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- 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

Determine the AQL to use in the Master Table: Since there are standard AQLs used in the Master Tables, you need to convert the AQL per table below:

Determine the Sample-Size Code Letter to use in the Master Table: ANSI/ASQ Z1.9 Table A.2 Formulas for the Q Value:

Formulas for the Q Value:

For Section B – Standard Deviation Method (σ Unknown):

Note: For 2-sided spec limits, an AQL can be assigned to both limits combined, or to each end of the spec limit separately.

Table B-1 Standard Deviation Method Master Table B-1 for Normal and Tightened Inspection for Plans Based on Variability Unknown (Single Specification Limit)

Obtain the k Value from the Master Table:

What would be the variables sampling plan (sigma unknown) for the following conditions? High P_{a} (α = .05) for a fraction non-conforming (P_{1}) of .005, with a low P_{a} (β = .05) for a fraction conforming (P_{2}) of .03.

Solution

Note: with the same operating characteristics, an attribute sampling plan would require n = 274.

Example (Method: Population Sigma Known)

A lot of 1500 bobbins is submitted for inspection. Inspection level II, normal inspection, with AQL = .65%, is to be used. The specified minimum yield value for the tensile strength is 25.0 lbs. The variability σ is known to be 2.4 lbs.

The sample size code letter from Table A.2 is K. In Table D-2 (p. 86 in ANSI/ASQ Z1.9-2003), for reduced inspection, the required sample size is 7 and the k value is 1.80. The 7 sample specimen’s tensile strengths are 25.7, 26.4, 26.1, 27.2, 25.8, 28.3, and 27.4. Q_{L} = (X̄-LSL)/σ = 24.6 – 25.0 / 2.4 = 0.63

Since Q_{L} < k, the lot does not meet the acceptability criterion and should be rejected.

What are the alpha and beta risks for sampling letter K (p. 23 in ANSI/ASQ Z1.9-2003), for an AQL of .65, for various incoming quality levels (P)?

P | P_{a} |
α | β | |

Relatively Good Quality | .25 | 99.5 | .5 | |

.50 | 96 | 4 | ||

Marginal | .75 | 90 | 10 | 90 |

1.5 | 62 | 38 | 62 | |

Poor | 2.00 | 46 | 46 | |

3.0 | 22 | 22 | ||

4.0 | 10 | 10 | ||

5.0 | 4.5 | 4.5 |

* All values are in Percentages

Why is the lot rejected even though none of the samples were out of spec? (Assuming this is a representative sample, a larger, +/- 3σ distribution would provide some product out of specification; in this case, in the left tail of the distribution.)

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