The number of years of continuous service required to receive a benefit under the SERP.

No definition available.

Name:	iiin_DefinedBenefitPlanEmploymentTerm
Namespace Prefix:	iiin_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

The number of consecutive years used to determine a Participant's highest average annual base salary in a supplemental employee retirement plan.

+ References

No definition available.

+ Details

Name:	iiin_DefinedBenefitPlanNumberOfYearsInAverageAnnualBaseSalary
Namespace Prefix:	iiin_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Defined benefit plan number of years preceding retirement for average annual base salary calculation

+ References

No definition available.

+ Details

Name:	iiin_DefinedBenefitPlanNumberOfYearsPrecedingRetirementForAverageAnnualBaseSalaryCalculation
Namespace Prefix:	iiin_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

The percentage of a Participant's highest average base salary that will be paid out to the Participant as supplemental retirement benefits if they meet the continuous service requirement.

+ References

No definition available.

+ Details

Name:	iiin_DefinedBenefitPlanPercentOfHighestAverageSalaryBase
Namespace Prefix:	iiin_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

The benefit will be reduced by a certain percentage for each month short of 30 years that the Participant was employed by the Company assuming the minimum continuous service and age requirements.

+ References

No definition available.

+ Details

Name:	iiin_DefinedBenefitPlanReductionForEachMonth
Namespace Prefix:	iiin_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

The minimum age that an employee may retire at to receive benefits.

+ References

No definition available.

+ Details

Name:	iiin_DefinedBenefitPlanRetirementAge
Namespace Prefix:	iiin_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	duration

- Definition

Represents the amount at which stop-loss insurance covers the remainder of the claim.

+ References

No definition available.

+ Details

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

- Definition

The maximum period of time that a Participant will be paid supplemental retirement benefits if they are eligible for full benefits.

+ References

No definition available.

+ Details

Name:	iiin_SupplementalRetirementBenefitPeriod
Namespace Prefix:	iiin_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount included in accumulated other comprehensive income (loss) for gain (loss) of defined benefit plan expected to be recognized in net periodic benefit (cost) credit for fiscal year following most recent annual statement of financial position.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 715
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (s)
-URI http://asc.fasb.org/extlink&oid=118255775&loc=d3e1928-114920

+ Details

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

- Definition

Amount of cost for defined contribution plan.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 715
-SubTopic 70
-Section 50
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=49170846&loc=d3e28014-114942

+ Details

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

- Definition

Percentage of employees' gross pay for which the employer contributes a matching contribution to a defined contribution plan.

+ References

No definition available.

+ Details

Name:	us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage employer matches of the employee's percentage contribution matched.

+ References

No definition available.

+ Details

Name:	us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Maximum percentage of employee gross pay the employee may contribute to a defined contribution plan.

+ References

No definition available.

+ Details

Name:	us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeePercent
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_RetirementPlanTypeAxis=us-gaap_SupplementalEmployeeRetirementPlanDefinedBenefitMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MinimumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RetirementPlanTypeAxis=iiin_ReducedSERPMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RetirementPlanTypeAxis=iiin_RetirementSavingsPlanMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RetirementPlanTypeAxis=iiin_RetirementSavingsPlanFirst1PercentOfEmployeeContributionMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RetirementPlanTypeAxis=iiin_RetirementSavingsPlanNext5PercentOfEmployeeContributionMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RetirementPlanTypeAxis=iiin_VEBAMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Note 11 - Employee Benefit Plans (Details Textual) - USD ($)	12 Months Ended
	Sep. 28, 2019	Sep. 29, 2018	Sep. 30, 2017
Defined Benefit Plan, Expected Amortization of Gain (Loss), Next Fiscal Year	$ 293,000
Supplemental Employee Retirement Plan [Member]
Supplemental Retirement Benefit Period	15 years
Defined Benefit Plan Percent of Highest Average Salary Base	50.00%
Defined Benefit Plan Number of Years in Average Annual Base Salary	5 years
Defined Benefit Plan Number of Years Preceding Retirement for Average Annual Base Salary Calculation	10 years
Supplemental Employee Retirement Plan [Member] \| Minimum [Member]
Defined Benefit Plan Employment Term	30 years
Reduced SERP [Member]
Defined Benefit Plan Retirement Age	65
Defined Benefit Plan, Reduction for Each Month	0.0028%
Reduced SERP [Member] \| Minimum [Member]
Defined Benefit Plan Employment Term	10 years
Retirement Savings Plan [Member]
Defined Contribution Plan, Maximum Annual Contributions Per Employee, Percent	75.00%
Defined Contribution Plan, Cost	$ 1,200,000	$ 1,100,000	$ 1,100,000
Retirement Savings Plan, First 1% of Employee Contribution [Member]
Defined Contribution Plan, Employer Matching Contribution, Percent of Match	100.00%
Defined Contribution Plan, Employer Matching Contribution, Percent of Employees' Gross Pay	1.00%
Retirement Savings Plan, Next 5% of Employee Contribution [Member]
Defined Contribution Plan, Employer Matching Contribution, Percent of Match	50.00%
Defined Contribution Plan, Employer Matching Contribution, Percent of Employees' Gross Pay	5.00%
VEBA [Member]
Defined Contribution Plan, Cost	$ 5,800,000	$ 5,100,000	$ 5,600,000
Healthcare Coverage Claims in Excess of	$ 175,000