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Schedule II - Valuation and Qualifying Accounts - Allowance for Doubtful Accounts (Details) - USD ($) $ in Thousands | 12 Months Ended
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Sep. 29, 2018 | Sep. 30, 2017 | Oct. 01, 2016
Balance, beginning of year | $ 201 | $ 291 | $ 638
Amounts charged to earnings | 100 | (57) | (244)
Write-offs, net of recoveries | (6) | (33) | (103)
Balance, end of year | $ 295 | $ 201 | $ 291

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- Definition Amount of increase (decrease) in valuation and qualifying accounts and reserves from charge to earnings. + References No definition available. + Details
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Namespace Prefix: | iiin_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | duration

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- Definition Amount of valuation and qualifying accounts and reserves. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 235 -SubTopic 10 -Section S99 -Paragraph 4 -Subparagraph (SX 210.12-09) -URI http://asc.fasb.org/extlink&oid=26873400&loc=d3e24092-122690 + Details
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Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | instant

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- Definition Amount of decrease in valuation and qualifying accounts and reserves. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 235 -SubTopic 10 -Section S99 -Paragraph 4 -Subparagraph (SX 210.12-09) -URI http://asc.fasb.org/extlink&oid=26873400&loc=d3e24092-122690 + Details
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Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration