Methods of sampling of asbestos cement products

IS 7639: Scope - Key Formulas, Tables, and Specifications

Scope Summary

IS 7639 covers inspection procedures for lots of items, defining acceptance criteria based on sampling by attributes and variables.

Key Formulas for Acceptability Limit (Clause 5.2.6)

• X = Observed value
• K = Acceptability criterion (from Table 1, col 8)
• R = Range or tolerance

Sampling & Acceptance Criteria (Clause 5.1.6 - Table 1)

• Sampling is done in two stages (1st and 2nd samples).
• Acceptance and rejection numbers are given per lot size in the full table.

Summary

• Use K from Table 1 (col 8) based on lot size.
• Calculate AL using L or U and K.
• Accept or reject lots based on comparison of observed values X with AL.
• Sampling size and acceptance numbers depend on lot size.

flowchart TD
    A[Start: Identify

IS 7639 - Definitions & Key Inspection Formulas

Definitions (Clause 2.0)

• The standard defines terms related to inspection and acceptability criteria for lots.
• Key terms include Lower specified limit (L), Upper specified limit (U), Acceptability Limit (AL), and Inspection by Variables/Attributes.

Acceptability Limit (AL) Calculation (Clause 5.2.6)

• X = observed value
• K = acceptability criterion (from Table 1, col 8)
• R = range of sample values

Sampling & Acceptability Criterion (Clause 5.1.6, Table 1)

Summary

• Use K from Table 1 based on lot size.
• Calculate AL using the formula depending on whether L or U applies.
• Compare observed value X with AL to accept or reject the lot.

flowchart TD
    A[Start: Identify Lot Size] --> B[Select K from Table 1]
    B --> C{Limit Type?}
    C -->|Lower Limit (L)| D[Calculate AL = L + K·R]
    C -->

IS 7639: Sampling Procedure Key Points

1. Sampling Scale & Criteria (Clause 5.1.6, Table 1)

• Inspection by Attributes: Acceptance/rejection based on number of defective items.
• Inspection by Variables: Uses sample size (n) and acceptability criterion (K).

2. Acceptability Limit (Clause 5.2.6)

Calculate Acceptability Limit (AL):

• X = Sample mean
• K = Acceptability

IS 7639 - Inspection Methods: Key Formulas & Tables

1. Inspection by Variables (Clause 5.2.6)

Use the Acceptability Limit (AL) to decide acceptance/rejection:

• X = observed value
• K = constant (depends on sampling plan)
• R = standard deviation or range

2. Scale of Sampling & Criteria for Conformity (Clause 5.1.6, Table 1)

Determination of Acceptability of Inspection Lots (IS 7639 - Clause 5.1.6 & 5.2.6)

1. Inspection by Attributes (Clause 5.1.6 & Table 1)

• Acceptance Criterion:
  If the total defective items ≤ Acceptance Number (a) (Col 5, Table 1), the lot is acceptable.
• Rejection Criterion:
  If defective items > Rejection Number (r) (Col 6, Table 1), the lot is rejected.

(Refer full Table 1 for complete ranges)

2. Inspection by Variables (Clause 5.2.6)

• Acceptability Limit (AL):

[ \text{For Lower Specified Limit } L: \quad AL = L + K \times R ] [ \text{For Upper Specified Limit } U: \quad AL = U - K \times R ]

Where:

• (K) = Constant (depends on sampling plan)

• (R) = Standard deviation or tolerance range

• (X) = Sample mean

• Decision:

| Condition | Accept if | Reject if | |-------------------------------------

IS 7639: Key Formulas & Tables for Calculation Methods (Clause 5.2.6 & related)

1. Acceptability Limit (AL) Calculation

• X = Observed value
• K = Acceptability criterion from Table 1 (Clause 5.2.5)
• R = Range or tolerance value

2. Acceptability Criterion K (from Table 1, Clause 5.1.6)

3. Inspection Sampling Summary

• Sample size and acceptance/rejection numbers depend on lot size.
• Two inspection stages (1st and 2nd) with cumulative sample sizes.
• Acceptance and rejection numbers are provided for both attributes and variables.

4. Rounding Off

• Follow IS 2-1960 for rounding off final test/inspection values.

flowchart TD
    A[Start: Lot Size] --> B{Find Sample Size & K from Table 

IS 7639: Criteria for Conformity Summary

1. Sampling & Acceptance (Clause 5.1.6, Table 1)

• a: Acceptance number (max defects allowed)
• r: Rejection number (min defects to reject lot)
• K: Acceptability criterion for inspection by variables

2. Inspection by Variables (Clause 5.2.6)

• Compute Acceptability Limit (AL):

| Recommendation | AL Formula | Acceptance Condition | Rejection Condition | |----------------

IS 7639 - Related Standards and References: Key Formulas & Table

1. Acceptability Limit (AL) Calculation (Clause 5.2.6)

• X = Measured value
• K = Constant (depends on inspection level)
• R = Range of sample values

2. Purpose

• Used for inspection by variables to decide acceptability or rejection of product batches.
• Ensures quality control per IS 7639.

3. Related Standards

• IS 7639 complements other Indian Standards on asbestos cement products.
• Refer to these for detailed product specifications and testing methods.

Summary

• Use the above AL formulas to evaluate product quality.
• Accept if measurement is within limits; reject otherwise.
• Follow related IS codes for comprehensive compliance.

flowchart TD
    A[Start: Measure X] --> B{Is limit Lower (L) or Upper (U)?}
    B -->|Lower (L)| C[Calculate AL = L + KR (or R)]
    B -->|Upper (U)| D[Calculate AL = U - KR (or R)]
    C --> E{Is X > AL?}
    D --> F{Is X ≤ AL?}
    E -->|Yes| G[Accept]
    E -->|No| H[Reject]
    F -->|Yes| G
    F -->|No| H

For detailed product requirements, consult IS 7639 and referenced Indian Standards on asbestos cement products.