Acceptance Sampling

What is Acceptance Sampling?

To decide if a lot is acceptable, you could inspect every unit of that lot (100% inspection). But in many situations this is not practically possible, especially when inspection is destructive. Then you would have no usable product left after inspection. With acceptance sampling, draw a sample from the lot and based on that sample decide whether the whole lot can be accepted or not. The sample size and the rules for acceptance or rejection are based on statistics. But also if inspection is not destructive, there are great advantages with acceptance sampling:

Of course, there are also some inherent disadvantages compared to 100% inspection:

The standards for acceptance sampling are designed to keep these risks at appropriate levels.

Prerequisites

For acceptance sampling to be a valid option, some prerequisites apply:

Supported Standards

IFS Cloud supports:

Delimitations

ISO 2859-1:1999 - Sampling procedures for inspection by attributes - Part 1: Sampling schemes indexed by acceptance quality limit (AQL) for lot-by-lot inspection

ISO 2859-3:2005 - Sampling procedures for inspection by attributes - Part 3: Skip-lot sampling procedures

ISO 3951-2:2013 – Sampling procedures for inspection by variables – Part 2: General specification for single sampling plans indexed by acceptance quality limit (AQL) for lot-by-lot inspection of independent quality characteristics

Key Concepts of Acceptance Sampling

Inspection Level

The inspection level sets the relative amount of inspection. There are three general inspection levels, I, II and III. Unless otherwise specified, level II shall be used. I is used when less discrimination is required and III is used when greater discrimination is required. There are also four additional special levels, S-1, S-2, S-3 and S-4 which may be used when small sample sizes are necessary and larger sampling risks can be tolerated.

Acceptance Quality Limit (AQL)

AQL is defined as the worst tolerable process fraction (%) nonconforming items when a continuing series of lots is submitted for acceptance sampling.

Acceptability Constant k

A constant depending on the specified AQL value and the sample size, that is used in the criteria for accepting the lot in an acceptance sampling plan by variables.

Acceptance Number (Ac)

If the number of nonconforming items in the sample is not greater than this value, the lot will be accepted. Acceptance Number is used in attribute acceptance sampling.

Rejection Number (Re)

If the number of nonconforming items in the sample is equal to or greater than this value, the lot will be rejected. Rejection number is used in attribute acceptance sampling.

Sample Size

The number of items from the lot to be inspected. It will depend on the lot size, the inspection level and if single, double or multiple inspection is to be used.

Sampling Plans

With a single sampling plan for attributes, only one sample is drawn, and acceptance is decided from the number of nonconforming items in that sample. With a double sampling plan, the sample size is smaller. But the number of nonconforming items may fall in between the acceptance and rejection numbers requiring a second sample to be drawn to decide on acceptance or rejection. With a multiple sampling plan, the sample size is even smaller, but up to five consecutive samples can be drawn to decide on acceptance or rejection.

Switching Score

When a lot is accepted, the switching score gets increased. When the switching score is at a certain level, it is possible to switch to the reduced inspection. The reduced inspection will be carried on as long as the lots are accepted. When in reduced inspection, any rejected lot will set the switching score back to zero. Switching Scores are used in attribute acceptance sampling.

Sampling Plan Ac Switching Score
Single 2 or more Add 3 to the switching score if the lot would have been
accepted if the AQL had been one step tighter; otherwise reset the switching score to zero.
Single 0 or 1 Add 2 to the switching score if the lot is accepted; otherwise reset
the switching score to zero.
Double All Add 3 to the switching score if the lot is accepted after the first
sample; otherwise reset the switching score to zero.
Multiple All Add 3 to the switching score if the lot is accepted by the third
sample; otherwise reset the switching score to zero.

Switching Rules

Inspection Switching Rules
Reduced If a lot is not accepted, or production is irregular, or other conditions warrant a switch, switch to Normal inspection.
Normal If current value of switching score is at least 30, (attribute sampling), or 10 successive lots have been accepted (variable sampling), switch to Reduced Inspection.

If 2 out of 5 or fewer consecutive lots are not accepted, switch to Tightened inspection.

Tightened If 5 consecutive lots are accepted, switch to Normal inspection.

If 5 lots are not accepted while on tightened inspection, switch to Discontinued inspection.

Discontinued If quality is improved, and approved by the responsible authority, switch to Tightened.

The switching rules are used together with the results from preceding lots to switch between normal, tightened and reduced inspection. Start at normal inspection.

Inspection Frequency

With attribute skip-lot sampling, lots will be randomly selected for inspection with a probability defined by the inspection frequency. The number of lots that are needed for qualification will be used for determining the initial inspection frequency. The data from the most recent 20 or fewer lots will be used for qualification.

Qualification Score

The attribute sampling qualification score is used not only for qualification, but also for making decisions regarding a change in frequency, interruption of the procedure, requalification and disqualification. The rules given can be applied in
the same manner to each state.

Sampling plan Inspection Ac Qualification Score
Skip Lot -Single Normal 3 or more If the lot would have been accepted had the AQL been two steps tighter, add 5 to the qualification
score;
If the lot would have been accepted had the AQL been one step but not two steps tighter, add 3 to the qualification score;
Otherwise reset the qualification score to zero.
Skip Lot -Single Normal 2 If the lot is accepted with no nonconforming item in the sample, add 5 to the qualification score;
If the lot is accepted with one nonconforming item in the sample, add 3 to the qualification score;
Otherwise reset the qualification score to zero.
Skip Lot -Single Normal 1 If the lot is accepted with no nonconforming item in the sample, add 5 to the qualification score;
If the lot is accepted with one nonconforming item in the sample, add 1 to the qualification score;
Otherwise reset the qualification score to zero.
Skip Lot -Single Normal 0 If the lot is accepted, add 3 to the qualification score;
Otherwise reset the qualification score to zero. (only applicable during qualification period)
Skip Lot -Single/Double Reduced   Note:

5 for normal inspection can be replaced by 3 for reduced inspection

3 for normal inspection can be replaced by 1 for reduced inspection

Skip Lot -Double Normal 1 or more If the lot would have been accepted after the first sample if the AQL had been one step tighter, add 5  to the qualification score;
If the lot is accepted after the first sample but would not have been accepted if the AQL had been
one step tighter, add 3 to the qualification score;
Otherwise reset the qualification score to zero.
Skip Lot -Double Normal 0 If the lot would have been accepted after the first sample if the AQL had been one step tighter, add 5  to the qualification score;
If the lot is accepted after the first sample but would not have been accepted if the AQL had been
one step tighter, add 3 to the qualification score;
Otherwise reset the qualification score to zero.

Resetting of the Qualification Score

If any of the following occurs, the qualification score is reset to zero:

Switching Rules between Skip-lot States and Inspection Frequencies

Event State 1 - Lot By Lot State 2 - Skip-Lot State 3 - Skip-Lot Interruption
10 or more consecutive lots accepted, and the qualification score reaches or exceeds 50 within the last 20 consecutive lots. Switch to state 2 - Skip-Lot and set initial inspection frequency (see Inspection Frequency). Sampling plans for normal inspection with Ac >= 1 will be used. Switch to next lower inspection frequency (see Inspection Frequency. Sampling plans for normal inspection with Ac >= 1 will be used.  

Lot is not accepted, or lot is accepted and the qualification score is reset to zero (see Qualification Score).

  Switch to state 3 - Skip-Lot Interruption. Product is disqualified for Skip-Lot Inspection. Switching rules for Lot-By-Lot inspection apply.

Requalification: 4 to 6 consecutive lots accepted and the qualification score reaches or exceeds 18 within 6 lots.

 

    Switch back to state 2 - Skip-Lot and switch to next higher inspection frequency. Sampling plans for normal inspection with Ac >= 1 will be used.
Requalification is not achieved within 6 lots.

 

    Product is disqualified for Skip-Lot inspection. Switching rules for Lot-By-Lot inspection apply.

Example

Prerequisites:

Step Result
Find Sample Size Code Letter Sample size code letter is K according to table 1.
Find Sample Size Sample size is 125 for code letter K in the master table for single sampling plans for normal inspection (2-A).
Find Acceptance Number (Ac) and Rejection Number (Re) Ac is 2 and Re is 3 for AQL 0.65 and sample size code letter K in table 2-A.
Inspect A sample of 125 units is taken. 1 nonconforming unit is found.
Accept or reject 1 is lower than the Ac 2 so the lot is accepted.
Calculate switching score Ac is 2 or more, and if AQL had been 0.40, which is one step tighter, the Ac had been 1 and the lot would still have been accepted. So 3 is added to the switching score.
Decide on inspection This is the first lot, so switching score is now 3. At least 30 is needed for Reduced inspection, so inspection is kept at Normal.

Implementation

Tables

Tables for sample size code letters, as well as single sampling plans for normal, tightened and reduced inspection are stored within the system and are used when creating an analysis using attribute or variable acceptance sampling. However, they are read-only and not visible. 

Control Plan and Control Plan Template

Acceptance sampling can be used with purchasing and manufacturing control plans. Acceptance sampling cannot be used with production schedules. Inspection level and AQL are set on the control plan. If you use control plan template, you can set these values on the template and then apply the template to parts on creating the control plans. On the data point, a system-defined inspection code will determine whether the acceptance sampling is to be used.

Lot size and splits

The acceptance sampling standards only apply to lot sizes larger than 1. This means that you cannot perform receipts with lot size 1 with an acceptance sampling control plan. If you still need to do that, you must switch temporarily to another control plan. On a shop order with lot size 1, you may exclude the acceptance sampling data points.

Note: If the lot size of a shop order is changed after the analysis has been created, no changes are made to the created analysis. If a shop order is splitted, a new analysis will be created for the new shop order. The analysis for the original shop order will remain untouched. To get the correct sampling plan, you should cancel that analysis and create a new one. We do not recommend splitting the shop order after the analysis has been confirmed, since you will have to perform an analysis again for the new shop order and the same product will be evaluated twice.

Analysis

When acceptance sampling is used, an analysis for acceptance sampling data points will be created at receipt for purchase orders, and at start of shop order. The sample size and acceptance and rejection numbers will be determined by the system when the analysis is created. When the analysis is confirmed, the analysis result will be used by the system to calculate the switching score and to decide if inspection is going to be normal, tightened or reduced the next time an analysis is created.

Acceptance and Rejection

When the analysis is confirmed, the acceptance status will be rejected if any of the acceptance sampling data points are rejected. However, the system does not decide what to do with the rejected lot. It may be received into inventory, scrapped or sent for rework.

Switching Rules

 The switching score is calculated and the switching rules are evaluated when an analysis is confirmed. If inspection has been set to Discontinued, it is necessary to create a new control plan revision to enable acceptance sampling again. If a product has been disqualified for skip-lot inspection, it means that lot-by-lot inspection is carried out, and the switching rules for lot-by-lot inspection apply. Please note that the switching rules are evaluated when the analysis is created and when it is confirmed. If the result of an analysis causes a switch, it does not affect other already created analyses created for the same part and control plan.