Vacated and remanded by published opinion. Judge Niemeyer wrote the opinion, in which Judge Widener and Judge Keeley joined.

NIEMEYER, Circuit Judge:

The question presented in this case is whether an arbitrator exceeded the scope of his authority — defined both by a collective bargaining agreement and by the grievance presented to him — when he entered an award in favor of employees at the lead-battery manufacturing plant of Yuasa, Inc., in Sumter, South Carolina. The arbitrator interpreted an incentive plan in the collective bargaining agreement through which the parties intended to reward production quality. Yuasa brought this action to set aside the arbitrator's award, contending that the arbitrator illegitimately went beyond the scope of the grievance and ignored the plain language of the applicable agreement.

The district court vacated a portion of the award, finding that the arbitrator had exceeded his authority in rendering the award. Because we conclude that the arbitrator acted within the scope of the grievance presented to him and arguably construed or applied the collective bargaining agreement, we vacate that part of the district court's ruling setting aside the arbitrator's award and remand for further proceedings.

I

In April 1998, Yuasa, Inc., and the International Union of Electronic, Electrical, Salaried, Machine and Furniture Workers, AFLCIO ("the Union"), which was the exclusive collective bargaining representative for approximately 400 production and maintenance employees at Yuasa's Sumter plant, entered into a collective bargaining agreement, which included the substitution of a"Gainsharing Plan" for the then-existing incentive plan. Under the Gainsharing Plan, the Union agreed to accept a reduction in base pay in exchange for "the opportunity to earn more money than the incentive plan" through bonuses based on four performance criteria: quality, on-time delivery, health, and productivity. The stated objective of the Gainsharing Plan was "to improve long term job security and customer satisfaction by providing the employees with the opportunity to earn additional monies for achieving specified levels of performance, particularly verifiable improvements."

Under the Plan, quality of performance was to be measured by a "First Pass Yield" (sometimes "FPY") determined pursuant to a formula for each of eight production departments in the Sumter plant. When the plant-wide First Pass Yield — the production yield of "good product" — equaled or exceeded 85%, each employee would receive a bonus.

While the method for computing the First Pass Yield in each of the eight departments is expressly set forth in the collective bargaining agreement, the agreement does not specify how the FPY percentages from the eight departments are to be aggregated to produce a plantwide FPY percentage. The Union believed that the yields from the eight departments were to be averaged, and the company believed that the yields from the departments were to be multiplied.

The collective bargaining agreement establishes a grievance procedure for resolving disputes under the agreement. An employee or union steward who fails to resolve a grievance with a supervisor must reduce the dispute to writing. The agreement provides: "In order to avoid misunderstandings, the written grievance must cite the specific clause of the Agreement which is claimed to be violated and the remedy which is being sought." Once a grievance is submitted to a human resources manager, "[v]iolations of other contract provisions cannot be alleged" in that grievance. If the parties are unable to resolve the dispute on their own, either party may refer the dispute for "final and binding" arbitration. "The arbitrator may only interpret the contract and apply it to the particular case presented, as specified in the written grievance," and he has "no authority to add to or subtract from or modify any of the terms of Agreement."

Shortly after the Gainsharing Plan went into effect, a dispute arose between the Union and Yuasa concerning the calculation of bonus pay. The Union filed a grievance on June 22, 1998, charging Yuasa with violating Article XXIV, Section 1, of the collective bargaining agreement and describing its grievance as Yuasa's "[v]iolation of the intent of language to determine the percentages for`First pass Yield.'" The Union requested as relief that the First Pass Yield be determined by "using average of each Department added and divided by the number of Departments." Yuasa had been calculating plantwide FPY by multiplying together the FPY value for each department.

Unable to resolve the dispute through negotiation, the Union pursued its grievance to arbitration, and the arbitrator issued a written opinion sustaining the Union's grievance. While the arbitrator rejected the Union's claim that the departmental rates should be averaged as opposed to being multiplied, he found that Yuasa had violated Article XXIV, Section 1, of the collective bargaining agreement by calculating the FPY in the gridcasting department — one of the plant's eight departments — in a manner that frustrated the ability of Union members to earn bonus pay.

