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Note 5 - Restructuring - Restructuring Activity (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 28, 2024	Sep. 30, 2023	Oct. 01, 2022
Liability as of October 2, 2021		$ 0	$ 10
Restructuring charges (recoveries), net	$ 0	0	(318)
Cash payments			(314)
Non-cash charges			622
Liability as of October 1, 2022			0
Facility Closing [Member]
Liability as of October 2, 2021		0	10
Restructuring charges (recoveries), net			304
Cash payments			(314)
Non-cash charges			0
Liability as of October 1, 2022			0
Gain on Sale of Property and Equipment [Member]
Liability as of October 2, 2021		$ 0	0
Restructuring charges (recoveries), net			(622)
Cash payments			0
Non-cash charges			622
Liability as of October 1, 2022			$ 0

X

- Definition

Amount of expenses (recoveries) associated with exit or disposal activities pursuant to an authorized plan. Excludes expenses (recoveries) related to a discontinued operation or an asset retirement obligation.

+ References

No definition available.

+ Details

Name:	iiin_RestructuringChargesRecoveries
Namespace Prefix:	iiin_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

X

- Definition

Amount of increase (decrease) in the reserve for full or partial settlement through consideration other than cash.

+ References

No definition available.

+ Details

Name:	iiin_RestructuringReserveNoncashCharges
Namespace Prefix:	iiin_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

X

- Definition

Amount of cash payments made as the result of exit or disposal activities. Excludes payments associated with a discontinued operation or an asset retirement obligation.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482017/420-10-50-1

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 230
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 17
-Subparagraph (f)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482740/230-10-45-17

+ Details

Name:	us-gaap_PaymentsForRestructuring
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

X

- Definition

Carrying amount (including both current and noncurrent portions of the accrual) as of the balance sheet date pertaining to a specified type of cost associated with exit from or disposal of business activities or restructuring pursuant to a duly authorized plan.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SAB Topic 5.P.4.b.2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479823/420-10-S99-2

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482017/420-10-50-1

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Details

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Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

Name:	us-gaap_RestructuringCostAndReserveAxis=iiin_GainOnSaleOfPropertyAndEquipmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: