Six Sigma DMAIC: Measuring and Sampling

Types of Metrics:

  • Discret: Countable, e.g. integer.
  • Continuous: The degree of conformance to specifications.

Effective metrics: SMART:
Simple. Measurable. Actionable. Related. Timely.

Select the right metrics (QTC, a.k.a. KPIs): identify the customer, requirements, processes, then evaluate measure usefulness.

Data collection (entry): Ask: What: questions. What: data can answer them. Where: is the data. Who: provides access to data. The minimum effort and error.

• Data Collection Steps: Define measures. Get an unbiased experienced collector. Design forms and instructions. Train, audit and validate.

Sampling: Ask: the objective, sample type, cost and potential errors.

Sample types: to choose n-sized sample from N sized population:

  1. Simple Random Sample (SRS): each item has equal probability to be selected.
  2. Stratified: Divide the population into strata (known groups) and take SRS within each group.

  3. Systematic: order items randomly and select every item moving with N/n steps.

  4. Cluster: choose a subgroup of items and apply SRS within it.

  5. Judgement/expert sampling: ask an expert to provide a representatice sample.

Acceptance sampling: concluding whether a process comply with specifications without testing all its products.

Criteria for sampling:

  1. Lowest cost.
  2. Best representation of population.

  3. Precision and

  4. Reliability.

Sampling Error types: Statistical. Systematic. Sample size and design.

Gage R&R: Repeatibility and Reproducibility.
Repeatibility: equipment variation: variation by same tester.
Reproducibility: variation using the same machinemultitesters.

Process Capability: “Cp“: The range of natural variation under stable conditions. Steps:

1- Choose the process, its conditions, an operator and materials.
2- choose measurement method and record measurements.
3- Ask the customer for the Upper and Lower Tolerance Limits (UTL & LTL), i.e. the range of variation the customer may accept.
4-Build a histogram and calculate mean X̅ and standard deviation S.
5- Compare its Standard deviation with tolerance degrees:

Cp = (UTL – LTL)/ 6σ  |   Cpu = (UTL – μ)/ 3 σ   |    Cpl = (LTL – μ)/ 3 σ | Cpk = min(Cpu , Cpl)

Three Sigma Process
σ is larger than 6 Sigma process, i.e. high variation in population

Three Sigma Process

Six Sigma Process
σ is small in comparison to Tolerance, i.e. low variation in population
Six Sigma Process
For Six Sigma, the deviation should small such that it should equal half the tolerance (UTL – LTL). Thus it allows the mean X̅ to shift up to 1.5 σ. And in real life the mean may shift due to common or special causes of variation. Thus 6 σ is robust because, even if the whole mean X̅ shifted (not only σ) for up to 1.5, the process will stay within the tolerance boundaries, i.e. the limits tolerated by the customer.

Six Sigma with 1.5 sigma shift

S    Cp      Defects(ppm)
3    1          66810
4    1.33      6210
5    1.667      233
6    2                  3.4 

Benchmarking and Best Practices: Very helpful in finding the problem and the solutions. Benchmarking is making comparative study against the best practices of the Best-In-Class companies. Best practices are the practices that performed exceptional results in industries and are famous to customers and suppliers.

Benchmarking Types: Competitive (same industry) and Process Benchmarking (different industry but common/similar process).

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