<strong>10</strong> <strong>Years</strong> <strong>of</strong> <strong>International</strong> Cooperation: FTI, Nippon Keidanren and TU<strong>SIIT</strong> <strong>Commemorative</strong> <strong>Publication</strong>, 2002control approach are not easy to implement. Forexample, it is recommended that workers rotate amongworkstations to reduce their daily noise exposurelevels. Since there are numerous combinations <strong>of</strong> workassignments to consider, it is almost impossible for thesupervisor to find the optimal work assignmentsolution.An Excel-based computer program called “NoiseManager” is developed to assist safety practitioners topractically implement several recommendations basedon the administrative approach. Noise Manager can beused to evaluate existing noise conditions andrecommend practical solutions. It consists <strong>of</strong> eightmodules. The first four modules are for noiseevaluation and the last four are for noise management.The user can select the preferred module from themenu as shown in Fig. 190n ⎡ L j − ⎤D T = 12.5 C 25∑⎢ ⎥j(2)j=1⎢ ⎥⎣ ⎦3.2 Module 2 – Calculation <strong>of</strong> Noise Level andPermissible Duration at any LocationTo predict the combined noise level at any location,Noise Manager needs information such as the ambientnoise level, noise levels <strong>of</strong> all noise sources in the workarea, and the locations (in x and y coordinates) <strong>of</strong> thosenoise sources. The following formula can be used todetermine the combined noise level at location i ( L i ).L i =⎡n ( Lj−120)/<strong>10</strong>( 120)/<strong>10</strong> <strong>10</strong> ⎤Lab−<strong>10</strong>log ⎢<strong>10</strong> + ∑ ⎥+1202⎢⎣j=1 dij⎥(3)⎦where d ij is the distance between location i and noisesource j, L j the noise level <strong>of</strong> noise source j, and L ab theambient noise level.If the worker is required to be at one location for theentire day, it is possible to determine the permissibleexposure time (T) at that location from the known noiselevel.−1−90⎡ L ⎤5T = 8(4)⎢2⎣⎥⎦Fig. 1 Noise Manager and its modules.3.1 Module 1 – Calculation <strong>of</strong> TWA and Noise Dose<strong>of</strong> an 8-hour DayA time-weighted average (TWA) is an index thatmeasures the amount <strong>of</strong> long-term noise exposure. Todetermine the 8-hour TWA, Noise Manager needs toknow the noise levels at the locations that the worker ispresent and the exposure duration at those locations. Itthen uses the following formula to calculate the 8-hourTWA (W) in dBA,3.3 Module 3 – Construction <strong>of</strong> Noise Contour Map<strong>of</strong> a FacilityA noise contour map depicts noise levels at variouslocations in the work area. Usually, locations that havethe same noise level are connected together by thesame contour line. To analytically construct a noisecontour map, Eq. (3) can be used to determine thecombined noise level. Figure 2 shows an example <strong>of</strong> a3-dimensional noise contour map constructed by NoiseManager.W =⎡ ⎧90nLC ⎛ j − ⎞⎫⎤j16.61⎢ ⎪log ⎜2 5 ⎟ ⎪⎥+ 90⎢ ⎨∑ ⎬(1)j=1 8 ⎜ ⎟ ⎥⎢ ⎪ ⎝ ⎠⎪⎣ ⎩⎭⎥⎦where C j and L j are the exposure duration and thecombined noise level at workstation j, respectively.The daily noise dose (D T ), in percent, can also becalculated using the same data. The daily noise doseand the 8-hour TWA present similar information aboutthe noise condition (Nanthavanij 1998).Fig. 2 A noise contour map.78
<strong>10</strong> <strong>Years</strong> <strong>of</strong> <strong>International</strong> Cooperation: FTI, Nippon Keidanren and TU<strong>SIIT</strong> <strong>Commemorative</strong> <strong>Publication</strong>, 20023.4 Module 4 – Estimation <strong>of</strong> Ambient andMachine Noise LevelsThe important pieces <strong>of</strong> information that are verydifficult to obtain are the ambient noise level and thenoise levels <strong>of</strong> noise sources in the work area. This isbecause it is not practical to shut <strong>of</strong>f all other noisesources so that the noise level <strong>of</strong> the given noise sourcecan be separately measured. Noise Manager allows theuser to conveniently estimate the wanted information.It uses a simple linear algebra approach to set up a set<strong>of</strong> linear equations in which the ambient noise andmachine noise levels are unknown variables. Theequations are then simultaneously solved to determinethe unknown variables.Note that in order to solve for the ambient noise leveland the noise levels <strong>of</strong> n sources, n + 1 known noiselevels are required. In practice, any locations in thework area may be chosen for noise measurements. It ishowever recommended that the locations that are farfrom the wall or corner be chosen to avoid the effect <strong>of</strong>sound reflection.3.5 Module 5 – Determination <strong>of</strong> Minimax WorkAssignments (Heuristic)The minimax work assignments are the assignmentsdeveloped for m workers, n workstations, and p workperiods per day. Generally the assignment will specifythat “who will do what during when.” According toNanthavanij and Yenradee (1999b), the minimax workassignments are a set <strong>of</strong> work assignments that themaximum noise level that any <strong>of</strong> the workers receive isminimized. Noise Manager determines the minimaxwork assignments based on the heuristic approachdeveloped by Tarathorn and Nanthavanij (underreview). It can solve both balanced (m = n) andunbalanced (m > n) problems, and both unconstrainedand constrained problems.Figure 3 shows the data and the minimax workassignments determined by Noise Manager. When thenumber <strong>of</strong> workers is greater than the number <strong>of</strong>workstations, some workers will be idle in some workperiods. Also, note that the maximum noise exposurelevel may be beyond 90 dBA.The mathematical model <strong>of</strong> the complex workassignment model can be described as follows. Let a ijrepresent a component <strong>of</strong> a matrix A that definesworker-workstation feasible assignments, where a ij = 1if worker i can be assigned to workstation j, and a ij = 0Lj−901otherwise. The term 25is viewed as a noisepweight per period <strong>of</strong> a given workstation j (or w j ). Anyworker who is assigned to that workstation will alwaysreceive that amount <strong>of</strong> noise weight.Minimizesubject toZ⎡ ⎧ n p⎪ ⎫⎪⎤16.61⎢log<strong>10</strong>⎨ wx j ijk⎬⎥+90⎢⎣⎪⎩j= 1k=1 ⎪⎭⎥⎦nxijkj=1∑∑ ≤ Z, i = 1,…, m∑ ≤ 1 i = 1,…, m; k = 1,…, pm∑ x ijki=1m pxijki= 1k=1≤ 1∑∑ ≤ p j = 1,…, nx ijk ≤ a ijx ijk = 0, 1}j = 1,…, n; k = 1,…, pi = 1,…, m; j = 1,…, n; k = 1,…, pi = 1,…, m; j = 1,…, m; k = 1,…, pThe number <strong>of</strong> possible work assignments (orsolutions) is equal to (m!) p . For a small workassignment problem in which there are five workers(m = 5) and a workday is divided into four workperiods (p = 4), there are 207,360,000 assignments toconsider.Fig. 3 Input data screen and the work assignment solution.79
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