This appeal arises from the termination from employment of the petitioner, James Cole, by the respondent, the New Hampshire Department of Information Technology (DOIT). The New Hampshire Personnel Appeals Board (PAB) upheld Cole's termination. On appeal, Cole argues that his termination did not comply with New Hampshire Administrative Rules, Per 1002.08 because he did not receive three written letters of warning in accordance with New Hampshire Administrative Rules, Per 1002.04 for the same or substantially similar conduct or offense. DOIT argues that we lack subject matter jurisdiction to decide this case, and, in the alternative, that Cole's termination complied with Per 1002.08 and Per 1002.04. Finding that we have jurisdiction, we affirm the PAB's decision.
*953I
The following facts were found by the PAB or are otherwise derived from the record. Cole had been a DOIT employee for fifteen years as of May 2015. During that month, his position was defunded and he was transferred to a new position within DOIT at the New Hampshire Department of Transportation. Cole's supervisor in his new position was Charles Burns.
One of Cole's initial assignments was overhauling an Account Security Form (ASF). This was intended to be a short-term project. Although some aspects of Cole's work on this project were satisfactory, his incorrect processing of other aspects of the overhaul resulted in audits being conducted on the forms to ensure accuracy. Cole was also initially assigned a "Wireless Access Point" Project (WAP). This project required communication with customers who were requesting installation of a WAP, and coordination with the persons who were to install the WAPs. However, Cole's communications were inadequate. This resulted in customers not knowing how to use the WAPs after they were installed, or even that the WAPs had been installed.
On March 1, 2016, Burns issued Cole a memorandum of counsel to document and address his concerns with Cole's work on the ASF and WAP projects. The memorandum included recommended corrective actions to address the problems with both projects. After the memorandum was issued, however, Cole continued to have problems with the ASF project. Customers continued to complain that there were problems with the form. An audit revealed that 20% of a sample of forms that Cole processed contained errors, the majority of which were serious. Cole ultimately performed eleven major revisions to the ASF, but the revised form was substantially similar to the original one and the project took much longer to complete than intended.
On April 13, 2016, Burns issued Cole a letter of warning. The letter cited Cole's "failure to meet any work standard" and "failure to take corrective action as directed" under Per 1002.04(b)(1) and (2) as grounds for its issuance. The letter also detailed Cole's mishandling of the ASF project, and contained a corrective action plan.
On May 6, 2016, Cole was issued a second letter of warning. This letter also cited Cole's "failure to meet any work standard" and "failure to take corrective action as directed" under Per 1002.04(b)(1) and (2). This letter partially concerned Cole's work on the "IMP" project. Cole was originally assigned this project in December of 2015. Cole was responsible for holding a "kickoff" meeting to discuss the details of the project. Despite being reminded on several occasions by Burns about the need to hold the meeting, Cole did not hold one until April 2016. Even after the kickoff meeting was held, there was no timeline for the project and customers did not have some necessary information. The May 6, 2016 letter of warning also addressed issues with a different project that had been assigned to Cole to establish internet connectivity at a particular location. Cole had problems establishing timelines for this project, communicating with interested parties, and keeping customers satisfied. This letter of warning, like the first letter as well as the memorandum, contained a corrective action plan to address the problems identified in the letter.
On June 7, 2016, Burns conducted a performance evaluation of Cole. Burns noted several ongoing concerns, including Cole's lack of communication, his lack of progress and timelines, and general inaccuracies in his work. Two days later, when Burns spoke to Cole about an overdue *954project, Cole told Burns that he was not given enough time to complete the project. A short time later, Burns saw Cole doing a crossword puzzle at his desk during work hours. When asked if he was on a break, Cole said he was not.
On June 16, 2016, the DOIT Commissioner, Denis Goulet, issued Cole a third letter of warning. This letter stated that the quality of Cole's work continued to be below expectations, as detailed in the June 7 performance evaluation and the previous letters of warning and memorandum of counsel. The letter also referenced the crossword puzzle incident. Cole was dismissed from employment on July 29, 2016, as detailed in a final notice of dismissal dated August 1, 2016.