Yuasa's Sumter plant manufactures lead-core batteries, and the first step in the manufacturing process is gridcasting, during which lead is melted down and cast into lead grids or lattices, which form part of the core of a battery. After the lead is melted down in a ladleshaped pot, which is part of the gridcasting machine, the machine pours the lead into molds to form grids. At the same time, a counter on the machine counts each pour. If a grid contains a defect at this early stage in the process, the employees simply throw the defective grid back into the lead pot to be melted down and poured again. After the grid production process is complete, the employees place the finished grids on a pallet where quality-assurance workers later examine the grids for defects.

The collective bargaining agreement sets forth a formula for calculating the gridcasting department's First Pass Yield and defines the components of that formula as follows:

FPY = (Good Product — External Scrap) / Counter number

Numerator: The Good Product comes from product that is counted by the operator and entered on the production report. External Scrap is product identified on M90 reports by operators in subsequent processes.

Denominator: The Counter is attached to the grid casting machine and counts each ladle pour as it is made.

The units of measure are grids.

The arbitrator determined that Yuasa was calculating the gridcasting department's FPY in a manner inconsistent with the intent of the parties as expressed in the collective bargaining agreement. Instead of measuring the quality of product effected by the performance of employees, Yuasa was also counting defective pours that resulted from machine malfunctions not attributable to the quality of employee work, which, the arbitrator found, represented between 20% and 40% of the pours coming out of the machine. The arbitrator concluded that the FPY formula could not be interpreted to include pours resulting from a malfunctioning machine.

In short, the arbitrator sustained the Union's grievance but denied the Union's requested relief, finding that multiplying together the FPY percentages of the eight departments was most consistent with the previous practice of the company and the nature of the productivity incentives under the Gainsharing Plan. The arbitrator instead found that Yuasa was miscalculating the FPY for the gridcasting department and accordingly ordered Yuasa to pay backpay to Union members as "determined either by agreement of the parties or by this arbitrator who maintains jurisdiction of this dispute."

Yuasa filed this action under § 301 of the Labor Management Relations Act, 1947, 29 U.S.C. § 185, seeking to vacate that portion of the arbitration award which determined that Yuasa had improperly calculated the FPY for the gridcasting department, and the Union filed a counterclaim, seeking to enforce the entire arbitration award. The district court entered an order affirming the award"only insofar as it [found] that plant-wide FPY should be calculated by multiplication of individual FPYs," and vacating all other portions of the award. The court concluded that the arbitrator had exceeded the contractually drawn bounds of his authority, first, by addressing an issue — the calculation of the gridcasting department's FPY — that was not raised in the written grievance, and second, by failing to draw the essence of his award from the collective bargaining agreement, specifically its formula for the calculation of the gridcasting department's FPY.

The Union filed this appeal, challenging only that portion of the district court's order which set aside a portion of the arbitration award.

II

The parties to this case quickly found themselves in disagreement over how to apply a quality-performance measurement, to which they had agreed only shortly before. The chosen method for resolution of this dispute was arbitration, and the arbitrator provided the parties with that resolution — one with which Yuasa disagrees. Our function in this type of case is not to review the substance of the arbitration award or even the rationality of the arbitrator's approach but to determine whether the arbitrator arguably functioned within the scope of the powers given him by the arbitration agreement. Allowing final adjustment of disputes to be achieved through the arbitration process is a policy adopted both by the Labor Management Relations Act, see 29 U.S.C. § 173(d) ("Final adjustment by a method agreed upon by the parties is declared to be the desirable method for settlement of grievance disputes arising over the application or interpretation of an existing collective-bargaining agreement"), and by the cases interpreting it, see, e.g., United Steelworkers v. American Mfg. Co., 363 U.S. 564, 566 (1960). This is because "arbitration of labor disputes under collective bargaining agreements is part and parcel of the collective bargaining process itself." United Steelworkers v. Warrior Gulf Navigation Co., 363 U.S. 574, 578 (1960).

For these reasons, particularly in the labor context, we defer to an arbitrator "as long as the arbitrator is even arguably construing or applying the contract." United Paperworkers Int'l Union v. Misco, Inc., 484 U.S. 29, 38 (1987); see also Champion Int'l Corp. v. United Paperworkers Int'l Union, 168 F.3d 725, 728 (4th Cir. 1999). Our province is not to decide the merits of the dispute between Yuasa and the Union, but rather to "determine only whether the arbitrator did his job — not whether he did it well, correctly, or reasonably, but simply whether he did it." Mountaineer Gas Co. v. Oil, Chem. Atomic Workers Int'l Union, 76 F.3d 606, 608 (4th Cir. 1996). Accordingly, we may vacate an arbitrator's award only if it "violates clearly established public policy, fails to draw its essence from the collective bargaining agreement, or reflects merely the arbitrator's personal notions of right and wrong." Champion Int'l, 168 F.3d at 729. One way we determine whether an arbitrator's award fails to draw its essence from the collective bargaining agreement is to ask "whether the award ignored the plain language of the [agreement]." Mountaineer Gas, 76 F.3d at 608; see also Champion Int'l, 168 F.3d at 729. Summarized succinctly,

