Learn Six Sigma in 4 weeks. Buy our Six Sigma Handbook 19.95$

- Six Sigma Tutorial
- Six Sigma DMAIC process
- Six Sigma Acceptance Sampling
- Sampling Plan Variation vs Lot Size Variation in Acceptance Sampling
- AQL Based Sampling Plans
- Decision Tree for Selecting Type of Variables in Sampling Plan
- FMEA – Failure Mode and Effects Analysis
- Types Of FMEA: Design FMEA (DFMEA), Process FMEA (PFMEA)
- The FMEA Quality Lever – Where To Put The Effort
- FMEA Quiz
- Six Sigma Confidence Intervals
- Confidence Limits
- Confidence Interval Formulas
- Z Confidence Interval for Means – Example
- t Confidence Interval for a Variance – Example
- Six Sigma Defect Metrics – DPO, DPMO, PPM, DPU Conversion table
- Fishbone Diagram – Fishbone Analysis
- Cost of Quality Defects and Hidden Factory in Six Sigma
- Pareto Analysis using Pareto Chart
- Six Sigma Calculators – DPMO, DPM, Sample Size
- How to select a Six Sigma project? Download selection grid template.
- How to create Six Sigma Histogram? Download Excel template
- Scatter Plots – Free Six Sigma Scatter Plot template
- How to create, use Six Sigma SIPOC tool? Download SIPOC Template
- Quality Function Deployment (QFD) – Download free templates
- What is Decision Matrix or Decision Making Matrix ?
- The nature of Process Variation
- What is RACI or RASCI Matrix/Chart/Diagram? Download free templates

- ANSI/ASQ Z1.4-1993 (MIL-STD 105E was withdrawn in February 1995) sampling plans are based on the use of AQL – the percent defective that is considered acceptable as a process average for the purposes of acceptance sampling.
- With these plans, it is not necessary to assume the provision of 100% screening (with replacement of all defective units) of all rejected lots.
- To enter any of these tables, you must first decide on the AQL to use (and determine the sample size code letter); from the table you will get the acceptance number (A
_{c}) and the rejection number (R_{e}) for the plan. - There are also separate tables to provide the AQL for different values of AQL and sample code letters

– More serious defects should have a lower AQL as the acceptance criterion, and less serious defects can have higher AQLs – using a Classification of Defects system.

– Tightened inspection should be used whenever the quality history is unsatisfactory or when there are other good reasons for being suspicious about quality – keeping the beta risk down.

– Reduced inspection can be used when the quality history is shown to be good enough through Normal inspection.

– These plans are generally chosen to protect the producer under normal conditions, i.e., not to reject submitted lots that are at the AQL or better when there are no reasons to be suspicious about quality.

• There is usually less sampling than for a single sampling plan

• The OC curve is better than the c = 0 curve for the single sampling plan with a smaller R (for better discrimination)

Exercise

Desired α risk of .05 for a P1 of .008, along with a desired risk of .10 for a P2 of .06. Use Table 4-4.

1. Determine R:

R = P_{2}/P_{1} = .060/.008= 7.5

2. Enter Duncan’s Double Sampling Tables and find the closest R to the calculated value in step 1.

The closest table value is 7.54 in Plan Number 2. This is very close to 7.5. Note the c_{1} value of 1 and the c_{2} value of 2.

3. For P_{a1-α} = .95, obtain the nP_{1} (Pn_{1} in the table) value. Then calculate n from:

n = nP_{2}/P_{2} = 0.52/0.008 = 65.

The acceptance sampling plan is n_{1} = 65, c_{1} = 1; n_{2} = 65, c_{2} = 2.

ANSI/ASQ Z1.9 (MIL-STD-414 is withdrawn) sampling plans are based on the use of variable data (from an assumed normal distribution).

Actual measurements are made on the samples : the sample data is used to calculate a statistic, such as X̄, R, or S and then the calculated statistic is compared to the critical value from a table.

Acceptance criteria must be applied separately to each quality characteristic (vs. overall lot accept vs. reject for attribute sampling), so it’s more expensive than attribute sampling for larger lots, so it’s generally best to use only on key characteristics, with attribute sampling on the rest.

Compared to attribute plans, these plans, for the same n, provide a greater quality protection in judging a single quality characteristic, or for the same amount of risk, a smaller n is OK.

The use of variable data can provide more information about the extent of nonconformity – How? (Hint: think frequency distribution and what you can do with this information).

These sampling procedures are based on the assumption that the quality characteristic is normally distributed (it is possible to use data transformation if it is not). Procedure:

To use any of these plans, you must first decide on the:

- Inspection level (II is the default for Z1.9)
- Method to use – S or R, with variability (population sigma) known or unknown (see Decision Tree)
- AQL
- Lot size

Determine the sample-size code letter from the table

Calculate the Q value

Enter the Master Table by sample size code letter and AQL, and look up the k value.

Compare the k and Q values – if the calculated Q value is ? than the critical k value from the table, accept the lot. If not, reject it.

Learn all the Six Sigma Concepts explained here plus many more in just 4 weeks. Buy our Six Sigma Handbook for only 19.95$ and learn Six Sigma in just 4 weeks. This handbook comes with 4 weekly modules. Eeach module has around 250 powerpoint slides containing six sigma concepts, examples and quizzes.