NR 440.644(6)(d)
(d) Each owner or operator of an undertread cementing operation, sidewall cementing operation, green tires spraying operation where organic solvent-based sprays are used, Michelin-A operation, Michelin-B operation, or Michelin-C- automatic operation who seeks to comply with a specified VOC monthly usage limit shall maintain records of monthly VOC use and the number of days in each compliance period.
NR 440.644(6)(e)
(e) Each owner or operator that is required to conduct monthly performance tests, as specified under
sub. (4) (b) 1., shall maintain records of the results of all monthly tests.
NR 440.644(6)(f)
(f) Each owner or operator of a tread end cementing operation and green tire spraying operation using water-based cements or sprays containing less than 1.0% by weight of VOC, as specified under
sub. (4) (b) 4., shall maintain records of formulation data or the results of Method 24 analysis conducted to verify the VOC content of the spray.
NR 440.644(7)(a)(a) Each owner or operator subject to the provisions of this section shall provide a written report to the department declaring for each undertread cementing operation, each sidewall cementing operation, each green tire spraying operation where organic solvent-based sprays are used, each Michelin-A operation, each Michelin-B operation, and each Michelin-C-automatic operation the emission limit the owner or operator intends to comply with and the compliance method, where
sub. (4) (j) is applicable, to be employed.
NR 440.644(7)(b)
(b) Each owner or operator subject to the provisions of this section shall specify the monthly schedule (each calendar month or a 4-4-5-week schedule) to be used in making compliance determinations.
NR 440.644(7)(c)
(c) Each owner or operator subject to the provision of this section shall report the results of all initial performance tests, as required under
s. NR 440.08 (1), and the results of the performance test required under
sub. (4) (b) 2. and
3. The following data shall be included in the report for each of the performance tests:
NR 440.644(7)(c)1.
1. For each affected facility for which the owner or operator seeks to comply with a VOC monthly usage limit specified under
sub. (3) (a): the monthly mass of VOC used (M
o) and the number of days in the compliance period (T
d).
NR 440.644(7)(c)2.
2. For each affected facility that seeks to comply with a VOC emission limit per tire or per bead specified under
sub. (3) (a) without the use of a VOC emission reduction system: the mass of VOC used (M
o), the number of tires cemented or sprayed (T
o), the mass of VOC emitted per tire cemented or sprayed (N), the number of beads cemented (B
o), and the mass of VOC emitted per bead cemented (N
b).
NR 440.644(7)(c)3.
3. For each affected facility that uses a VOC emission reduction system with a control device that destroys VOC (e.g., incinerator) to comply with a VOC emission limit per tire or per bead specified under
sub. (3) (a): the mass of VOC used (M
o), the number of tires cemented or sprayed (T
o), the mass of VOC emitted per tire cemented or sprayed (N), the number of beads cemented (B
o), the mass of VOC emitted per bead cemented (N
b), the mass of VOC used per tire cemented or sprayed (G), the mass of VOC per bead cemented (G
b), the emission control device efficiency (E), the capture system efficiency (F
c), the face velocity through each permanent opening for the capture system with the temporary openings closed, and the overall system emission reduction (R).
NR 440.644(7)(c)4.
4. For each affected facility that uses a VOC emission reduction system with a control device that destroys VOC (e.g., incinerator) to comply with a percent emission reduction requirement specified under
sub. (3) (a): the emission control device efficiency (E), the capture system efficiency (F
o), the face velocity through each permanent opening in the computer system with the temporary openings closed, and the overall system emission reduction (R).
NR 440.644(7)(c)5.
5. For each affected facility that uses a carbon adsorber to comply with a VOC emission limit per tire or per bead specified under
sub. (3) (a): the mass of VOC used (M
o), the number of tires cemented or sprayed (T
o), the mass of VOC used per tire cemented or sprayed (G), the number of beads cemented (B
o), the mass of VOC used per bead (G
b), the mass of VOC recovered (M
r), the overall system emission reduction (R), the mass of VOC emitted per tire cemented or sprayed (N), and the mass of VOC emitted per bead cemented (N
b).
NR 440.644(7)(c)6.
6. For each affected facility that uses a VOC emission reduction system with a control device that recovers VOC (e.g., carbon adsorber) to comply with a percent emission reduction requirement specified under
sub. (3) (a): the mass of VOC used (M
o), the mass of VOC recovered (M
r), and the overall system emission reduction (R).
