Session No. 750 The Implemenaion of Business Decision-Making Tools in Inciden Rae Predicion Samuel A. Oyewole, Ph.D. Deparmen of Energy and Mineral Engineering The Pennsylvania Sae Universiy Universiy Park, PA Inroducion This paper provides an overview of he applicaion of forecasing echnique in he predicion of inciden raes from a business-oriened perspecive. This research shows ha radiional business and financial managemen ools could be used by occupaional healh and safey professionals in he ques for making realisic advance predicions of inciden raes. From earlier research, acual inciden rae daa were obained, and new inciden raes were prediced, using he double exponenial smoohing mehod. The model validaion was achieved by comparing he acual and he prediced inciden raes in a one-year period. Forecas accuracy indicaed 71.58% wih a racking signal of -4.08. The abiliy o predic inciden raes does no only help in reducing safey inervenion coss, bu would make i possible for managers and op-level execuives o beer undersand he financial implicaions and consequences of ineffecive safey programs and policies. Due o he increasing need for safey professionals o effecively presen heir proposals and plans o he non-safey-oriened op managemen and financial execuives, i is has become highly necessary o incorporae some business decision-making ools ino safey and healh programs. To se a foundaion for he implemenaion of hese business ools in safey and healh, his paper uses business decision-making forecasing echnique o predic inciden raes. Forecasing could be described as he process of uilizing previous or curren siuaions o esimae or predic fuure unknown siuaions. Forecasing is ofen applied o several aspecs of human lives (Armsrong, 2001). This predicive ool is ofen used by many organizaions o make sraegic (long-erm), acical (medium-range) and operaional (shor-erm) decisions (Chopra and Meindl, 2006). Forecasing is widely used in meeorology (o predic climae, weaher, hurricanes, ornadoes and flooding); supply chain (o make demand forecass); economics and business (o make predicions for invesmen on socks and bonds); ransporaion planning (o predic he number of passengers); seismology (o predic earhquakes); and peroleum engineering and geology (o predic oil reserves). Some oher recen applicaions of forecasing include populaion
growh, healhcare, spors (o predic winning chances of players and eams), as well as poliics (o predic winners in elecions). Several decision-makers use forecasing as he readily available ool o plan ahead and make predicions based on uncerainy (Armsrong, 2001). Since a forecas is an inference of wha is likely o occur in he fuure, forecass do no always provide he accurae esimaes of he acual siuaions; herefore, he accuracy of a forecas is deermined based on he differences in he acual and he prediced values (forecas error). I should be noed ha long-erm forecass are usually less accurae han shor-erm forecass. This is due o he larger value of he sandard deviaion of error relaive o he mean of he daa samples or observaions (Chopra and Meindl, 2006). Forecasing is used in siuaions involving ime series or rends. In non-saionary (moving) daa, forecasing is used o esimae he mean of he probabiliy of he disribuions. Lieraure Review Previous research sudies have advocaed he incorporaion of probabilisic processes used in financial decision-making o he risk assessmen conceps and mehodologies used by healh and safey professionals. Toffel and Birkner (2002) argued ha, since healh and safey programs ofen require he allocaion of financial resources ha needs o be approved by business and governmenal managers, he uilizaion of business-oriened echniques ino he safey and healh policies would make i easier for he managemen o beer undersand and appreciae he safey and healh programs. Safey and healh programs ha are designed based on sraegies used in business would be easily approved, since he decision-makers and managers are familiar wih he financial decision-making and risk assessmen conceps. In heir research, Toffel and Birkner (2002) demonsraed he use of inciden probabiliies, hisoric oucome informaion, and incremenal impac analysis in he esimaion of risks involving muliple alernaives in he chemical process indusry. The findings of heir research indicaed ha cerain, easily undersood and applied probabilisic risk assessmen mehods used by business planners and managers o assess financial and oucome risks could be adoped ino healh and safey analysis. The researchers suggesed ha safey and healh programs could be improved upon by linking he business decision-making aciviies wih healh and safey risk assessmen processes o securing resources. Also, safey and healh policies could be easily undersood by managers when addiional se of ools for healh and safey risk assessmen are provided. Toffel and Birkner concluded heir research by suggesing ha he incorporaion of financial ools ino he evaluaion of safey and healh programs would make i easy for he safey personnel o consider muliple risks and provide differen decision-making alernaives o managemen. In agreemen wih he suggesions proposed by Toffel and Birkner (2002), Iyer e al. (2005) used forecasing echniques o predic inciden raes based on he mahemaical model developed in earlier research (Iyer e al., 2004). In heir research, he values obained from he forecas were used o validae heir model over a period of 22 weeks. Iyer e al. (2005) adoped weighed moving averages and exponenial smoohing echniques o idenify changes in he saisical relaionship beween inervenions and inciden raes (Haigh e al., 2001a and b). In heir sudy, he researchers inegraed and relaed pas safey performance (inciden raes) wih he curren raes o obain an esimae of he fuure inciden raes.
