A Statistical Analysis of Well Failures in Baltimore County

Transcription

1 Jurnal f Data Siene 7(9), A Statistial Analysis f Well Failures in Baltimre Cunty Xiayin Wang 1 and Kevin W. Kepenik 1 Twsn University, Twsn and Baltimre Cunty Department f Envirnmental Prtetin and Resure Management Abstrat: A statistial evaluatin f the Baltimre Cunty water well database is perfrmed t gain insight n the sustainability f dmesti supply wells in rystalline bedrk aquifers ver the last 15 years. Variables ptentially related t well yield that are nsidered inluded well nstrutin, gelgy, well depth, and stati water level. A variety f statistial methds are utilized t assess rrelatin and signifiane frm a database f apprximately,5 wells, and a lgisti regressin mdel is develped t predit the prbability f well failure by gelgy type. Results f a tw-way analysis f variane tehnique indiate that the average well depth and yield are statistially different amng the established gelgy grups, and between failed and nn-failed wells. The stati water level is shwn t be statistially different amng the gelgy grups but nt amng failed and nn-failed wells. A lgisti regressin mdel results that well yield is the mst influential variable fr prediting well failure. Stati water level and well depth was nt fund t be signifiant in prediting well failure. Key wrds: ANOVA, Bx-Cx transfrmatin, influene analysis, lgisti regressin, residual, preditin. 1. Intrdutin The Baltimre Cunty Master Plan 1 (Baltimre Cunty Cunil, ) inrprates the designatin f tw land management areas: the urban area and the rural area. The bundary separating these tw land management areas is alled the Urban-Rural Demaratin Line (URDL). The urban areas have publi water and sewer infrastruture, and the rural areas rely n individual private wells and septi systems. Apprximately, peple live in the rural areas where the gelgy nsists f a grup f rystalline rk aquifers (metamrphi and igneus) that are mmnly referred t as the Piedmnt physigraphi prvine. Grund water urrene (yield) within the rystalline rks is extremely variable, and there are nted frmatins where there is relatively pr well prdutivity (Nutter

2 11 Xiayin Wang and Kevin W. Kepenik and Otten, 199). The Piedmnt aquifers are als unnfined, and therefre, suseptible t ntaminatin frm land use praties. Given the nature f the gelgy, it is imprtant that new develpment in these rural areas be arefully evaluated t ensure that dmesti well water supplies are reasnably prteted and sustainable. The Baltimre Cunty Department f Envirnmental Prtetin and Resure Management (DEPRM) is harged with the respnsibility f ensuring safe and adequate water supplies fr prpsed develpment in Baltimre Cunty utilizing wells fr their dmesti water needs. DEPRM nsiders the existing setbak requirements, well nstrutin regulatins, and develpment regulatins t be reasnably adequate t prtet existing and prpsed water supplies. Hwever, there is ntinuus nern frm residents as t whether r nt prpsed new develpment in the rural areas will have adverse impats n existing land uses. Therefre, gaining a better understanding f well yield sustainability and whether r nt well yield failure in the Piedmnt an be pratially predited is f great interest t the regulatry, develpment, and residential mmunities in Baltimre Cunty. The findings presented in this study may be used t address sme f the many questins that have arisen ver the years nerning whether existing regulatins and praties are suffiient and effetive in prteting and preserving dmesti water well supplies. In the setins t fllw, we will desribe the data set that will be used in this study, analyze sme harateristis f the wells, and develp a lgistis regressin mdel t predit the well failure prbability. We will disuss influene diagnstis t determine the mdel s auray, and als assess the predit pwer f the estimated mdel. Finally, we will disuss the ptential ramifiatins f hw the data might be used t hange and/r supprt existing regulatins gverning rural develpment.. Data Struture DEPRM manages all the well rerds fr drilling in Baltimre Cunty, whih inludes infrmatin abut well latins, well usage, well yield, stati water level (distane frm the land surfae t the depth f water in the well), and ttal well depth. There are different gelgi frmatins in Baltimre Cunty. Hwever, fr the purpses f this study, the Piedmnt frmatins are ategrized int eight gelgi grups: Gneiss, Granite, Mafi, Marble, Lh Raven Shist, Prettyby Shist, Other Shists, and Serpentine. Table 1 displays the lassifiatin f the gelgy grups and the rrespnding ttal study area. DEPRM uses a Gegraphi Infrmatin System (GIS) t rrelate a gelgy grup with the latin f eah well that has a knwn address. Althugh database maintains rerds fr apprximately 1, dmesti wells as f February 5, nly,3 uld