Cole appealed his dismissal to the PAB. He was represented by the State Employees' Association/Service Employees' International Union (SEA/SEIU) at the PAB hearing. The PAB heard testimony from Burns, Burns' supervisor, a human resources administrator, and Cole, and received into evidence the memorandum of counsel, the three letters of warning, the June 7 performance evaluation, and the August 1 notice of dismissal. The PAB concluded that the letters of warning were issued for the "same or substantially similar conduct or offenses," thus satisfying the requirements of Per 1002.08(c)(1) for dismissal. The PAB found that "all three ... [letters] were issued to specifically address [Cole's] poor quality of work," and therefore all three letters were issued for "failure to meet any work standard" under Per 1002.04(b)(1). Specifically addressing the third letter and the crossword puzzle incident, the PAB noted that Cole stated he did not have enough time to complete a project, but was then found working on a crossword puzzle shortly afterwards during work hours. The PAB concluded that "[t]he fact [Cole] did not complete the project on time demonstrates that this, too, fits only into the category of failure to meet any work standard [in Per 1002.04(b)(1) ]."
Cole filed a motion for reconsideration and/or rehearing, which the PAB denied. SEA/SEIU filed this appeal thirty days later. DOIT then filed a motion to dismiss the appeal, arguing that we lack jurisdiction because SEA/SEIU named itself as the petitioner in the notice of appeal. A motion to amend the petition for appellate review to include Cole as the captioned petitioner was then filed, as well as an objection to DOIT's motion to dismiss. We denied DOIT's motion without prejudice, with the understanding that the parties would be allowed to brief the issues raised in DOIT's motion in their respective briefs. We granted the motion to amend the appeal document to include Cole as the captioned petitioner. Prior to oral argument, we asked the parties to address the implications of Atwater v. Town of Plainfield, 156 N.H. 265, 931 A.2d 1220 (2007), on the jurisdictional issue raised by DOIT. Both parties submitted memoranda of law on the matter.
On appeal, Cole argues that the PAB misapplied our holding in Appeal of Murdock, 156 N.H. 732, 943 A.2d 757 (2008), as well as Per 1002.08 and Per 1002.04, in reaching its conclusion that the three letters of warning concerned the same or substantially similar conduct. DOIT argues that we lack subject matter jurisdiction to answer this question because the SEA/SEIU initially listed itself, not Cole, as the petitioner in this case, and did not move to amend the appeal document with Cole's name until after the 30-day jurisdictional deadline of RSA 541:6 had passed. See RSA 541:6 (2007). Because the existence or absence of jurisdiction determines whether we may proceed to the merits of the appeal, *955we turn first to the jurisdictional issue.
II
Subject matter jurisdiction is jurisdiction over the nature of the case and the type of relief sought: the extent to which a court can rule on the conduct of persons or the status of things. Gordon v. Town of Rye, 162 N.H. 144, 149, 27 A.3d 644 (2011). In other words, it is a tribunal's authority to adjudicate the type of controversy involved in the action. Id. A court lacks power to hear or determine a case concerning subject matter over which it has no jurisdiction. Id. A party may challenge subject matter jurisdiction at any time during the proceeding, including on appeal, and may not waive subject matter jurisdiction. Id.
Because the scope of our power to hear appeals from the PAB is governed by statute, see RSA 21-I:58, II (2012), a determination of our jurisdiction in this case requires statutory interpretation, see Gordon, 162 N.H. at 150, 27 A.3d 644. The interpretation of a statute is a question of law. STIHL, Inc. v. State of N.H., 168 N.H. 332, 334, 126 A.3d 1192 (2015). In matters of statutory interpretation, we are the final arbiters of the legislature's intent as expressed in the words of the statute considered as a whole. Id. When construing a statute's meaning, we first examine the language found in the statute, and where possible, we ascribe the plain and ordinary meanings to the words used. Id. We interpret statutory provisions in the context of the overall statutory scheme. Id. at 335, 126 A.3d 1192.
Adjudicative decisions made by the PAB are subject to appeals to this court within the parameters of RSA chapter 541. RSA 21-I:58, II. All such appeals must be filed within thirty days of the denial of a motion for rehearing submitted to the PAB, or, if the motion for rehearing is granted, within thirty days after the decision on such rehearing. RSA 541:6. Compliance with this statutory thirty-day rule "is a necessary prerequisite to establishing jurisdiction in the appellate body." Dermody v. Town of Gilford, 137 N.H. 294, 296, 627 A.2d 570 (1993) (quotation omitted). If an appeal is filed outside of the thirty-day window, subject matter jurisdiction does not vest. See Appeal of Carreau, 157 N.H. 122, 123, 945 A.2d 687 (2008) (dismissing for lack of jurisdiction an appeal brought under RSA chapter 541 filed one day late). We do not have authority to waive this jurisdictional deadline: if the appeal is filed even one day after the thirty-day mark, we are required to dismiss it for lack of jurisdiction. See id.
In this case, Cole's motion for reconsideration and/or rehearing was denied by the PAB on April 26, 2017. A notice of appeal of the PAB's decision was filed in this court on May 26, 2017, within the thirty-day appeal period. However, the appeal document named the SEA/SEIU as the petitioner, not Cole. The motion to amend the appeal document to specifically name Cole was not filed until June 23, 2017, after the thirty-day window had closed. DOIT argues that the failure to amend the appeal document within the thirty-day appeal period deprives this court of jurisdiction.
A similar situation arose in Atwater. At issue there was an appeal of a town planning board's decision to the superior court pursuant to RSA 677:15, which also has a thirty-day jurisdictional filing deadline. Atwater, 156 N.H. at 266-67, 931 A.2d 1220 ; see RSA 677:15 (Supp. 2006) (amended 2009, 2013). The petitioners mistakenly named an intervenor as the defendant in their caption rather than the town, the town being the proper defendant.
*956Id. at 266, 931 A.2d 1220. After the thirty-day window had closed, the petitioners moved to substitute the town as the defendant. Id. The town moved to dismiss for lack of jurisdiction due to noncompliance with RSA 677:15. Id. The superior court granted the motion, but we reversed. Id. at 266, 269, 931 A.2d 1220.
Noting that the statute at issue required only that the petition be filed by a certain date, we concluded that the "filing of the appeal within thirty days of the planning board's [decision] ... established jurisdiction," even though the petitioners named an incorrect defendant. Id. at 268, 931 A.2d 1220. Unlike other cases where a new defendant is sought to be substituted after a statute of limitations has run, we explained that an administrative appeal is simply the continuance of the original suit first heard in the administrative forum, which would otherwise become final without filing the appeal document. See id. In order to transfer jurisdiction, RSA 677:15 required "no more than timely fil[ing of] the petition." Id. at 267-68, 931 A.2d 1220. Thus, jurisdiction vested and the case was transferred to superior court upon the filing of the appeal document, even though a party was inaccurately named. See id. at 268, 931 A.2d 1220.
We find the reasoning of Atwater equally applicable to this case. Both RSA 677:15 and RSA 541:6 contain a filing deadline as a prerequisite to establishing appellate jurisdiction over decisions of an administrative body. In both contexts, by filing the appeal document within the jurisdictional window, the appellant extends the life of the case originally brought in the administrative forum. No new case or cause of action is brought. Seasonable filing of the appeal document transfers jurisdiction from the administrative to the appellate body, but deficiencies in case-captioning do not disrupt the extension of the case's lifetime. See id. at 267-68, 931 A.2d 1220. In other words, neither the instant case nor Atwater presents the situation seen in Carreau, because both here and in Atwater the appeal document was filed within the thirty-day window, see Atwater, 156 N.H. at 266, 931 A.2d 1220, whereas in Carreau, the initial filing of the appeal document just one day after the window had closed precluded jurisdiction, see Carreau, 157 N.H. at 123-24, 945 A.2d 687.
DOIT argues that Atwater does not control. Atwater concerned a timely petition brought by persons who were proper petitioners with standing to appeal. DOIT argues that this case involves an appeal document filed by a party who lacks standing to appeal: SEA/SEIU. Because SEA/SEIU lacks standing to appeal, DOIT argues, its petition for appellate review had no legal effect and there was no legal instrument in existence by the time the jurisdictional window had closed that could be amended to include Cole.
DOIT correctly notes that standing, like the filing deadline of RSA 541:6, is a jurisdictional prerequisite. See Duncan v. State, 166 N.H. 630, 640, 102 A.3d 913 (2014). However, we have long allowed for "substitution of an entirely new party as plaintiff, including substitution of a plaintiff with standing for an original plaintiff with no standing, when required to prevent injustice and in the absence of resultant prejudice to the defendant." Nat'l Marine Underwriters, Inc. v. McCormack, 138 N.H. 6, 8, 634 A.2d 1008 (1993) (emphasis added); see also RSA 514:9 (2007) (affirming court's power at "any stage of the proceedings" to allow nonprejudicial amendments when necessary to prevent injustice). Amendments may be given retroactive effect to a petition's filing date in order to cure a defective form of action if justice so requires.
*957Morphy v. Morphy, 112 N.H. 507, 510-11, 298 A.2d 580 (1972). We have declined to interpret statutory filing requirements similar to the one at issue here as jurisdictional necessities. See Simonsen v. Town of Derry, 145 N.H. 382, 384, 765 A.2d 1033 (2000) (declining to define the verification requirement of RSA 677:15 as a jurisdictional prerequisite to appeal of an administrative decision). We likewise decline to do so in this case. DOIT has not been prejudiced by the inaccurate captioning of the appeal document. See Edgewood Civic Club v. Blaisdell, 95 N.H. 244, 247, 61 A.2d 517 (1948) (finding it was "proper" for trial court to allow an amendment substituting plaintiffs with standing for a plaintiff with no standing after a thirty-day period for appeal of a zoning decision had expired); RSA 514:9. Furthermore, the original appeal document, on the very first page, states that it is appealing the decision of the PAB in "APPEAL OF JAMES COLE," and provides the docket number of the PAB's decision immediately thereafter. We conclude that DOIT was on fair notice of which PAB decision was being appealed, and was not otherwise prejudiced. See Nat'l Marine, 138 N.H. at 8, 634 A.2d 1008.
DOIT also argues that a consideration of the merits in this case would amount to this court "creating jurisdiction" outside of the scope set by the legislature in RSA 541:6, and in contravention of our decision in Carreau. We disagree. A plaintiff with standing may be substituted for a plaintiff without standing. See id. ; Blaisdell, 95 N.H. at 247, 61 A.2d 517. Such a substitution may be given retroactive effect if justice so requires and in the absence of prejudice to the opposing party. See Nat'l Marine, 138 N.H. at 8, 634 A.2d 1008. For us to have jurisdiction over the appeal of a PAB decision, the appeal document must be filed within thirty days of the denial of a motion for rehearing submitted to the PAB, or, if the motion for rehearing is granted, within thirty days after the decision on such rehearing. RSA 541:6. That requirement was not satisfied in Carreau, which is why we lacked jurisdiction in that case. See Carreau, 157 N.H. at 123, 945 A.2d 687. Here, by contrast, the appeal document was filed within the thirty-day window of RSA 541:6. Because the appeal document was timely filed, and because we conclude that RSA 541:6 does not make accurate case-captioning a jurisdictional prerequisite, we have authority to decide this case on the merits in the absence of any prejudice to DOIT.
DOIT also argues that Cole is prohibited from making arguments for jurisdiction not made in his objection to DOIT's motion to dismiss/motion for summary affirmance. DOIT argues that Cole was on notice of DOIT's jurisdictional argument at the time he submitted his brief but chose not to address it outside of a short reference to the initially inaccurate caption. Citing our decision in Panas v. Harakis & K-Mart Corp., 129 N.H. 591, 529 A.2d 976 (1987), DOIT asserts that Cole waived any argument as to the existence of jurisdiction by not addressing the issue in his brief. Even assuming, without deciding, that an argument related to subject matter jurisdiction can be "waived," but see Gordon, 162 N.H. at 149, 27 A.3d 644, DOIT's argument is misplaced. In Panas, the petitioners raised an argument for the first time on appeal in their reply brief. Panas, 129 N.H. at 617, 529 A.2d 976. We concluded that reply briefs may only respond to the opposing party's brief, and cannot raise entirely new issues. Id. In this case, DOIT, not Cole, is the party raising the jurisdictional issue. Cole did not address DOIT's jurisdictional arguments in his brief, but did respond to them in a reply brief. Our order granting the motion to amend the appeal document to include *958Cole stated that it was "subject to [DOIT's ] ability to present in its brief the arguments set forth in its motion to dismiss." (Emphasis added). The order then stated that the parties "may" address the jurisdictional issue in their respective briefs. Cole's response to DOIT's jurisdictional argument is the proper subject of a reply brief, not the improper assertion of a new issue in a reply brief. See State v. Blunt, 164 N.H. 679, 685, 62 A.3d 1285 (2013).
In light of the above, we conclude that we have jurisdiction to proceed to the merits of this appeal. We do so now.
III
RSA chapter 541 governs our review of PAB decisions. See Appeal of Morton, 158 N.H. 76, 78, 960 A.2d 332 (2008). We will not set aside the PAB's order except for errors of law, unless the petitioner proves by a clear preponderance of the evidence that the order is unjust or unreasonable. RSA 541:13 (2007). The PAB's findings of fact are presumed prima facie lawful and reasonable. Id. In reviewing the PAB's findings, our task is not to determine whether we would have found differently or to reweigh the evidence, but rather to determine whether its findings are supported by competent evidence in the record. Appeal of Collins, 171 N.H.----, ----, 189 A.3d 316 (decided June 8, 2018) (slip op. at 2). However, we review the PAB's interpretations of statutes and administrative rules de novo. Appeal of Alexander, 163 N.H. 397, 401, 42 A.3d 804 (2012). When interpreting both statutes and administrative rules, we ascribe the plain and ordinary meanings to words used, looking at the rule or statutory scheme as a whole, and not in a piecemeal fashion. Morton, 158 N.H. at 78, 960 A.2d 332.