The exponenial moving average and he moving average of errors were used o obain he inciden rae forecas. Alhough Iyer e al. (2005) provided he background for he incorporaion of forecasing echniques ino he predicion of inciden raes, he sudy did no propose any addiional sudy for he invesigaion of he behaviors of he observed rend. The exponenial smoohing mehod used in he research assumed consan-level ime series. This is acually no he case; in realiy, inciden raes are no consan, and several facors could accoun for he changes in he rend levels of varying inciden raes. Conrary o he forecasing mehodologies adoped by Iyer e al. (2005), his sudy uilizes he rend-correced exponenial smoohing echnique (Hol s model) o predic he inciden raes based on he developed safey inervenion model. Hol s model is an improvemen or modificaion of he simple exponenial smoohing mehod, which accouns for changes in coninuing rends (Chopra and Meindl, 2006). Hol s model is very applicable for predicing inciden raes due o is rend correcion capabiliy. Hol s model is also known as he double exponenial smoohing mehod. The Double Exponenial Smoohing Mehod Time series could be described as a se of observaions, which are generaed sequenially over ime. In siuaions where he se is coninuous, hen a rend is generaed. Double exponenial smoohing (Hol s model) is a refinemen of he simple exponenial smoohing mehod, bu he addiion of he rend-correced componen o exponenial smoohing akes ino accoun he behavior of any rend in he daa. The simple exponenial smoohing mehod works bes wih daa wih no rend or seasonaliy. Simple exponenial smoohing does no ofen make reasonable forecass in siuaions where he daa exhibis eiher an increasing or decreasing rend over ime. The double exponenial smoohing mehod is herefore designed o address his ype of rend siuaion in daa series (Chopra and Meindl, 2006). The double exponenial smoohing mehod is used for modeling he behavior of ime series (rends) based on a simple linear regression equaion obained in siuaions where he inercep and slope of he plos of he observaions vary slowly over a given ime. Unlike he simple exponenial smoohing mehod, Hol s model applies unequal weighing on he exponenially decaying parameers so ha newer observaions ge a higher weighing han older ones (Bowerman and O'Connell, 1993). The degree of exponenial decay is deermined by he parameer α, where α [0, 1). The evolving regression equaion could be used o make inciden rae predicions. Applicaion of Hol s Model o Inciden Rae Predicion Inciden rae forecass could be obained using Hol s model when he inciden rae is assumed o have a level and a rend (where inciden rae (y) = level + rend). I is herefore necessary o obain he iniial esimae of he level ( l ) and rend ( 0 b ) by running a linear regression beween 0 inciden rae (Y ) and he ime period as shown in Equaion (1): Y = m() + c (1)
