Note 9 - Employee Benefit Plans (Details Textual)	9 Months Ended
Jun. 27, 2026
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 (Year)	5 years
Defined Benefit Plan Number of Years Preceding Retirement for Average Annual Base Salary Calculation (Year)	10 years
Supplemental Employee Retirement Plan [Member] \| Minimum [Member]
Defined Benefit Plan, Employment Term (Year)	30 years
Reduced SERP [Member]
Defined Benefit Plan Retirement Age	55
Defined Benefit Plan, Reduction for Each Month	0.28%
Reduced SERP [Member] \| Minimum [Member]
Defined Benefit Plan, Employment Term (Year)	10 years

The number of years of continuous service required to receive the maximum 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:	dtr-types: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:	dtr-types: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

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

- 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: