Pith Number

pith:ENSSUIMI

pith:2026:ENSSUIMIBFGVYSQ5B762HYZ52Z

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Preventive Maintenance of a Two-Unit Priority Standby System with Repair

Alexandros Carballo (UH), Jos\'e E Vald\'es (UH), Marelys Crespo

Preventive maintenance improves mean time to system failure in two-unit priority standby systems when the priority unit has a bathtub or upside-down bathtub hazard rate.

arxiv:2605.02895 v2 · 2026-03-20 · math.OC · math.PR

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Claims

C1strongest claim

In the general case, we derive necessary and sufficient conditions under which maintenance improves the mean time to system failure. When the hazard rate of the priority unit exhibits either a bathtub-shaped or an upside-down bathtub-shaped, we establish conditions for the existence of both a threshold time beyond which maintenance enhances the mean time to system failure and an optimal maintenance time. We also derive explicit expressions for these quantities in terms of the hazard rate and the mean residual life function.

C2weakest assumption

The results rely on the priority unit having a bathtub-shaped or upside-down bathtub-shaped hazard rate and on standard assumptions about independent unit lifetimes and repair times; if real-world failure behavior deviates from these shapes or independence, the derived conditions and optimal times may not apply.

C3one line summary

Derives necessary and sufficient conditions under which preventive maintenance improves mean time to system failure in a two-unit priority standby system, with explicit threshold and optimal maintenance times for bathtub or upside-down bathtub hazard rates.

Receipt and verification

First computed	2026-05-27T01:05:56.114010Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

23652a2188094d5c4a1d0ffda3e33dd66afe1bb311fdf9f5263a5194c113a494

Aliases

arxiv: 2605.02895 · arxiv_version: 2605.02895v2 · doi: 10.48550/arxiv.2605.02895 · pith_short_12: ENSSUIMIBFGV · pith_short_16: ENSSUIMIBFGVYSQ5 · pith_short_8: ENSSUIMI

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ENSSUIMIBFGVYSQ5B762HYZ52Z \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 23652a2188094d5c4a1d0ffda3e33dd66afe1bb311fdf9f5263a5194c113a494

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4f598369958865bc74f0ef19f8a7963bcdee05e13b9e3d3d83a384c426dd17e",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-03-20T08:11:13Z",
    "title_canon_sha256": "f73f5719fc7a207f2e4b411d667def26ec1e7c2e6b6e8530f94ee0e8b2a51bc4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.02895",
    "kind": "arxiv",
    "version": 2
  }
}