The consan (c) measures he esimae of he inciden rae a period = 0, which is he required esimae of he iniial level ( l ). The slope (m) measures he rae of change in he inciden rae 0 per period, which is he required esimae of he iniial rend ( b ). The rend a ime () could 0 herefore be given as ( b ) while he level a ime () is given as ( l ), hen he inciden rae could be prediced using he following rend-correced exponenial smoohing as shown in Equaions (2) and (3): l = α y + (1 α )[ l + b ] (2) 1 1 b = γ[ l l ] + (1 γ ) b (3) 1 1 Where α and γ are smoohing consans beween 0 and 1. The iniial values l and 0 b could be obained based on he esimaes of he previous inciden 0 raes. Summing up Equaions 2 and 3, and he τ -sep-ahead inciden rae forecas from for y τ, he prediced inciden rae [F + +τ ], a ime is = +, and could be given as shown in Equaion (4): yˆ + τ = l + τ b (4) The 95% predicion inerval could be obained for y + (when τ = 1), as shown in Equaion (5): 1 ( l + b ) ± z s (5).025 From Equaion (5), he 95% predicion inerval for he τ -sep forecas of as shown in Equaion (6): y could be obained, + τ.025 τ 1 ( l + τb) ± z s 1 + α (1 + jτ) τ j= 1 2 2 (6) Where he sandard deviaion is obained, as shown in Equaion (7): [( yj ( lj 1+ bj 1)] SSE j= 1 s = = n 2 2 2 (7)
Measures of Inciden Rae Forecas Error I should be noed ha every insance of he inciden rae forecas has a random componen, which is considered as he forecas error. Proper esimaion of inciden rae forecas errors would enable he managemen o deermine wheher he forecasing mehod accuraely predics inciden raes. The accuracy of he inciden rae forecas is necessary in order o effecively plan ahead, based on he need o adequaely allocae resources o he safey inervenion aciviies ha minimize inciden raes. The esimaion of he inciden rae forecas could also be used o deermine wheher he forecasing echnique adoped is consisenly producing very posiive error (overesimaion) or negaive error (underesimaion). Forecasing errors ha are wihin hisorical error esimaes indicae a high level of consisency and accuracy of he forecasing echnique. Forecas errors ha are well beyond he hisorical esimaes could indicae ha he forecasing mehod is no longer accurae or appropriae. The commonly measured ypes of forecasing errors include he forecas or residual error, forecas accuracy, he mean squared error (MSE), absolue deviaion (AD), mean absolue deviaion (MAD), he mean absolue percenage error (MAPE), he percen mean absolue deviaion (PMAD), bias (BIAS), and racking signal (TS). Forecas/Residual Error The forecas or residual error (in erms of inciden rae) is he difference beween he forecas for period () and he acual inciden rae in period (). I may be imporan for he safey personnel o esimae he forecas error of inciden raes far in advance. This is necessary in order o make decisions and planning on he ype of resources o be allocaed o a paricular safey inervenion aciviy before he occurrence of any inciden. The forecas error (E ) is measured as shown in Equaion (8): E = F Y (8) Where F is he forecas a period () and Y is he acual inciden rae a period (). The percen forecas error is measured as he raio of he forecas error and he forecas a period ().The mahemaical represenaion of he error (%) is shown in Equaion (9): Error (%) = / Y F / Y / Acual Forecas / Acual (9) The forecas error could be larger han he forecas or he acual inciden rae a ime (), bu no boh. A zero forecas accuracy or very inaccurae forecas is obained in siuaions where he percen forecas error [Error (%)] is higher han 100%.
