Example of creating a variables acceptance sampling planmain topic interpreting results session command see also
Example of creating a variables acceptance sampling planSuppose you receive weekly shipments of 2" plastic pipe segments for your unit operation assemblies per shipment. The lot size is 2500.
You decide to implement a sampling plan to verify the wall thickness. The lower specification for the wall thickness of the piping is 0.09". You and the supplier agree that the AQL is 100 defectives per million and the RQL is 300 defectives per million.
1 Choose Stat > Quality Tools > Acceptance Sampling by Variables >Create / Compare.
2 Choose Create a sampling plan.
3 In Units for quality levels, choose Defectives per million.
5 In Acceptable quality level (AQL), enter 100. In Rejectable quality level (RQL or LTPD), enter 300.
6 In Producer's risk (Alpha), enter 0.05. In Consumer's risk (Beta), enter 0.10.
7 In Lower spec, enter 0.09.
8 In Historical standard deviation, enter 0.025.
9 In Lot size, enter 2500. Click OK.
Session window output
Acceptance Sampling by Variables - Create/Compare
Lot quality in defectives per million
Lower Specification Limit (LSL) 0.09 Historical Standard Deviation 0.025 Lot Size 2500
Acceptable Quality Level (AQL) 100 Producer’s Risk (α) 0.05
Rejectable Quality Level (RQL or LTPD) 300 Consumer’s Risk (β) 0.1
Generated Plan(s)
Sample Size 104 Critical Distance (k Value) 3.55750
Z.LSL = (mean - lower spec)/historical standard deviation Accept lot if Z.LSL ≥ k; otherwise reject.
Defectives Probability Probability Per Million Accepting Rejecting AOQ ATI 100 0.950 0.050 91.1 223.2 300 0.100 0.900 28.6 2261.4
Average outgoing quality limit (AOQL) = 104.6 at 140.0 defectives per million. |
Graph window output
Graphs - Acceptance Sampling by Variables
For each lot of 2500 pipe segments, you need to randomly select and inspect 104 of them. From the measurements of your random sample, determine the mean and the standard deviation to calculate the Z value. Z = (mean - lower spec)/ standard deviation. If a historical standard deviation is known, use that.
If Z.LSL is greater than the critical distance, in this case k = 3.55750, accept the entire lot; otherwise reject it.
In this case, the probability of acceptance at the AQL (100 defectives per million) is 0.95 and the probability of rejecting is 0.05. When the sampling plan was set up, the consumer and supplier agreed that lots of 100 defectives per million would be accepted approximately 95% of the time to protect the producer. The probability of accepting at the RQL (300 defectives per million) is 0.10 and the probability of rejecting is 0.90. The consumer and supplier agreed that lots of 300 defectives per million would be rejected most of the time to protect the consumer.
Acceptance sampling processes usually require corrective action when lots are rejected. When the corrective action is to perform 100% inspection and rework the defective items, the Average Outgoing Quality (AOQ) represents the average quality of the lot and the Average Total Inspection (ATI) represents the average number of inspected items after additional screening.
The Average Outgoing Quality (AOQ) level is 91.1defectives per million at the AQL and 28.6 defectives per million at the RQL. This is because when lots are very good or very bad the outgoing quality will be good because of the rework and reinspection for poor lots. The Average outgoing quality limit (AOQL) represents the worse case outgoing quality level.
The Average Total Inspection (ATI) per lot represents the average number of pipes inspected at a particular quality level and probability of acceptance. For the quality level of 100 defectives per million, the average total number of pipes inspected per lot is 223.2. For the quality level of 300 defectives per million, the average total number of pipes inspected per lot is 2261.4.