A manufacturing engineer receives weekly batches of 2-inch plastic pipe segments for an assembly process.
The lot size is 2,500.The engineer decides to create a sampling plan to check the thickness of the pipe wall. The lower specification for pipe wall thickness is 0.
09 inches. It is agreed between the engineer and the supplier that the acceptable quality level (AQL) is 100 non-compliant per million and that the dischargeable quality level (NQR) is 300 nonconforming per million.Select Stat > Quality Tools > Measure Control Plans > Create / Compare .In the drop-down list, select Create Sampling Plan .
In Units of Quality Levels , select Defective for a Million .In the Acceptable Quality Level (AQL) field , type 100.In the Rejectable Quality Level (NQR or LTPD) box , type 300.In the Vendor Risk (Alpha) field , enter 0,05.In the Buyer Risk (Beta) box , type 0,10.
In the Lower Specification box , type 0,09.In the Historical Standard Deviation box , type 0,025.In the Batch Size box , type 2500.Click OK .
Results interpretationFor every 2,500 pipe segments, the engineer must randomly select 104 pipes and measure their thickness.If the Z.LSI value is greater than the critical distance k (here 3,55750), the engineer accepts the whole lot. Otherwise, he rejects it.In this case, the probability of acceptance at the AQL (100 non-compliant per million) is 0.
95 and the probability of rejection is 0.05. The engineer and the vendor agreed that batches with 100 non-compliant per million would be accepted approximately 95% of the time to protect the vendor.
The probability of acceptance at the NQR (300 non-compliant per million) is 0.10 and the probability of rejection is 0.90. The engineer and the supplier agree that lots with 300 non-compliant per million would be rejected most of the time to protect the buyer.When whole batches are rejected, they are usually subjected to a 100% inspection, after which the defective items are replaced or resumed. This type of control is called restart control. Use the following measures to understand the implications of 100% control and recovery:The average quality after inspection (QMAC) represents the average quality of the lot after a new control and a recovery.
The QMAC level is 91.1 non-compliant per million to the NQA and 28.6 non-compliant per million to the NQR.
The average quality limit after control (LQMAC) is 140.6 for a defective level of 140 per million and represents the worst possible level of quality.Average Controlled Units (CTM) represents the average number of items checked after additional control and recovery. The batch CTM value represents the average number of hoses tested for a specific quality level and probability of acceptance.
For a quality level of 100 defective per million, the average total number of hoses tested is 223.2 per batch. For a quality level of 300 defective per million, the average total number of pipes inspected is 2,261.4 per batch.