Forecas Accuracy Forecas accuracy is described as he proporion of deviaion of he acual inciden rae from he prediced inciden rae in a period (). Decreasing errors indicae increasing accuracy since he inenion of he forecas is o predic inciden raes ha are idenical o he acual values (Chopra and Meindl, 2006). Forecas accuracy is measured as shown in Equaion (10). Accuracy (%) = [1 Error (%)] (10) In mos siuaions, several forecass yield accuracies which are beween 0 and 100%. A perfec forecas is achieved when accuracy is 100%, while an absoluely incorrec or inaccurae forecas is obained when accuracy is 0%. Mean Squared Error The mean squared error (MSE) is relaed o he variance of he forecas error. In his case, he random componen of he inciden rae is assumed o have a mean of zero and a variance of MSE. The mean squared error (variance of forecas error) is shown in Equaion (11) as: MSE N = = 1 N E 2 (11) Where N = Toal number of observaions or sample size. Absolue Deviaion The absolue deviaion (A ) of an inciden rae forecas in period () is defined as he absolue value of he forecas error (E ) in period (). The mahemaical represenaion of he absolue deviaion of he inciden rae forecas is shown in Equaion (12) as: A = E (12) Mean Absolue Deviaion The mean absolue deviaion (MAD) or he mean absolue error (MAE) is described as he average of he absolue deviaion of he inciden rae forecas for he oal observaions (Chopra and Meindl, 2006). The mean absolue deviaion is expressed mahemaically, as shown in Equaion (13): MAD = N / E / 1 = N (13)
In siuaions where he random componen of he inciden rae forecas is normally disribued, hen he esimae of he sandard deviaion (σ), wih he mean equal zero, could be obained, as shown in Equaion (14): σ = 1.25 MAD (14) Mean Absolue Percenage Error The mean absolue percenage error (MAPE) is described as he average value obained from he summaion of he absolue values of all he percenage errors (Chopra and Meindl, 2006). The mahemaical represenaion of he mean absolue percenage error is shown in Equaion (15): (15) Percen Mean Absolue Deviaion The percen mean absolue deviaion (PMAD) could be described as he parameer obained from he division of he absolue oal errors and he absolue oal of he prediced inciden raes. This is mahemaically represened as shown in Equaion (16): (16) Bias The errors of a ruly random, non-biased forecas should flucuae around zero, wih he bes sraigh line passing hrough zero (Chopra and Meindl, 2006). The bias of he inciden rae forecas could be obained by summing up all he forecas errors, as shown in Equaion (17): Bias N E = N = 1 (17) Tracking Signal The racking signal (TS) could be described as he raio of he bias and he mean absolue deviaion (MAD). This is represened as shown in Equaion (18):
Bias TS = (18) MAD The range of any racking signal (TS) is + 6. A forecas is eiher underesimaed/ biased (TS < -6) or overesimaed (TS > +6). Daa Collecion Mehodology In order o show ha inciden raes could be effecively prediced, a safey inervenion model, which was developed from an earlier safey and healh inervenion effeciveness research conduced by Oyewole and Haigh (2009), was validaed using he proposed forecasing mehodology. An addiional 52 weeks (one year) of daa were colleced from he same oil exploraion and producion company in he Niger Dela region of Nigeria. The colleced daa were based on he recommendaions and he applicaion of he suggesed desirable resource allocaion mehod proposed by Oyewole and Haigh (2009). Using he averages of he pas 52 weeks of he model developmen daa, Hol s double exponenial smoohing mehod was used o predic he inciden raes for he nex 52 weeks. Seing each of he alpha (α) and gamma (γ) levels o 0.25, he Hol s double exponenial smoohing echnique was used o predic he inciden rae as shown in he Figure 1. Figure 1. Time series plo for inciden rae (prediced vs. acual)
The prediced inciden raes and he acual inciden raes were compared using saisical measures and forecasing errors, such as he forecas or residual error, forecas accuracy, mean squared error (MSE), absolue deviaion (AD), mean absolue deviaion (MAD), mean absolue percenage error (MAPE), he percen mean absolue deviaion (PMAD), bias (BIAS), and racking signal (TS). The saisical measuremens used for he comparison of he prediced inciden raes and he acual inciden raes (based on he developed model) include he mean, median, quarile, and sandard deviaion. The saisical comparison of he smoohed/prediced inciden raes and he acual inciden raes is shown in Table 1. Table 1. Measures of Saisical Comparison for Inciden Raes (Prediced vs. Acual) Saisical Measure Smoohed/Prediced Inciden Raes Inciden Raes (Acual) Mean 3.75 3.82 Median 3.83 3.65 Sandard Deviaion 1.69 2.45 1s Quarile (Q1) 2.49 1.49 3rd Quarile (Q3) 5.04 5.63 Sample Size 52 52 The boxplos and he normal probabiliy plos for he prediced inciden raes and he inciden raes (model) obained from he analysis are shown in Figures 2 and 3, respecively.
10 Boxplo of Smoohed/Pred. Inciden Rae, Inciden Rae (Model) 8 6 Daa 4 2 0 S moohed/pred. Inciden Rae Inciden Rae (Model) Figure 2. Boxplos for Prediced and Acual Inciden Raes Probabiliy Plo of Inciden Rae (Model), Smoohed/Pred. Inciden Normal - 95% CI Percen 99 95 90 80 70 60 50 40 30 20 Variable Inciden Rae (Model) Smoohed/Pred. Inciden Rae Mean SDev N AD P 3.815 2.451 52 0.524 0.174 3.747 1.689 52 0.194 0.889 10 5 1-5.0-2.5 0.0 2.5 5.0 Daa 7.5 10.0 12.5 Figure 3. Normal Probabiliy plos for Inciden Raes (Prediced vs. Acual)
The hisogram plos for he prediced inciden raes and he inciden raes (model) obained from he analysis are shown in Figures 4 and 5, respecively. Figure 4. Hisogram Plo for Prediced Inciden Raes Hisogram of Inciden Rae (Model) Normal 10 M ean 3.815 SDev 2.451 N 52 8 Frequency 6 4 2 0-2 0 2 4 6 Incide n Ra e (M o de l) 8 10 Figure 5. Hisogram Plo for Acual Inciden Raes
The model validaion process, which was based on he measures of he forecasing errors, indicaed ha using he appropriae forecasing echniques, inciden raes could be accuraely prediced. Table 2 shows he values obained from he analysis of he prediced and model inciden raes, based on he forecas or residual error, forecas accuracy, mean squared error (MSE), absolue deviaion (AD), mean absolue deviaion (MAD), mean absolue percenage error (MAPE), he percen mean absolue deviaion (PMAD), bias (BIAS), and racking signal (TS). Table 2. Measures of Forecasing Error for Prediced Inciden Raes Measure of Forecasing Error Obained Values Mean Forecas/Residual Error 0.07 Forecas Accuracy (%) 71.58 Mean Squared Error (MSE) 4.76 Absolue Deviaion (AD) 7.46 Mean Absolue Deviaion (MAD) 1.83 Mean Absolue Percenage Error (MAPE) 28.43 Percen Mean Absolue Deviaion (PMAD) 3.62 Bias (BIAS) -7.46 (slope = 0.018) Tracking Signal (TS) -4.08 From Table 2, he obained forecas accuracy value of 71.58% is wihin he accepable limi of 0% o 100%. Based on he value of he obained forecas accuracy, inciden raes could be accuraely prediced in more han 70% of he ime. The obained level of forecas accuracy (71.58%) could be explained due o he similariies in seasonaliy or rends. For example, periodic milian aciviies (someimes occurring wice in a hree-monh period) could be a reason for he high spikes or ouliers in he acual and he prediced inciden rae daa. An oulier could be described as an observaion or daa poin which lies a an abnormal disance, when compared o he oher values in he daa. Despie his observaion, he obained 71.58% inciden rae predicion accuracy could be viewed as a saring advanage for healh and safey managers and decision-makers, since i would enable he safey personnel o effecively plan ahead and appropriaely allocae resources o he safey inervenion aciviies, which would furher lower inciden raes. A bias value of - 7.46 (wih a slope value of 0.018) indicaes ha he forecas error is ruly random and no biased in any way. Figure 6 shows he plo of he bes sraigh line, indicaing a slope value of +0.0184
for he linear equaion of he forecas error. The slope value is no significan and revolves around zero. Figure 6. Residual Plo of Forecas Error Discussion and Conclusion The obained value of he racking signal (-4.08) shows ha he signal for he forecas is no biased and wihin he accepable range (TS + 6). The negaive sign of he racking signal could be explained, based on he use of he averaging echnique for he iniial esimaes of he inciden rae and level. An excessively large negaive value of he racking signal could indicae he underesimaion of he inciden rae, while an excessively large posiive value of he racking signal could indicae he overesimaion of he inciden rae. This is no he case in his sudy, since he obained value of he racking signal is wihin he accepable range. The use of he double exponenial smoohing echnique (Hol s model) o predic inciden raes provided he opporuniy o validae he developed safey inervenion model, based on he analysis of he measures of he forecasing errors. The obained predicion accuracy (71.58%) could be improved upon in siuaions where sensiiviy analysis is incorporaed ino he double exponenial smoohing echnique. Sensiiviy analysis could be performed on he forecasing mehodology in order o furher reduce bias, improve he value of he racking signal, and ulimaely increase he level of he forecas accuracy. The adjusmen of he alpha (α) and gamma (γ) levels, based on he preference of he safey personnel, as well as he selecion of a beer esimaion echnique for he iniial value of he inciden rae and rend level, could also improve he predicion capabiliy and accuracy of he forecasing mehodology.
