy. Estimation of Latent Performance from Damage Measurements. Ph.D. dissertation, Department of Civi Engineering, Massachusetts Institute of Technoogy, Cambridge, June Pubication of this paper sponsored by Committee on Pavement Management Systems.