3 Statistial Analysis f Well Failures 113 be gegraphially lated and mathed t a gelgy grup beause the database des nt have aurate address infrmatin fr the thers. This reflets the apprximate number f dmesti wells that have been mpleted sine 199, when address infrmatin was added t the well database. Hwever, it des nt reflet any knwn bias tward well gelgy type, yield, depth, SWL, r well failure. Table 1: Gruping f gelgi frmatins and well distributins Grup Title Frmatins inluded in grup # f failed wells (Area) / # f wells Gneiss Baltimre Gneiss, Franklinville Gneiss, 17/1,5 (3,11 Are) Gunpwder Gneiss,Setters Gneiss, (1.9%) Perry Hall Gneiss, Sykesville Gneiss, Cld Spring Gneiss, Slaughterhuse Gneiss Granite Ellitt City Granite, Wdstk Granite / (1,11 Are) (7.1%) Lh Raven Shist Lh Raven Shist 3/3,733 (3,99 Are) (11.3%) Mafi Mt. Washingtn Amphiblite, 1/33 (1, Are) Hllfield Layered Ultramafite, (3.%) Bradshaw Layered Amphiblite, James Run-Druid Hill Amphiblite, Raspeburg Amphiblite Marble Ckeysville Marble, Hydes Marble 9/39 (3,151 Are) (9.39%) Prettyby Shist Prettyby Shist /1,3 (3,353 Are) =.% Other Shists Pleasant Grve Shist, Sykesville Shist, /933 (3,753 Are) Oella Frmatin, Piney Run Frmatin, =.93% Setters Shist Serpentine Serpentine Ultamafite 3/39 (3,3 Are) =7.9% Amng the,3 wells, there are ttal 77 (9%) failed wells. Table 1 displays the ratis f the number f failed wells t the number f wells in eah gelgy grup, with the resulting perentages being shwn in parentheses. The Lh Raven Shist wells have the highest well failure rate f 11.%, and the Mafi wells have the lwest well failures rate f 3.9%. It shuld als be nted that the relatively small number f wells in the Granite and Serpentine grups might lessen the signifiane f statistial inferenes fr these tw gelgy grups. 3. Data Analysis 3.1 Crrelatin analysis The first questin we wuld like t answer is that if there is a statistially signifiant rrelatin exists between gelgy type and the well failure. A Chisquare test fr independeny has the results f χ = 13.9 with df = 7 and

4 11 Xiayin Wang and Kevin W. Kepenik p value <.1. This implies that there is a statistially signifiant assiatin between gelgy type and failed/nn-failed wells. 3. Tw-way ANOVA In the database, there is als infrmatin abut the harateristis f wells, suh as well depth, stati water level and well yield. Table displays the summary statistis f these measures f failed and nn-failed wells in eah gelgy grup. The average well depth, stati water level and well yield are different amng gelgy grups, and are different between failed and nn-failed wells. Tw-way analysis f variane tehnique is applied t study the differene f these measures amng the gelgy grups, and between the failed and nn-failed wells, where the main effets are ge-grup fr the gelgy grups, and respnse with fr failed ( 1 ) and nn-failed ( ) wells. Due t the missing values in the database, nly, 99 and 7 wells are used respetively in the analysis f well depth, stati water level and well yield. Table : Average (standard deviatin) f well depth, stati water level and yield Ge-grup depth (ft) swl (ft) yield (1galln/min) Gneiss Nn-Failed 55.7 (115.31) 3.5 (1.3) 9.7 (7.3) Failed (1.5) 3. (15.). (.1) Granite Nn-Failed 17.9 (.) 9.1 (1.) 1.3 (9.5) Failed 5. (1.7).5 (.7). (9.9) Lh Raven Nn-Failed 31.5 (13.) 39. (1.). (.) Shist Failed 35.5 (15.77).53 (15.).1 (.17) Mafis Nn-Failed 3. (15.5) 9.5 (13.7) 9.9 (7.79) Failed 3. (19.) 3.7 (1.). (.1) Marble Nn-Failed 7.1 (1.71) 33.3 (1.93) 1. (1.33) Failed 7. (17.1) 3.95 (1.93) 9. (.) Pretty by Nn-Failed 55.3 (1.1) 3.35 (15.).3 (.5) Shist Failed 9.5 (1.9) 5.39 (1.3) 5.7 (5.3) Other Shists Nn-Failed. (117.5).9 (1.) 9.1 (7.5) Failed 9.5 (1.9) 3. (1.) 5.3 (.1) Serpentine Nn-Failed 1.7 (1.7) (19.1) 1.5 (9.1) Failed.7 (5.33) 3 (na) 5.3 (3.5) Starting frm a full mdel with bth main and interatin effets, the results reveal that interatin effets are nt statistially signifiant. Therefre, we applied an analysis with the tw main effets nly. Hwever, the residual analysis shws a ertain degree f disagreement with the equal errr variane and the nrmality f errr assumptins, see Figure 1(a) the residual plts in part, and (b) nrmal prbability plts. T remedy these departures frm the mdel assumptins, we need t apply transfrmatins n the respnse variable. It is ften

5 Statistial Analysis f Well Failures 115 diffiult t determine frm residual plts whih transfrmatin is mst apprpriate. The Bx-Cx predure autmatially identifies a transfrmatin frm a family f pwer funtins, and is the mst ppular used predure. The Bx-Cx transfrmatin with the ptimal λ value prvided by SAS is applied t the data. The residual plts after Bx-Cx transfrmatin in Figure 1() shw that the errr variane appear t be mre stable, and the nrmal prbability plts after Bx-Cx transfrmatin in Figure 1(d) fall rughly n straight lines. The test results fr equal means f well depth, stati water level and well yield amng gelgy grups are illustrated in Table 3. It nfirms that the average well depth and yield are nt the same amng the gelgy grups, nr between the failed and nn-failed wells. The data set des nt prvide enugh evidene t nlude that the stati water level is different between failed and nn-failed wells, but differenes amng the gelgy grups are statistially signifiant. studentized residuals - 1 studentized residuals - studentized residuals predit yield predit depth predit SWL yiled depth - SWL Quantiles f Standard Nrmal - - Quantiles f Standard Nrmal - - Quantiles f Standard Nrmal studentized residuals - - studentized residuals - - studentized residuals predit yield predit depth predit SWL yiled - - depth SWL Quantiles f Standard Nrmal - - Quantiles f Standard Nrmal - - Quantiles f Standard Nrmal Figure 1: Nrmal Prbability Plts and Studentized Residual Plts (a) Studentized Residual Plts Befre Bx-Cx Transfrmatin (b) Nrmal Prbability Plts Befre Bx-Cx Transfrmatin () Studentized Residual Plts After Bx-Cx Transfrmatin (d) Nrmal Prbability Plts After Bx-Cx Transfrmatin

6 11 Xiayin Wang and Kevin W. Kepenik Table 3: Tw-way analysis f variane f well depth, stati water level and yield depth SWL yield F p-value F p-value F p-value Ge-grup.7 (<.1) 3.39 (<.1) 7.7 (<.1) Failed/Nn-Failed.33 (<.1) (<.1) Tukey-Kramer tehnique is a well-knwn predure used t perfrm pair-wise mparisns simultaneusly (Neter, et. 199). Tukey s pair-wise multiple mparisn shws that the wells in Lh Raven Shist are deeper and have less yield, the wells in the Mafi are shallwer, and the wells in the Marble have higher yield than thse in ther gelgy grups. The average stati water levels f wells are different between mst f the gelgy grups. The majrity f test results regarding the gelgy grups f Granite and Serpentine are nt statistially signifiant due t small data rerds. 3.3 Lgisti regressin Lgisti regressin mdels are the mst mmnly used prbabilisti mdels fr a binary (suess-failure) respnse variable suh as a yes/n questin. It has wide appliatins in bimedial fields, genetis, reliability engineering experiments, sial siene researh, business and envirnmental studies. A lgisti regressin mdel is develped using the well data frm DEPRM fr the purpses f estimating the well failure prbability related t ertain variables. Table : Summary f stepwise seletin Step Effet DF Number Sre p-value Entered Remved in Chi-Square 1 Yield <.1 Ge-Grup <.1 3 Yield*Ge-Grup Fr this study, we nsidered fur main fatrs in the mdel; well depth, stati water level, well yield, and gelgy grup, as well as the 11 interatin effets amng them. In rder t find the mst effiient mdel, a stepwise autmati searh predure with.5 level f signifiane fr bth entering and remving, is applied t identify the best subset f useful effets t be inluded in the final mdel. The summary f mdel seletin results is displayed in Table. The utme mdel inludes tw main effets, well yield and gelgy grup. Therefre, the final lgisti regressin mdel an be written as p ij lg( ) = α + α i + β (yield ij ) + β i (yield ij ) + ɛ ij, 1 p ij

7 Statistial Analysis f Well Failures 117 where i represents the ge-grups with 1 fr Gneiss, fr Granite, 3 fr Mafi, fr Marble, 5 fr Lh Raven Shist, fr Prettyby Shist, 7 fr all ther shist, and fr Serpentine; j represents eah well, and p ij represents the prbability f failure fr the jth well in the ith gelgy grup. Here α is a baseline r average lg(dds) fr all the ge-grups when the yield equals t. It is nt imprtant that a well having yield equals t be realisti; rather α represents a referene pint, and α i is the deviatins frm α due t the effet f ge-grup i; β is a baseline r average derease f lg(dds) fr every inrease f 1 galln/min in yield, and β i is the deviatin frm β due t the effet f ge-grup i. The assumptins fr the mdel are as fllws: α i = ; i=1 β i = ; i=1 the randm errr mpnent f the mdel, ɛ ijs, are independent and idential nrmal distributins with mean and variane 1. The statistial sftware SAS (Allisn, 1; Cdy& Smith 5) was used t perfrm the estimates f these parameters. With the estimated the parameters, we have the equatins that an be used t predit the well failure prbability, p, based n the initial yield and the gelgy grup, see Table 5. A plt f eah equatin, shwn in Figure, reveals that all f the gelgy grups have an expnential derease in the prbability f well failure with inreasing yield. At lw yields (1-3 gpm), in partiular, the rate f predited well failure ranges nsiderably by gelgy type. It is interesting t nte that the Mafi and Prettyby Shist wells shw a signifiantly lwer prbability f well failure at the minimum allwable well yield even thugh the average yield fr bth f the gelgy types is lwer than nearly all ther gelgy types with the exeptin f Lh Raven Shist. The Marble and Granite gelgy grups shw a markedly slwer deline than ther gelgy grups. In fat, at well yields abve.33 gpm, the Marble bemes the gelgy grup with the highest prbability f well failure. The reasn fr this differene is nt exatly lear, but in the ase f the Marble, it may be due t gelgi reasns. Fr instane, the presene f relatively large subsurfae slutin hannels is knwn t exist in the Marble aquifers and is nsidered ne f the primary reasns fr the bserved high well yields in this gelgy grup. These slutin hannels may asinally llapse r beme filled with sediment, thereby reduing what was a high yielding well int a nn-prdutive well. As mentined earlier, the relatively small data set fr the Granite uld limit the mdels reliability fr this gelgy type. The predited prbabilities and dds f

8 11 Xiayin Wang and Kevin W. Kepenik well failure at tw speifi amunt f well yield, 1 gpm (minimum allwable well yield) and 1 gpm, are listed in Table 5. Well failure prbability Gneiss Granite Lh Raven Shist Mafis Marble Pretty By Shist Other Shist Sepentine yield (galln/min) Figure : Predited well failure prbabilities

9 Statistial Analysis f Well Failures 119 Table 5: Predited prbabilities f well failure prbabilities and dds Ge-grup Equatin fr 1 galln/min 1 galln/min failure prbability Prbability Odd Prbability Odd Gneiss Serpentine Lh Raven Shist Marble Other Shists Granite Pretty by Shist Mafi exp( yield) 1+exp( yield) 3.9% 31.%.%.3% exp( yield) 1+exp( yield) 1.% 7.5%.39%.59% exp( yield) 1+exp( yield) 1.1% 1.97%.79% 7.% exp( yield) 1+exp( yield) 13.3% 1.9% 9.3% 1.% exp( yield) 1+exp( yield) 1.5% 11.7% 3.9% 3.% exp( yield) 1+exp( yield) 9.5% 1.93%.7% 7.3% exp( yield) 1+exp( yield) 7.59%.1% 3.% 3.31% exp( yield) 1+exp( yield).57% 7.3% 3.15% 3.5%. Residual Analysis and Influene Diagnstis It is always very imprtant t examine the utliers and influential bservatins in the data t refine the mdel. The estimated mdel uld be quite different if there is an utlier with a large influene. Plts f residuals against explanatry variables and the predited prbabilities are very useful tls t identify utliers. There are tw sets f plts in Figure 3. The first set, part (a) nsists f satter plts f tw types f residuals, whih are the deviane residuals and the Pearsn residuals, against well yield, and the predited well failure prbabilities. In eah plt, the residuals are lustered int tw grups. The upper grup f residuals is frm the nn-failed wells, and the lwer grup is frm failed wells. N bvius utlier is exhibited in the satter plt f deviane residuals with well yield r the prediated well failure prbabilities. Hwever, the satter plts f the Pearsn residuals indiate that ne bservatin with a high value f greater than 1 might be an utlier. In rder t identify this ptential utlier, satter plts f the Pearsn residuals against well yield f eah gelgy grups were nstruted, see part (b) f Figure 3. It an be seen that the ptential utlier is referring t a well in Lh Raven Shist. Hwever, it seems t fllw the trend line f the ther residuals in the upper grup. As mentined by Agresti, when explanatry variables are ntinuus, there are nly ne residual fr eah setting, and a signal residual is ften uninfrmative.

10 1 Xiayin Wang and Kevin W. Kepenik Deviane residuals 3 1 Deviane residuals yield Prbability 1 1 Pearsn residuals 1 Pearsn residuals yield Prbability Pearsn residual Pearsn residual Gneiss yield Granite yield Pearsn residual 3 1 Pearsn residual Serpentine yield Mafis yield Pearsn residual 1 1 Pearsn residual Lh Raven Shist yield Marble yield Pearsn residual Pearsn residual 1 1 Other Shist yield Prettyby Shist yield Figure 3: Residual plts: (a) Overall residual plts, (b) Pearsn residual plts f eah gelgy grup Other helpful tls used t assess the fitness f a mdel are diagnstis f an bservatin s influene n parameter estimates. The greater an bservatin s leverage, the greater its ptential influene. The mst mmnly used tl t assess the influene f an bservatin is thrugh the measure f the hange in sme statistis when the bservatin is remved frm the data. Three standard statistis that serve this purpse are: the jint nfidene interval fr the parameters, dented by ; the hi-square gdness-f-fit statisti, dented by χ ; and

11 Statistial Analysis f Well Failures 11 the deviane gdness-f-fit statisti, dented by G. The larger the hange, the higher influene the bservatin has n the estimatin f the parameter (Agresti ). G-square 1 G-square 1 1 yield Prbability Chi-square 1 5 Chi-square yield Prbability yield Prbability Figure : Influene diagnsti Figure illustrates the satter plts f the hanges f thse measures when an bservatin is deleted against the explanatry variable, well yield, and the predited well failure prbabilities. Similar t Figure 3, there are tw lusters in

12 1 Xiayin Wang and Kevin W. Kepenik hi-square hi-square 1 5 hi-square 1 5 hi-square Gneiss yield Granite yield Serpentine yield Mafis yield hi-square hi-square hi-square hi-square Lh Raven Shist yield Marble yield Other Shist yield Prettyby Shist yield Gneiss yield Granite yield Serpentine yield Mafis yield Lh Raven Shist yield Marble yield Other Shist yield Prettyby Shist yield Figure 5: Influene Diagnsti f Eah Gelgy Grup: (a) Change n Chisquare Gdness-f-fit Statisti, (b) Change n Cnfidene Interval. eah plt. The measures frm failed wells are the upper grup; the nn-failed wells are the lwer grup f eah plt. The tw plts in the tp panel f Figure illustrate the hanges in G when an bservatin is deleted against well yield and predited well failure prbabilities, respetively. The largest hange in G is mre than 1. Hwever, there is n lear evidene that this bservatin has unusually larger influene n G than the thers. The tw plts in the middle panel f Figure illustrate the hanges in χ when an bservatin is deleted. It