This research shows ha injury inciden raes can be effecively prediced, using radiional business decision-making and forecasing ools and echniques. The abiliy o predic inciden raes helps in he idenificaion of significan safey inervenion facors, which are aimed a reducing safey inervenion coss. This would also make i possible for managers and op-level execuives o beer undersand he financial implicaions and consequences of ineffecive safey programs and policies. This could be seen as an added advanage, since he obained informaion from he inciden rae forecas could be used o make beer decisions on he level of resources o allocae o safey and healh programs. Fuure Work The expansion of he curren sample size of he daa by incorporaing and comparing safey aciviies from oher unis or organizaions would be beneficial in order o achieve higher predicion accuracies for inciden raes. Increasing he daa sample size would also allow managemen o adequaely undersand he impac of allocaing sufficien budge and resources o he various asks, operaions, inervenion aciviies, and safey programs ha reduce inciden raes. Seing of safey decision-making sandards by incorporaing weighs o he facors would also be beneficial o his sudy. This could provide a more realisic value of inciden raes and could indicae he level of willingness of he managemen in he allocaion of resources owards he safey aciviies wih he help of an effecive inciden rae predicion echnique. References Armsrong, J.S. 2001. Principles of Forecasing: A Handbook for Researchers and Praciioners (Inernaional Series in Operaions Research & Managemen Science). Norwell, MA: Kluwer Academic Publishers. Bowerman, B.J. and R.T. O'Connell. 1993. Forecasing and Time Series: An Applied Approach. Belmon, CA: Duxbury Thomson Learning. Chopra, S and P. Meindl. 2006. Supply Chain Managemen: Sraegy, Planning and Operaion, 3rd ediion. Upper Saddle River, NJ: Prenice Hall. Haigh, J. M., R. E. Thomas, L. A. Smih, R. L. Bulfin Jr. and B. K. Hopkins. 2001a. Inervenion Effeciveness Research: Phase 1, Developing a Mahemaical Relaionship beween Inervenions and Inciden Raes for he Design of a Loss Prevenion Sysem. American Sociey of Safey Engineers Technical Forum: 38-44. Haigh, J. M., R. E. Thomas, L. A. Smih, R. L. Bulfin Jr. and B. K. Hopkins. 2001b. Inervenion Effeciveness Research: Phase 2 Design, Opimizaion & Verificaion of he Loss Prevenion Sysem & Analysis Models. Professional Safey: The Journal of he America Sociey of Safey Engineers: 33-37.
Iyer, P., J.M. Haigh, E. del Casillo, B.W. Tink, and P.W. Hawkins. 2004. Inervenion effeciveness research: Undersanding and opimizing indusrial safey programs using leading indicaors. Chemical Healh and Safey, 11(2), 9-19. Iyer, P., J.M. Haigh, E. del Casillo, B.W. Tink, and P.W. Hawkins. 2005. A Research Model Forecasing Inciden Raes from Opimized Safey Program Inervenion Sraegies. Journal of Safey Research, Vol. 36, Number. 4, pp. 341-351. Oyewole, S.A and J.M. Haigh. 2009. Making he Business Case: Assessmen of Safey Inervenion and Resource Allocaion and Opimizaion. In he Proceedings of 2009 Safey Conference and Exposiion organized by he American Sociey of Safey Engineers (ASSE), San Anonio, TX. June 28 July 1, 2009. Toffel, M. W. and L. R. Birkner. 2002. Esimaing and Conrolling Workplace Risk: An Approach for Occupaional Hygiene and Safey Professionals. Applied Occupaional and Environmenal Hygiene, Volume 17, Number 7, pp. 477-485(9).