[T]he arbitrator's award settling a dispute with respect to the interpretation or application of a labor agreement must draw its essence from the contract and cannot simply reflect the arbitrator's own notions of industrial justice. But as long as the arbitrator is even arguably construing or applying the contract and acting within the scope of his authority, that a court is convinced he committed serious error does not suffice to overturn his decision.

Misco, 484 U.S. at 38.

With these principles in hand, we must decide in this case: (1) whether the arbitrator went beyond the scope of the grievance in deciding the correct application of the gridcasting department's FPY formula, and (2) whether the arbitrator's interpretation of that formula drew its essence from the language of the collective bargaining agreement.

III

The Union contends first that the district court erred in concluding that the arbitrator went beyond the scope of the grievance when he decided the proper application of the FPY formula for the gridcasting department. It argues that the language of its grievance addressing plant-wide FPY encompasses also the FPY of the plant's individual departments. Yuasa, on the other hand, contends that the district court was correct because the Union's grievance only implicated the proper method of calculating plant-wide FPY under the agreement.

The Union's grievance reads as follows:

NATURE OF GRIEVANCE: Violations of the intent of language to determine the percentages for "First pass Yield."

The grievance refers to Article XXIV, Section 1, of the collective bargaining agreement, by which the parties agreed to"implement a Gainsharing Plan which will provide the opportunity to earn more money than the incentive plan."

This complaint is broad and would appear to encompass almost any dispute involving the Gainsharing Plan. We have long recognized that it is the grievance that serves as "both the source and limit of the arbitrator's authority and power." Textile Workers Union v. American Thread Co., 291 F.2d 894, 898 (4th Cir. 1961). And in the absence of any express limitation or reservation included in the grievance, we presume that the parties, who agreed to arbitration, agree that the authority to address everything necessary to resolve the particular grievance is conferred upon the arbitrator. See Ormsbee Dev. Co. v. Grace, 668 F.2d 1140, 1146 (10th Cir. 1982); see also O'Neil v. Hilton Head Hosp., 115 F.3d 272, 273-74 (4th Cir. 1997) (noting that "any doubts concerning the scope of arbitrable issues should be resolved in favor of arbitration" (quoting Moses H. Cone Mem'l Hosp. v. Mercury Constr. Corp., 460 U.S. 1, 24-25 (1983))). While Yuasa points to the relief requested in the grievance — which was directed at the proper computation of plant-wide First Pass Yield — as limiting the grievance, any relief requested, by its very nature, is included to redress the grievance, not to limit its scope.

Consistent with Yuasa's argument, the district court in this case characterized the issue before the arbitrator as"the singular question of plant-wide FPY calculation." Even if that accurately stated the scope of the issue, we would still conclude that the arbitrator was empowered to determine, as components of that plant wide FPY, the individual department's FPY values. This is because the plant-wide calculation necessarily implicates the calculations of the individual departments. Indeed, it is the company's manner of calculating plantwide FPY that puts such a great emphasis on the individual departments' FPY values. If the company's method of calculating the plantwide FPY is accepted, then any single departmental value below the 85% threshold would defeat a Gainsharing Plan bonus based on "quality." Thus, when the arbitrator addressed the proper method of arriving at the FPY percentage for the gridcasting department, he acted within the scope of the authority given to him to determine the proper plant-wide FPY.

IV

The Union contends also that the district court erred in finding that the arbitrator's award did not draw its essence from the collective bargaining agreement. The Union argues that the arbitrator, faced with a conflict between the stated objective of the Gainsharing Plan and the literal reading of the gridcasting department's FPY formula, was properly authorized to interpret the formula in a manner that avoided the conflict but yet was faithful to the bargain struck by the parties. Yuasa asserts, on the other hand, that the arbitrator ignored the plain language of the gridcasting department's FPY formula and substituted for the agreed-upon formula his "own notions of industrial justice." Misco, 484 U.S. at 38; see also United Steelworkers v. Enterprise Wheel Car Corp., 363 U.S. 593, 597 (1960).