NR 440.644(7)(c)7.
7. For each affected facility that elects to comply with the alternate limit specified under
sub. (3) (b): The mass VOC used (M
o), the number of tires processed (T
o), and the mass of VOC emitted per tire processed (N).
NR 440.644(7)(d)
(d) Each owner or operator of an undertread cementing operation, sidewall cementing operation, green tire spraying operation where organic solvent-based sprays are used, or Michelin-B operation who seeks to comply with the requirements described under
sub. (4) (j) shall include in the initial compliance report a statement specifying, in detail, how each of the equipment design and performance specifications has been met. The initial compliance report also shall include the following data: the emission control device efficiency (E), the face velocity through each permanent enclosure opening with all temporary enclosure openings closed, the total area of all permanent enclosure openings, the total area of all temporary enclosure openings, the maximum solvent use rate (kg/hr or lb/hr), the types of VOC used, the lower explosive limit (LEL) for each VOC used, and the length of time each component is enclosed after application of cement or spray material.
NR 440.644(7)(e)
(e) Each owner or operator of an affected facility shall include the following data measured by the required monitoring devices, as applicable, in the report for each performance test specified under
par. (c):
NR 440.644(7)(e)1.
1. The average combustion temperature measured at least every 15 minutes and averaged over the performance test period of incinerator destruction efficiency for each thermal incinerator.
NR 440.644(7)(e)2.
2. The average temperature before and after the catalyst bed measured at least every 15 minutes and averaged over the performance test period of incinerator destruction efficiency for each catalytic incinerator.
NR 440.644(7)(e)3.
3. The concentration level or reading indicated by the organics monitoring device at the outlet of the adsorber, measured at least every 15 minutes and averaged over the performance test period of carbon adsorber recovery efficiency while the vent stream is normally routed and constituted.
NR 440.644(7)(e)4.
4. The appropriate data to be specified by the department where a VOC recovery device other than a carbon adsorber is used.
NR 440.644(7)(f)
(f) Once every 6 months each owner or operator subject to the provisions of
sub. (6) shall report, as applicable:
NR 440.644(7)(f)1.
1. Each monthly average VOC emission rate that exceeds the VOC emission limit per tire or per bead specified under
sub. (3) (a), as applicable for the affected facility.
NR 440.644(7)(f)2.
2. Each monthly average VOC use rate that exceeds the monthly VOC usage limit specified under
sub. (3) (a) as applicable for the affected facility.
NR 440.644(7)(f)3.
3. Each monthly average VOC emission reduction efficiency for a VOC recovery device (e.g., carbon adsorber) less than the percent efficiency limit specified under
sub. (3) (a) as applicable for the affected facility.
NR 440.644(7)(f)4.
4. Each 3-hour period of operation for which the average temperature of the gas stream in the combustion zone of a thermal incinerator, as measured by the temperature monitoring device, is more than 28
°C (50
°F) below the combustion zone temperature measured during the most recent determination of the destruction efficiency of the thermal incinerator that demonstrated that the affected facility was in compliance.
NR 440.644(7)(f)5.
5. Each 3-hour period of operation for which the average temperature of the gas stream immediately before the catalyst bed of a catalytic incinerator, as measured by the temperature monitoring device, is more than 28
°C (50
°F) below the gas stream temperature measured before the catalyst bed during the most recent determination of the destruction efficiency of the catalyst incinerator that demonstrated that the affected facility was in compliance, and any 3-hour period of which the average temperature difference across the catalyst bed (i.e., the difference between the temperatures of the gas stream immediately before and after the catalyst bed), as measured by the temperature monitoring device, is less than 80% of the temperature difference measured during the most recent determination of the destruction efficiency of the catalytic incinerator that demonstrated that the affected facility was in compliance.
NR 440.644(7)(f)6.
6. Each 3-hour period of operation during which the average concentration level or reading of VOCs in the exhaust gases from a carbon adsorber is more than 20% greater than the exhaust gas concentration level or reading measured by the organics monitoring device during the most recent determination of the recovery efficiency of the carbon adsorber that demonstrated that the affected facility was in compliance.
