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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

If the lot size N changes, the below curves change very little. However, the curves will change quite a bit as sample size n changes. So, basing a sampling plan on a fixed percentage sample size will yield greatly different risks. For consistent risk levels, it is better to fix the sample size at n, even if the lot sizes N vary. Question: If n = 10 & c = 2, what is the alpha risk for a vendor running at p = .02? Answer: P_{a} is about .55, so alpha is about .45. Question: What is the beta risk if the worst-case quality the customer will accept is 3%? Answer: (about 15%). To lower alpha and beta, you can increase n and c.

Is c = 0 the best plan for the producer and the consumer?

At the 2.8% lot defect rate, both plans give the producer equal protection: P_{a} = 11%, or P_{rej} = 89%. Which one gives better protection against rejecting relatively good lots, e.g., at the .5% lot defect rate, and why?

For (1), α = about 8% and for (2), α = about 30%.

(1) has a lower α error so less chance of rejecting good lots. With (2), you will reject any lot of 500 if there is even 1 defect in the sample, but it will lead to higher costs.

Is c = 0 the best plan for the producer and the consumer?

At the 2.8% lot defect rate, both plans give the producer equal protection: P_{a} = 11%, or P_{rej}. = 89%. Which one gives better protection against rejecting relatively good lots, e.g., at the .5% lot defect rate, and why? For (1), α = about 8%; for (2), α = about 30%. (1) has a lower α error so less chance of rejecting good lots. With (2), you will reject any lot of 500 if there is even 1 defect in the sample, but it will lead to higher costs.

Discrimination is the ability of a sampling plan to distinguish between relatively good levels of Quality and relatively bad levels of quality. In other words, having

- A high P
_{a}(e.g., 95%, 1-α) associated with a good level of quality P_{1}(e.g., .5% or better) - A low P
_{a}(e.g., 10%, β) associated with a bad level of quality P_{2}(e.g., 3% or worse)

The Operating Ratio is defined as

R = P_{2}/P_{1} = P_{β}/P_{1-α}Example: R = .03/.005 = 6.0

Derive a plan that comes as close as possible to satisfying two points on the OC curve. The two points are (P_{1}, 1-α) and (P_{2}, β). The derived plan will contain an n and a c value.

Example

Desired α risk of .05 for a P_{1} of .005, along with a desired risk of .05 for a P_{2} of .03.

1. Determine R:

R = P_{2}/P_{1} = .030/.005 = 6.0

2. Enter the Values of Operating Ratio Table with α and β and find the closest R to the calculated value in step 1.

For α = .05 and β = .05, the closest table value is 5.67. This is acceptable since it is slightly more discriminating than 6.0. Note the c value of 3 in the far left column.

3. Obtain the nP_{1} value in the far right column. Then calculate n from:

n = nP_{1}/P_{1} = 1.366/.005 = 273.2 or 274.

The acceptance sampling plan is n = 274, c = 3.

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.