The collective bargaining agreement provides that the First Pass Yield is measured for the gridcasting department by deriving a percentage from the ratio of "Good Product" (lead grids entered on the department's production report) minus "External Scrap" (defective grids identified on M90 reports in subsequent processes) divided by the "Counter number" (the reading of the counter that is attached to the gridcasting machine and mechanically counts each ladle pour).

Yuasa argues that this formula and the definitions of its components leave no room for interpretation by an arbitrator. It asserts that the components of the applicable ratio are determined mechanically, through reference to certain forms and to the gridcasting machine's counter. To interpret the formula in a manner requiring the company to disregard defective pours by the gridcasting machine, Yuasa contends, does violence to the plain language of the formula and effectively rewrites the agreement's terms, altering the bargain struck by the parties.

The Union argues that Yuasa's mechanical interpretation cannot be so absolute because it would defeat the essence of the parties' agreement. Thus, it maintains that when the gridcasting machine malfunctions and for that reason produces defective pours unrelated to employees' performance, the defective pours should not be counted against the employees. Yuasa responds that even though such defective pours could defeat any Gainsharing Plan bonuses, they are not excluded by the terms of the agreement. Counsel for Yuasa conceded at oral argument, however, that if the counter itself were broken and improperly recorded pours, the improperly counted pours could not, consistent with the parties' collective bargaining agreement, be used in computing the FPY. This necessary acknowledgment by counsel — a reading from a counter that does not function cannot be a reading at all — is consistent with the arbitrator's conclusion that defective pours resulting from an otherwise malfunctioning machine were not intended by the parties to be included in the First Pass Yield calculation. The broken-machine scenario was not addressed by the collective bargaining agreement and therefore had to be addressed through interpretation.

The arbitrator in this case examined the collective bargaining agreement's formula for calculating the gridcasting department's FPY in light of circumstances that the agreement did not expressly address — the production of a high percentage of defective grids caused by malfunctioning gridcasting machines. He determined that, in these circumstances, the parties intended the formula to reflect the productivity of the workers in the department, not the failure of the machine. Informed by the stated objective of the Gainsharing Plan to "provide the employees with the opportunity to earn additional monies for achieving specified levels of performance," the arbitrator found that the parties' choice of the term "Excess Scrap," defined as "product identified on M90 reports by operators in subsequent processes" (emphasis added), conveyed an intent not to include those grids thrown back into the lead melting pot during the gridcasting process because the machine was defective. Likewise, he determined that the parties intended the term "Counter number," defined with reference to the machine counter, to reflect machine-defect-free pours, a number that would be recorded by the machine's counter if the machine were not malfunctioning. Thus, the arbitrator did not ignore the plain language of the collective bargaining agreement. Rather, he construed it to apply to unaddressed circumstances in a manner that was consistent with the parties' intent as manifested in the agreement itself. See Restatement (Second) of Contracts 202(1) (1981) ("Words . . . are interpreted in the light of all the circumstances, and if the principal purpose of the parties is ascertainable it is given great weight"); see also id. 202(5) ("Wherever reasonable, the manifestations of intention of the parties to a promise or agreement are interpreted as consistent with each other and with any relevant course of performance, course of dealing, or usage of trade").

While the proper resolution of this scope-of-arbitration issue is not entirely free from doubt, we must resolve such doubt in favor of arbitration. See Moses H. Cone Mem'l Hosp. v. Mercury Constr. Corp., 460 U.S. 1, 24-25 (1983). When we do so, we conclude that the arbitrator was authorized to construe the FPY formula for circumstances not addressed in the agreement and that his interpretation of the formula drew its essence from the agreement.See Misco, 484 U.S. at 38. Thus, whether or not we agree with the arbitrator's decision on the merits, we believe that the arbitrator was authorized to construe the formula to measure employee production quality by machine-defect-free ladle pours rather than by a number mechanically rendered by a defective machine.

Because we have determined that the arbitrator's award was within the scope of the grievance presented by the parties for his resolution and that the award drew its essence from the parties' collective bargaining agreement, the portion of the district court's order vacating the arbitrator's award is vacated and the case is remanded to the district court for further proceedings consistent with this opinion.

IT IS SO ORDERED.