DMAEC – Measure

Basic Statistics

2 general types of data

• Discrete Data (Attribute Data or Count Data)
• Continuous Data (Variable Data)

Measures of Location (central tendency)

• Mean (Average)
• Median (50% position)
• Mode (The value that occurs most frequent)

Measures of Spread (Variation)

• Range
• Variance
• Standard Deviation

Sampling Methods

• Random Sampling: All items in the population have an equal chance of being chosen in the sample.
• Stratified Sampling: When the population consists of mixture of more than one strata, each forming a homogeneous group, Stratified sampling can assure that the sample represents the population adequately.
• Clustered Sampling: Select a random sample of the clusters and assume that these clusters represent the population as a whole. Opposite to Stratified Sampling.
• Systematic Sampling: Selection of samples from a population according to a set schedule or plan.

How to determine the sample size? n = square(1.96 * σ / Δ). Where Δ represents the precision or accuracy.

Data Collection Process

1. Determine What to Measure

2. Develop Operational Definitions and Procedures

3. Validate the Measurement System

Measurement System Analysis (MSA)

• Accuracy: Distance to the target.
• Precision: Distance within the samples.
• Linearity
• Stability
• Resolution
• Repeatability: The same result when one person uses the same equipment and process.
• Reproducibility: The same result when different person use the same equipment and process.

4. Begin Data Collection

5. Continue Improving Measurement Consistency

Determine Process Capability

DPMO: Defect per Million Opportunities

The sigma level: Z-score = (x – μ) / σ. Where μ is the target value. It is the number of σ (standard deviation).

Z.short-term = Z.long-term + 1.5

Yield: The percentage of products produced defect-free (defect area is 10%, then yield area is 90%.). Some standard yields: One-sided Yield: 50%, 84.13%, 97.73% and 99.865%; Two-sided Yield: 68.27%, 95.46%.

DMAEC – Analyse

Identify Source of Variation

Check sheets, Graphs, Bar charts and Pareto charts