This element represents acquisition-related costs incurred to effect a business combination which costs have been expensed during the period. Such costs include finder's fees; advisory, legal, accounting, valuation, and other professional or consulting fees; general administrative costs, including the costs of maintaining an internal acquisitions department; and may include costs of registering and issuing debt and equity securities.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 10
-Section 25
-Paragraph 23
-URI http://asc.fasb.org/extlink&oid=123586518&loc=d3e1043-128460

+ Details

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

- Definition

Amount of consideration transferred, consisting of acquisition-date fair value of assets transferred by the acquirer, liabilities incurred by the acquirer, and equity interest issued by the acquirer.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 30
-Section 30
-Paragraph 8
-URI http://asc.fasb.org/extlink&oid=116859721&loc=d3e6613-128477

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 30
-Section 50
-Paragraph 1
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=120321790&loc=d3e6927-128479

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 30
-Section 30
-Paragraph 7
-URI http://asc.fasb.org/extlink&oid=116859721&loc=d3e6578-128477

+ Details

Name:	us-gaap_BusinessCombinationConsiderationTransferred1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of liabilities incurred by the acquirer as part of consideration transferred in a business combination.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 30
-Section 30
-Paragraph 7
-URI http://asc.fasb.org/extlink&oid=116859721&loc=d3e6578-128477

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 30
-Section 25
-Paragraph 5
-URI http://asc.fasb.org/extlink&oid=6911189&loc=d3e6405-128476

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 30
-Section 50
-Paragraph 1
-Subparagraph (b)(3)
-URI http://asc.fasb.org/extlink&oid=120321790&loc=d3e6927-128479

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 30
-Section 30
-Paragraph 8
-URI http://asc.fasb.org/extlink&oid=116859721&loc=d3e6613-128477

+ Details

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

- Definition

This element represents the amount of revenue of the acquiree since the acquisition date included in the consolidated income statement for the reporting period.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (h)(1)
-URI http://asc.fasb.org/extlink&oid=79982066&loc=d3e1392-128463

+ Details

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

- 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

- 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
-Publisher FASB
-Name Accounting Standards Codification
-Topic 420
-SubTopic 10
-Section 50
-Paragraph 1
-Subparagraph (b)(2)
-URI http://asc.fasb.org/extlink&oid=6394359&loc=d3e17939-110869

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 420
-SubTopic 10
-Section S99
-Paragraph 2
-Subparagraph (SAB TOPIC 5.P.4(b)(2))
-URI http://asc.fasb.org/extlink&oid=115931487&loc=d3e140904-122747

+ Details

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

- Details

Name:	us-gaap_BalanceSheetLocationAxis=iiin_AccruedExpensesMember
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_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis=iiin_SummervilleFacilityAcquiredInSTMAcquisitionMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_BusinessAcquisitionAxis=iiin_STMAcquisitionMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Note 5 - Business Combination (Details Textual) - USD ($)		12 Months Ended
	Mar. 16, 2020	Oct. 02, 2021	Oct. 03, 2020	Sep. 28, 2019
Restructuring Reserve, Ending Balance		$ 10,000	$ 171,000
Business Combination, Acquisition Related Costs		0	195,000	$ 0
Accrued Expenses [Member]
Restructuring Reserve, Ending Balance		10,000	171,000
Restructuring Charges [Member] \| Summerville Facility Acquired in STM Acquisition [Member]
Impairment of Long-Lived Assets to be Disposed of		$ 1,400,000
STM Acquisition [Member]
Business Combination, Consideration Transferred, Total	$ 19,400,000
Business Combination, Consideration Transferred, Liabilities Incurred	$ 1,000,000.0
Business Combination, Pro Forma Information, Revenue of Acquiree since Acquisition Date, Actual			3,000,000.0
Business Combination, Acquisition Related Costs			$ 195,000