13 Statistial Analysis f Well Failures 13 Sensitivity Speifiity Figure : Reeiver perating harateristi urve seems that there is ne bservatin, whih has larger influene n the χ than the thers, and has the value greater than 15. The bttm panel f Figure illustrates the hange in when an bservatin is deleted. There are several large values (>.) in the plts. In rder t identify thse ptential high influene bservatins, satter plts f the hanges in χ and against well yield f eah gelgy grup are nstruted as shwn in Figure 5. The tp setin, part (a), f Figure 5 nsists the satter

14 1 Xiayin Wang and Kevin W. Kepenik plts f the hanges in χ against well yield f eah gelgy grup. It shws that the ptential high influene bservatin is lated in Lh Raven Shist. Hwever, it seems t fllw the trend f the line f failed wells. The bttm setin, part (b) f Figure 5 presents satter plts f the hanges in against well yield f eah gelgy. These satter plts shw that nly ne bservatin frm Mafi with the hange in greater than. may have high influene n the mdel. A lgisti regressin mdel was fitted withut these ptential utliers and high influene bservatins. The resulting estimated mdel des nt hange signifiantly frm the frmer estimated mdel. Therefre, we used the frmer estimatin as ur final estimated mdel, and t predit the prbability f well failure. 5. Pwer f the Preditin The pwer f the preditin f a lgisti mdel an be summarized by tw measures: sensitivity and speifiity. Fr sme given utff value π, if the predited prbability is greater than π, then the well is predited t fail, therwise the well is predited t nt fail. The perentage f rretly prediting well failure is alled sensitivity, and the perentage f rretly prediting nn-failed well is alled speifiity. Fr multiple utffs π, a reeiver perating harateristi (ROC) urve is a mmnly used tl t assess the pwer f preditin f a lgisti mdel. It is a plt f sensitivity against (1-speifiity) fr all pssible utffs π. This urve usually has a nave shape. The larger the area under the urve, the better the preditin. Figure is the ROC urve f ur estimated lgisti mdel f prediting well failures. The area under the urve is idential t the value f anther measure f predit pwer, the nrdane index, whih measures the prbability that the preditins and the utmes are nrdant. Fr ur study, the nrdane index is.7, meaning that verall, we will have a 71% hane f rretly prediting the prbability f well failure.. Disussin In Baltimre Cunty, DEPRM reviews all prpsed dmesti well latins t ensure adherene t minimum setbak distanes frm dmesti wells t ther wells, t ptential sures f ntaminatin (e.g., septi systems, undergrund petrleum strage tanks, et.), t prperty lines, rads and t buildings. Setbak distanes and well nstrutin standards were established ver 5 year ag t minimize ptential influenes between wells and t prtet well water quality. DEPRM s experiene has been that these regulatins have generally been effetive. Hwever, there are n allwanes prvided in the regulatin fr the

15 Statistial Analysis f Well Failures 15 ptential need t drill replaement water supplies at sme pint in the future. Unlike the requirements fr utilizing an n-site sewage dispsal system (OSDS) where a septi reserve area must be established prir t issuane f a building permit, there is n requirement in fr a well reserve area. There have been many instanes ver the years where replaement water supplies annt meet the minimum setbak requirements, partiularly fr undersized lts f rerd, and subdivisins where lts are less than ares in size. Prperty wners must seek varianes t existing setbaks and in sme ases have had t aquire easements n neighbring prperties t attain adequate well yield and/r water quality. The prblem f finding a suitable replaement well latin bemes even mre prblemati when multiple drilling attempts are required t attain a suitable yield. Frtunately, this senari appears t ur n a relatively small number f ases. Sine 199, when the number f unsuessful drill attempts (dry hles) per lt were first traked, ver 95% f drilling attempts fr replaement wells were suessful n the first attempt; % had mre than 1 drilling attempt; and less than.5% had mre than 5 drilling attempts. The statistial analysis prvided in this study may be used t argue fr regulatry hanges that wuld require well reserve areas n all new lts. This wuld likely inrease verall lt size and, therefre, derease building density. Alternately, ne may argue the raising the minimum well yield wuld prvide better prtetin fr prperty wners. Hwever, this may reate a large number f unbuildable areas, and indiretly affet the resale value f existing hmes with well yields belw the minimum. Of urse, the data presented des nt take int aunt ther fatrs that may impat the well failure rate. In, Maryland experiened arguably ne f the wrst drughts n rerd. During that year, there was a 5-fld inrease in the number f replaement wells drilled ver the previus 1-year average. While the drught aused grave nern fr rural residents, the rughly 35 replaement wells drilled in represent less than 1% f the ttal number f wells in Baltimre Cunty, and nly abut % f the well ppulatin used in this study. The relatively lw perentage f wells impated during the drught seems t indiate that well sustainability in the Piedmnt may nt be as sensitive t hanges in preipitatin as generally assumed. The spatial distributin f replaement wells during the drught year indiates that highest perentage f well failure urred in the Mafi at.%, mpared with all ther gelgy grups that had failure rates between.9% and 1.5%. This seems ntrary t the mdel presented in this study whih indiates that the Mafi wells have the lwest verall failure rate. Hwever, as explained belw, the verall well ppulatin used t alulate these statistis inludes many wells that may be mre suseptible t well failure.

16 1 Xiayin Wang and Kevin W. Kepenik In 19, the state f Maryland adpted regulatins requiring mre stringent well nstrutin and yield testing praties. In additin, Baltimre Cunty enated legislatin in 197 requiring that upn transfer f real prperty, dmesti wells must be able t prdue a sustained minimum yield f 1 galln/minute. It is estimated that almst half f the wells urrently in use in Baltimre Cunty were drilled prir t 19 fr whih there may be little r n well nstrutin infrmatin. Sine these lder wells are generally shallwer, and nsidered mre suseptible t drught and yield prblems, it is nt surprising that DEPRM rerds shw that nearly 7% f the wells replaed due t yield prblems frm were wells drilled prir t 19. Clearly, the lder wells are slwly being replaed as prperties are being transferred and/r residents experiene yield prblems. The findings in this study shuld nt be strngly influened strngly by lder wells sine nly wells with mplete well infrmatin were used (i.e. wells drilled after 19). Sial trends may als affet the number f well replaements as water nsumptin in the U.S. has risen ver the last few deades. Arding t the U.S. Envirnmental Prtetin Ageny, the average husehld nw uses apprximately 11 gallns/day, mpared with nly 1 gallns/day in 197. The mre prevalent use f private swimming pls, landsaping and ther utdr watering needs may add a nsiderable strain t a dmesti well water supply with a lw yield. 7. Cnlusins The main gal f this study was t assess whether the well data lleted uld be used t predit the prbability f well failure in the Piedmnt. Analysis f the bserved data learly indiates that well failure is rrelated strngly with well yield and t a lesser degree with gelgy type. The relatively high perentage f failure fr lw yielding wells in ertain gelgy types may be gd reasn t nsider a requirement fr well reserve areas during the building/subdivisin apprval press. This study des nt address the pssibility that eventually all wells may fail. Certainly, it wuld require a muh lnger perid f data lletin (perhaps - years) t determine fr average well lngevity fr new and replaement wells. Aknwledgments We appreiate the Twsn University Applied Mathematis Labratry direted by Dr. Mihael O Leary wh brught a team f students and faulty t wrk n the earlier phases f this prjet. The members f the first year team direted by Dr. Andrew Angel are Jennifer Zeigenfuse, Adam Durana, Kristin Seifarth, Alzie Nwk and Renee Simen. The members f the send

17 Statistial Analysis f Well Failures 17 year team direted by Dr. Xiayin Wang are Pete Surgent Christpher DeZag, Adam Warfield, Allysn Rthman, Mihael Stephen, and Christpher DeZag. Referenes Agresti, A. (). Categrial data analysis, nd ed. Wiley-Intersiene. Allisn, P. D. (1). Lgisti Regressin Using the SAS System: Thery and Appliatin. Jhn Wiley & sn, In. and SAS Institute In. Cdy, R. P. and Smith, J. K. (5). Language, 5th ed. Prentie Hall. Applied Statistis and the SAS Prgramming Neter, J, Kutner, M. H., Nahtsheim, C. J. and Wasserman, W. (199). Applied Linear Statistial Mdels, th ed.. MGraw-Hill/Irwin. Nutter, L. T. and Ottn, E. G. (199). Grund water urrene in the Maryland Piedmnt, Reprt f investigatins N. 1. Maryland Gelgial Survey. Reeived Marh, 7; aepted Otber, 7. Xiayin Wang Mathematis Department Twsn University Twsn, MD 15, USA [email protected] Kevin W. Kepenik Baltimre Cunty Department f Envirnmental Prtetin and Resure Management Twsn, MD 1, USA [email protected]