Per 1002.08(c)(1) provides that:
An appointing authority may dismiss an employee for conduct described in Per 1002.04 when the employee has previously received 2 written warnings for the same or substantially similar type of conduct or offense within a period of 5 years, by issuing a final written warning and notice of dismissal as set forth in this rule ....
Per 1002.04(b) provides, in part, that:
An appointing authority may issue a written warning to an employee for unsatisfactory work performance or conduct including, but not limited to, the following:
(1) Failure to meet any work standard;
(2) Failure to take corrective action as directed;
...
(9) Disruptive, disorderly, or disrespectful conduct in the workplace, including the use of insulting or abusive language or gestures ....
Cole concedes that the first two letters of warning "likely" concern "the same or substantially similar" behavior. See N.H. Admin. R., Per 1002.08(c)(1). He argues on appeal that the PAB erred in finding that the third letter of warning concerned the same or substantially similar conduct or offense as the first two.
In Murdock, we reversed in part a decision of the PAB that upheld an employee's termination under the predecessor to Per 1002.08(c)(1). Murdock, 156 N.H. at 738, 943 A.2d 757. When Murdock was decided, the predecessor rule authorized termination upon the employee's receipt of "a third written warning for the same offense within a period of 5 years." Id. at 735, 943 A.2d 757 (quotation omitted). In that case, the employee had received a warning for transporting alcohol in a state vehicle, a *959warning for displaying inappropriate photographs in the workplace, and a warning for taking a lunch break outside of his allotted time. Id. at 733-34, 943 A.2d 757. Each warning asserted that the employee had violated the predecessor to Per 1002.04(b)(1); each warning was issued for conduct that purported to amount to a failure to meet any work standard. See id. In reversing the PAB's decision to uphold the employee's termination, we emphasized that the language "same offense" in the applicable administrative rule referred to the behavior giving rise to the warnings, rather than to "behavior that might be characterized as a similar violation." Id. at 738, 943 A.2d 757 (quotation omitted). Since that case was decided, however, the applicable administrative rule has been amended. The rule no longer requires the three written warnings to be for the "same offense." It now provides for termination after "2 written warnings for the same or substantially similar type of conduct or offense within a period of 5 years [upon] issuing a final written warning and notice of dismissal." N.H. Admin. R., Per 1002.08(c)(1) (emphasis added).
In light of Murdock, Cole argues that the third letter of warning was not issued for the same or substantially similar conduct or offense as the first two letters because the crossword puzzle incident has "nothing in common" with the concerns raised by the first two letters. To prevail in this argument on appeal, Cole must demonstrate that the PAB erred as a matter of law in reaching the opposite conclusion, or that its conclusion was unjust or unreasonable. See RSA 541:13. We conclude that Cole has not carried his burden.
After a full hearing, the PAB concluded that all three letters were issued for conduct properly grouped under Per 1002.04(b)(1) for "failure to meet any work standard." Addressing the third letter of warning, the PAB noted that the crossword puzzle incident occurred within the context of Cole's inability to complete his assignments in a timely fashion. The PAB concluded the crossword puzzle incident illustrated Cole's poor quality of work because it showed his inability to complete projects on time, and therefore the letter was properly issued under Per 1002.04(b)(1). Because all three letters arose from Cole's poor quality of work, as reflected in his inability to timely complete assignments, the PAB concluded that they concerned the same or substantially similar conduct or offenses within the meaning of Per 1002.08(c)(1). Based on our review of the record and evidence considered by the board, including all three letters of warning, we conclude that the board's decision is supported by competent evidence, and is neither erroneous as a matter of law nor unjust or unreasonable.
Cole also argues that, the amended language of Per 1002.08(c)(1) notwithstanding, Murdock requires reversal of the PAB's decision. According to his argument, Murdock demonstrates that if a particular behavior can be categorized in a Per 1002.04(b) category more specific than "failure to meet any work standard," it must be so categorized; otherwise the catch-all work standard category would render the others superfluous. Cole further argues that the crossword puzzle incident is more accurately defined as "[d]isruptive, disorderly, or disrespectful conduct" within the meaning of Per 1002.04(b)(9). However, based on our review of the record in this case, we cannot conclude that the PAB erred in finding that the only category in which the crossword puzzle incident fits is failure to meet any work standard. Evidence in the record *960supports the PAB's finding that the crossword puzzle incident occurred within the context of Cole being unable to complete assignments in a timely manner, and therefore was properly characterized as an issue of work quality. We therefore conclude that the PAB's decision was not unjust or unreasonable.
Affirmed.
HICKS and DONOVAN, JJ., concurred.