# Basic Statistical Concepts - Six Sigma

Large elements of the Six Sigma approach are statistical in nature. This text book does not purport to be a statistical textbook and so will not deal in detail with statistical tools and techniques; for a comprehensive treatment refer to “Essentials of Statistics” .

Probabilistic Thinking

In many organizations there is a tendency to think deterministically this basically means an expectation that there will be no variation in outcomes, and that a given input (or inputs) will always generate the same output (or outputs). This lies in the face of our general life experience; we know that, for example, that a particular Olympic runner will not always beat other runners over the same distance and in the same conditions. This does not, however, stop organizations for assuming that, for example, inspection systems will always reject products of poor quality and accept products of good quality.

Thinking probabilistically allows for more effective decision making by allowing us to quantify the probability of success or failure, risk and reliability. Deterministic thinking tends to lead to overly simplistic characterisation of situations and inappropriate responses when the simplistic model fails to predict reality effectively.

Probability Distributions

When there are a range of possible outcomes for a given process (for example the dimensions of a manufactured product or time taken to complete a task) we can predict the probability of each outcome and thereby develop a probability distribution which models the long - term outcomes of that process. This adds a layer of sophistication to the ability to make decisions with respect to whether processes can meet design intent, or whether to give a contract to a particular supplier.

There are a number of general distribution shapes which describe situations within certain parameters. Key distributions in the context of Six Sigma are Normal, Binomial, and Poisson.

Descriptive Statistics

When dealing with distributions and attempting to make appropriate decisions we need to summaries what we are dealing with. this requires us to understand three key things:

• Central Tendency: Where is the distribution centred? this can be important in, for example, seeing if the distribution of a process is centred on the target for that process.
• Spread: How variable is the distribution? In general we want as much consistency as possible for a distribution.
• Shape: For the same central tendency and spread differing shapes of distribution would lead to different decisions. The appropriate measures for central tendency and spread will vary with the particular measure, and the question being asked.

Hypothesis Testing

A key question in process improvement is ‘has something changed?’. We may ask this question in relation to deterioration of an existing process, or to establish whether an attempt to improve a process has been successful. There are a variety of tests associated with different situations and different underlying distributions, and even some which are independent of distribution. The essential question is whether the results under consideration can be explained by the natural variation within the process before the ‘deterioration’ or ‘improvement’.

A specific form of hypothesis testing relates to correlation, where we are attempting to understand whether the variation in one measure is related to the variation in another usually as a precursor to establishing causation. For example we might be concerned with whether a change in feed rate in a metal cutting process effects a change in the surface finish of the material.