NR 440.644(7)(g)
(g) Each owner or operator of an affected facility who initially elected to be subject to the applicable percent emission reduction requirement specified under
sub. (3) (a) and who later seeks to comply with the applicable total (uncontrolled) monthly VOC use limits specified under
sub. (3) (a) and who has satisfied the provision specified under
sub. (4) (k) shall furnish the department written notification no less than 30 days in advance of the date when the owner or operator intends to be subject to the applicable VOC use limit instead of the applicable percent emission reduction requirement.
NR 440.644(7)(i)
(i) The owner or operator of each undertread cementing operation and each sidewall cementing operation who qualifies for the alternate provisions as described in
sub. (3) (b), shall furnish the department written notification of the election no less than 60 days after September 19, 1989.
NR 440.644(7)(j)
(j) The owner or operator of each tread end cementing operation and each green tire spraying (inside, outside, or both) operation using water-based sprays containing less than 1.0%, by weight, of VOC as described in
sub. (4) (b) 1. shall furnish the department, within 60 days initially and annually thereafter, formulation data or Method 24 results to verify the VOC content of the water-based sprays in use. If the spray formulation changes before the end of the 12-month period, formulation data or Method 24 results to verify the VOC content of the spray shall be reported within 30 days of the change.
NR 440.644(8)(a)1.
1. Method 24 or formulation data for the determination of the VOC content of cements or green tire spray materials. In the event of dispute, Method 24 shall be the reference method. For Method 24, the cement or green tire spray sample shall be a 1-liter sample collected in a 1-liter container at a point where the sample will be representative of the material as applied in the affected facility.
NR 440.644(8)(a)2.
2. Method 25 as the reference method for the determination of VOC concentrations in each stack, both entering and leaving an emission control device. The owner or operator shall notify the department at least 30 days in advance of any test by Method 25. For Method 25, the sampling time for each of 3 runs shall be at least one hour. Method 1 shall be used to select the sampling site, and the sampling point shall be the centroid of the duct or at a point no closer to the walls than one meter (3.3 feet). The minimum sample volume shall be 0.003 dry standard cubic meter (dscm) (0.11 dry standard cubic feet (dscf)) except that shorter sampling times or smaller volumes, when necessitated by process variables or other factors, may be approved by the department.
NR 440.644(8)(a)3.
3. Method 2, 2A, 2C, or 2D, as appropriate, as the reference method for determination of the flow rate of the stack gas. The measurement site shall be the same as the Method 25 sampling. A velocity traverse shall be made once per run within the hour that the Method 25 sample is taken.
NR 440.644(8)(a)5.
5. Method 25 or Method 25A for determination of the VOC concentration in a capture system prior to a control device when only a single VOC is present, as described in
sub. (4) (f) 2. d. 7) and
8). The owner or operator shall notify the department at least 30 days in advance of any test by either Method 25 or Method 25A. Method 1 shall be used to select the sampling site and the sampling point shall be the centroid of the duct or at a point no closer to the walls than 1 one meter (3.3 feet). Method 2, 2A, 2C or 2D, as appropriate, shall be used as the test method for the concurrent determination of gas flow rate in the capture system.
NR 440.644(8)(a)5.a.
a. For Method 25, the sampling time for each run shall be at least 1 hour. For each run, a concurrent sample shall be taken immediately upwind of the application area to determine the background VOC concentration of air drawn into the capture system. Subtract this reading from the reading obtained in the capture system for that run. The minimum sample volume shall be 0.003 dscm (0.11 dscf) except that shorter sampling times or smaller volumes, when necessitated by process variable or other factors, may be approved by the department. Use Method 3 to determine the moisture content of the stack gas.
NR 440.644(8)(a)5.b.
b. For Method 25A, the sampling time for each run shall be at least 1 hour. Instrument calibration shall be performed by the procedure given in Method 25A using the single VOC present in the capture system. A different calibration gas may be used if the results are corrected using an experimentally determined response factor comparing the alternative calibration gas to the single VOC used in the process. After the instrument has been calibrated, determine the background VOC concentration of the air drawn into the capture system immediately upwind of the application area for each run. The instrument does not need to recalibrated for the background measurement. Subtract this reading from the reading obtained in the capture system for that run. The Method 25A results shall only be used in the alternative procedure for determination of capture efficiency described under
sub. (4) (f) 2. d. 7).
NR 440.644 History
History: Cr.
Register, September, 1990, No. 417, eff. 10-1-90; am. (4) (b) 1. and 2., (d) (intro.), (f) 2. (intro.), (j) (intro.) and 1., r. and recr. (1) (a) and (b), cr. (3) (b), (4) (b) 4., (f) 2. d. and (n), (6) (f), (7) (c) 7., (i), (j) and (8) (a) 5.,
Register, July, 1993, No. 451, eff. 8-1-93
; correction in (4) (b) 1. and (k) made under s. 13.93 (2m) (b) 7.,
Register, November, 1999, No. 527;
CR 06-109: am. (2) (a) (intro.), (3) (a) 1. b. 1) to 5), 2. b. 1) to 5), 3., 4., 5., 6. b. 1) to 5), and 7. (intro.) and a., 8. b. 1) to 5) and 9. b. 1) to 5), (4) (c) (intro.), (d) (intro.), (e) (intro.), (f) 2. d. 7) and 8), (j) 4. and 5. b., (n) (intro.) and 5., (6) (b) (intro.) and 2. and (d), (7) (a), (c) 1. to 3. and 5., (d), (f) 1. and 2., (j) and (8) (a) 2., 5. (intro.) and a., r. and recr. (2) (b), renum. (3) (a) 7. b., c. and d. to be (3) (a) 7. b. (intro.), 1) and 2) and am. b. (intro.) and 1), renum. (3) (b) 1. to be (3) (b) and am. Register May 2008 No. 629, eff. 6-1-08; corrections in (1) (c), (4) (c) (intro.), (g), (i) (intro.), (j) (intro.), (k), (7) (a) and (b) made under s. 13.92 (4) (b) 7., Stats., Register May 2008 No. 629. NR 440.647
NR 440.647 Volatile organic compound (VOC) emissions from the polymer manufacturing industry. NR 440.647(1)(1)
Applicability and designation of affected facilities. NR 440.647(1)(a)(a) The provisions of this section apply to affected facilities involved in the manufacture of polypropylene, polyethylene, polystyrene, or poly(ethylene terephthalate) as defined in
sub. (2). The affected facilities designated as follows for polypropylene and polyethylene are inclusive of all equipment used in the manufacture of these polymers, beginning with raw materials preparation and ending with product storage, and cover all emissions emanating from such equipment:
NR 440.647(1)(a)1.
1. For process emissions from any polypropylene and polyethylene manufacturing process that uses a continuous process, the affected facilities are each of the following process sections: each raw materials preparation section, each polymerization reaction section, each material recovery section, each product finishing section and each product storage section. These process sections are affected facilities for process emissions that are emitted continuously and for process emissions that are emitted intermittently.
NR 440.647(1)(a)2.
2. For process emissions from polystyrene manufacturing processes that use a continuous process, the affected facilities are each material recovery section. These process sections are affected facilities for only those process emissions that are emitted continuously.
NR 440.647(1)(a)3.
3. For process emissions from poly(ethylene terephthalate) manufacturing processes that use a continuous process, the affected facilities are each polymerization reaction section. If the process uses dimethyl terephthalate, then each material recovery section is also an affected facility. If the process uses terephthalic acid, then each raw materials preparation section is also an affected facility. These process sections are affected facilities for only those process emissions that are emitted continuously.
NR 440.647(1)(a)4.
4. For VOC emissions from equipment leaks from polypropylene, polyethylene and polystyrene (including expandable polystyrene) manufacturing processes, the affected facilities are each group of fugitive emissions equipment, as defined in
sub. (2), within any process unit, as defined in
sub. (2). This section does not apply to VOC emissions from equipment leaks from polyethylene terephthalate manufacturing processes.
NR 440.647(1)(a)4.a.
a. Affected facilities with a design capacity to produce less than 1,000 Mg/yr (1,102 ton/yr) shall be exempt from
sub. (4).
NR 440.647(1)(a)4.b.
b. Addition or replacement of equipment for the purposes of improvement which is accomplished without a capital expenditure will not by itself be considered a modification under
sub. (4).
NR 440.647(1)(b)
(b) The applicability date identifies when an affected facility becomes subject to a standard. Usually, a standard has a single applicability date. However, some polypropylene and polyethylene affected facilities have a September 30, 1987, applicability date and others have a January 10, 1989, applicability date. The following paragraphs identify the applicability dates for all affected facilities subject to this section.
NR 440.647(1)(b)1.
1. Polypropylene and polyethylene. Each process section in a polypropylene or polyethylene production process is a potential affected facility for both continuous and intermittent emissions. The applicability date depends on when the process section was constructed, modified or reconstructed and, in some instances, on the type of production process.
NR 440.647(1)(b)1.a.
a. The applicability date for any polypropylene or polyethylene affected facility that is constructed, modified or reconstructed after January 10, 1989, regardless of the type of production process being used, is January 10, 1989.
NR 440.647(1)(b)1.b.
b. Only some polypropylene or polyethylene process sections that are constructed, modified or reconstructed on or before January 10, 1989, but after September 30, 1987, are affected facilities. These process sections, and the type of emissions to be controlled, are identified by an “X" in Table 1. The applicability date for the process sections and the emissions to be controlled that are identified by an `X' in Table 1 is September 30, 1987. Since the affected facilities that have a September 30, 1987, applicability date are determined by the type of production process (for example, liquid phase, gas phase), each owner or operator shall identify the particular production process that applies to his or her particular process.
-
See PDF for table 
NR 440.647 Note
Note:
“X" denotes that process section is an affected facility for continuous or intermittent emissions or both, as shown, which has a September 30, 1987, applicability date.
NR 440.647 Note
“—" denotes that process section is not considered an affected facility for continuous or intermittent emissions or both, as shown, if the process section is constructed, modified, or reconstructed after September 30, 1987, and on or before January 10, 1989. These process sections are affected facilities if they are constructed, modified, or reconstructed after January 10, 1989.
NR 440.647(1)(b)2.
2. Polystyrene. The applicability date for each polystyrene affected facility is September 30, 1987.
NR 440.647(1)(b)3.
3. Poly(ethylene terephthalate). The applicability date for each poly(ethylene terephthalate) affected facility is September 30, 1987.
NR 440.647(1)(c)
(c) Any facility under
par. (a) that commences construction, modification or reconstruction after its applicability date as identified under
par. (b) is subject to the requirements of this section, except as provided in
par. (d) to
(f).
NR 440.647(1)(d)
(d) Any polypropylene or polyethylene affected facility with a September 30, 1987, applicability date that commenced construction, modification or reconstruction after September 30, 1987, and on or before January 10, 1989, with an uncontrolled emission rate, as defined in footnote a to Table 2, at or below those identified in Table 2 is not subject to the requirements of
sub. (3) unless and until its uncontrolled emission rate exceeds that rate listed for it in Table 2 or it is modified or reconstructed after January 10, 1989. At such time, such facility becomes subject to
sub. (3) and the procedures identified in
sub. (3) (a) shall be used to determine the control of emissions from the facility.
- See PDF for table
a “Uncontrolled emission rate" refers to the emission rate of a vent stream that vents directly to the atmosphere and to the emission rate of a vent stream to the atmosphere that would occur in the absence of any add-on control devices but after any material recovery devices that constitute part of the normal material recovery operations in a process line where potential emissions are recovered for recycle or resale.
b Emission rate applies to continuous emissions only.
c Emission rate applies to intermittent emissions only.
d Total emission rate for non-emergency intermittent emissions from raw materials preparation, polymerization reaction, material recovery, product finishing, and product storage process sections.
e See footnote d.
f Emission rate applies to both continuous and intermittent emissions.
g Emission rate applies to non-emergency intermittent emissions only.
h Applies to modified or reconstructed affected facilities only.
i Includes emissions from the cooling water tower.
j Applies to a process line producing low viscosity poly(ethylene terephthalate).
k Applies to a process line producing high viscosity poly(ethylene terephthalate).
l See footnote m.
m Applies to the sum of emissions to the atmosphere from the polymerization reaction section (including emissions from the cooling water tower) and the raw materials preparation section (i.e., the esterifiers).
NR 440.647(1)(e)1.1. Modified or reconstructed affected facilities at polystyrene and poly(ethylene terephthalate) plants with uncontrolled emission rates at or below those identified in Table 2 are exempt from the requirements of
sub. (3) unless and until its uncontrolled emission rate exceeds that rate listed for it in Table 2. This exemption does not apply to new polystyrene or poly(ethylene terephthalate) affected facilities.
NR 440.647(1)(e)2.
2. Emissions from modified or reconstructed affected facilities that are controlled by an existing control device and that have uncontrolled emission rates greater than the uncontrolled threshold emission rates identified in Table 2 are exempt from the requirements of
sub. (3) unless and until the existing control device is modified, reconstructed or replaced.
NR 440.647(1)(f)
(f) No process section of an experimental process line is considered an affected facility for continuous or intermittent process emissions.
NR 440.647(1)(g)
(g) Individual vent streams that emit continuous emissions with uncontrolled annual emissions of less than 1.6 Mg/yr or with a weight percent TOC of less than 0.10% from a new, modified or reconstructed polypropylene or polyethylene affected facility are exempt from the requirements of
sub. (3) (a) 1. If at a later date, an individual stream's uncontrolled annual emissions become 1.6 Mg/yr or greater, if the stream was exempted on the basis of the uncontrolled annual emissions exemption, or VOC concentration becomes 0.10 weight percent or higher, if the stream was exempted on the basis of the VOC concentration exemption, then the stream is subject to the requirements of
sub. (3).
NR 440.647(1)(h)
(h) Emergency vent streams, as defined in
sub. (2) from a new, modified or reconstructed polypropylene or polyethylene affected facility are exempt from the requirements of
sub. (3) (a) 2.
NR 440.647(1)(i)
(i) An owner or operator of a polypropylene or polyethylene affected facility that commenced construction, modification or reconstruction after September 30, 1987, and on or before January 10, 1989, and that is in a process line in which more than one type of polyolefin, that is, polypropylene, low density polyethylene, high density polyethylene or their copolymers, is produced shall select one of the polymer/production process combinations in Table 1 for purposes of determining applicable affected facilities and uncontrolled threshold emission rates.
NR 440.647 Note
Note:
The numerical emission limits in these standards are expressed in terms of total organic compounds, measured as total organic compounds less methane and ethane.
NR 440.647(1)(j)1.1. Owners or operators may choose to comply with
40 CFR part 65, subpart G, as in effect on December 14, 2000, for continuous process vents that are subject to this section, that choose to comply with
sub. (3) (a) 1. a. 1), 2) or 3) as allowed in
sub. (3) (a) 1. and
(b) 1. c. The requirements of
40 CFR part 65, subpart G, as in effect on December 14, 2000, satisfy the requirements of
par. (c) and
subs. (5) to
(7), except for
sub. (7) (g) 1. Other provisions applying to owners or operators who choose to comply with
40 CFR part 65, subpart G, as in effect on December 14, 2000, are provided in
40 CFR 65.1 NR 440.647(1)(j)2.
2. Owners or operators who choose to comply with
40 CFR part 65, subpart G, as in effect on December 14, 2000, shall also comply with
ss. NR 440.01,
440.02,
440.05,
440.06,
440.07 (1) (a) and
(d),
440.14 and
440.15 for those process vents. All sections or subsections from
ss. NR 440.01 to
440.19 not specified in this subdivision do not apply to owners or operators of process vents complying with
40 CFR part 65, subpart G, except that provisions required to be met prior to implementing
40 CFR part 65 still apply. Owners or operators who choose to comply with
40 CFR part 65, subpart G, as in effect on December 14, 2000, shall comply with
40 CFR part 65, subpart A.
NR 440.647(1)(j)3.
3. Each owner or operator subject to the provisions of this section that chooses to comply with
40 CFR part 65, subpart G, as in effect on December 14, 2000, at initial startup shall notify the administrator of the specific provisions of
40 CFR part 65, subpart G, as in effect on December 14, 2000, with which the owner or operator has elected to comply. Notification shall be submitted with the notification of initial startup required by
40 CFR 65.5 (b).
NR 440.647(2)(a)(a) As used in this section, all terms not defined shall have the meaning given them in
s. NR 440.02 or in
s. NR 440.62, and the following terms shall have the specific meanings given them.
NR 440.647(2)(a)1.
1. “Boiler" means any enclosed combustion device that extracts useful energy in the form of steam.
NR 440.647(2)(a)2.
2. “Capital expenditure" means, in addition to the definition in
s. NR 440.02, an expenditure for a physical or operational change to an existing facility that exceeds P, the product of the facility's replacement cost, R, and an adjusted annual asset guideline repair allowance, A, as reflected by the following equation:
P = R A,
