Note 6 - Fair Value Measurements (Details Textual) - USD ($) $ in Thousands	12 Months Ended
Oct. 02, 2021	Oct. 03, 2020
Disposal Group, Including Discontinued Operation, Assets, Total	$ 6,306	$ 7,778
Summerville Facility Acquired in STM Acquisition [Member]
Disposal Group, Including Discontinued Operation, Assets, Total		6,300
Summerville Facility Acquired in STM Acquisition [Member] \| Restructuring Charges [Member]
Impairment of Long-Lived Assets to be Disposed of	1,400
Non Financial [Member] \| Fair Value, Nonrecurring [Member]
Assets, Fair Value Disclosure	$ 0	$ 0

Fair value portion of probable future economic benefits obtained or controlled by an entity as a result of past transactions or events.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=123874694&loc=d3e19207-110258

+ Details

Name:	us-gaap_AssetsFairValueDisclosure
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount classified as assets attributable to disposal group held for sale or disposed of.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 205
-SubTopic 20
-Section 45
-Paragraph 10
-URI http://asc.fasb.org/extlink&oid=109222160&loc=d3e1107-107759

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 360
-SubTopic 10
-Section 50
-Paragraph 3
-Subparagraph (e)
-URI http://asc.fasb.org/extlink&oid=109226691&loc=d3e2941-110230

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 205
-SubTopic 20
-Section 50
-Paragraph 5B
-Subparagraph (e)
-URI http://asc.fasb.org/extlink&oid=109222650&loc=SL51721673-107760

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 205
-SubTopic 20
-Section 45
-Paragraph 11
-URI http://asc.fasb.org/extlink&oid=109222160&loc=SL51721533-107759

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 205
-SubTopic 20
-Section 50
-Paragraph 7
-URI http://asc.fasb.org/extlink&oid=109222650&loc=SL51721683-107760

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 205
-SubTopic 20
-Section 50
-Paragraph 5C
-Subparagraph (a)(2)
-URI http://asc.fasb.org/extlink&oid=109222650&loc=SL51721675-107760

+ Details

Name:	us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

The aggregate amount of write-downs for impairments recognized during the period for long-lived assets held for abandonment, exchange or sale.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 28
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=123570139&loc=d3e3602-108585

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 360
-SubTopic 10
-Section 45
-Paragraph 15
-URI http://asc.fasb.org/extlink&oid=123351718&loc=d3e2611-110228

+ Details

Name:	us-gaap_ImpairmentOfLongLivedAssetsToBeDisposedOf
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Details

Name:	us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis=iiin_SummervilleFacilityAcquiredInSTMAcquisitionMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_IncomeStatementLocationAxis=us-gaap_RestructuringChargesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FairValueByAssetClassAxis=iiin_NonFinancialMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FairValueByMeasurementFrequencyAxis=us-gaap_FairValueMeasurementsNonrecurringMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: