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Note 9 - Long-term Debt (Details Textual) - USD ($)	3 Months Ended		6 Months Ended
	Apr. 01, 2023	Apr. 02, 2022	Apr. 01, 2023	Apr. 02, 2022
Amortization of Debt Issuance Costs	$ 16,000	$ 16,000	$ 32,000	$ 33,000
Revolving Credit Facility [Member]
Line of Credit Facility, Maximum Borrowing Capacity	100,000,000.0		100,000,000.0
Line Of Credit Facility, Additional Borrowing Capacity			50,000,000.0
Long-Term Line of Credit, Total	0		0
Line of Credit Facility, Remaining Borrowing Capacity	98,600,000		98,600,000
Letters of Credit Outstanding, Amount	$ 1,400,000		$ 1,400,000
Debt Instrument, Interest Rate, Increase (Decrease)			2.00%
Fixed Charge Coverage Ratio			1.0
Credit Facility, Liquidity Amount			$ 10,000,000.0
Revolving Credit Facility [Member] | Federal Funds Rate [Member]
Debt Instrument, Basis Spread on Variable Rate			0.50%
Revolving Credit Facility [Member] | Secured Overnight Financing Rate (SOFR) [Member]
Debt Instrument, Basis Spread on Variable Rate			1.25%
Revolving Credit Facility [Member] | Secured Overnight Financing Rate (SOFR) [Member] | Minimum [Member]
Debt Instrument, Basis Spread on Variable Rate			1.25%
Revolving Credit Facility [Member] | Secured Overnight Financing Rate (SOFR) [Member] | Maximum [Member]
Debt Instrument, Basis Spread on Variable Rate			1.50%
Revolving Credit Facility [Member] | Secured Overnight Financing Rate (SOFR) Credit Adjustment [Member]
Debt Instrument, Basis Spread on Variable Rate			0.10%
Revolving Credit Facility [Member] | Base Rate [Member]
Debt Instrument, Basis Spread on Variable Rate			0.25%
Revolving Credit Facility [Member] | Base Rate [Member] | Minimum [Member]
Debt Instrument, Basis Spread on Variable Rate			0.25%
Revolving Credit Facility [Member] | Base Rate [Member] | Maximum [Member]
Debt Instrument, Basis Spread on Variable Rate			0.50%

X

- Definition

The minimum liquidity amount that would trigger a fixed charge coverage ratio requirement as part of a covenant under a credit facility.

+ References

No definition available.

+ Details

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Namespace Prefix:	iiin_
Data Type:	xbrli:monetaryItemType
Balance Type:	na
Period Type:	duration

X

- Definition

A ratio that indicates an entities ability to satisfy fixed expenses.

+ References

No definition available.

+ Details

Name:	iiin_FixedChargeCoverageRatio
Namespace Prefix:	iiin_
Data Type:	xbrli:pureItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Represents additional borrowing capacity of line of credit.

+ References

No definition available.

+ Details

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

X

- Definition

Amount of amortization expense attributable to debt issuance costs.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1F
-Subparagraph (b)(2)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481139/470-20-50-1F

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 230
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 28
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482740/230-10-45-28

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 835
-SubTopic 30
-Name Accounting Standards Codification
-Section 45
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482925/835-30-45-3

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 220
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03(8))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147483621/220-10-S99-2

+ Details

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

X

- Definition

Percentage points added to the reference rate to compute the variable rate on the debt instrument.

+ References

No definition available.

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Incremental percentage increase (decrease) in the stated rate on a debt instrument.

+ References

No definition available.

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

X

- Definition

The total amount of the contingent obligation under letters of credit outstanding as of the reporting date.

+ References

No definition available.

+ Details

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

X

- Definition

The carrying value as of the balance sheet date of the current and noncurrent portions of long-term obligations drawn from a line of credit, which is a bank's commitment to make loans up to a specific amount. Examples of items that might be included in the application of this element may consist of letters of credit, standby letters of credit, and revolving credit arrangements, under which borrowings can be made up to a maximum amount as of any point in time conditional on satisfaction of specified terms before, as of and after the date of drawdowns on the line. Includes short-term obligations that would normally be classified as current liabilities but for which (a) postbalance sheet date issuance of a long term obligation to refinance the short term obligation on a long term basis, or (b) the enterprise has entered into a financing agreement that clearly permits the enterprise to refinance the short-term obligation on a long term basis and the following conditions are met (1) the agreement does not expire within 1 year and is not cancelable by the lender except for violation of an objectively determinable provision, (2) no violation exists at the BS date, and (3) the lender has entered into the financing agreement is expected to be financially capable of honoring the agreement.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(22))
-SubTopic 10
-Topic 210
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 944
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(16)(a)(2))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479440/944-210-S99-1

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 942
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(16))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479853/942-210-S99-1

+ Details

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

X

- Definition

Maximum borrowing capacity under the credit facility without consideration of any current restrictions on the amount that could be borrowed or the amounts currently outstanding under the facility.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.19(b),22(b))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

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

X

- Definition

Amount of borrowing capacity currently available under the credit facility (current borrowing capacity less the amount of borrowings outstanding).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.19(b),22(b))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

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Period Type:	instant

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- Details

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- Details

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