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- SPC - Introduction

This will be the first of a series of articles created with the purpose of structuring some of the most important concepts for workers but hostile to so many professionals who have not been able to deepen the knowledge of such topics from a point of theoretical view.

Obviously, it will not be my intention to give a detailed description but a view of the whole and I hope it is exhaustive for practical use.

Let's start with some definitions that will return useful during reading.

**Measurement: **Trivializing the concept , it is simply a numerical, unique assignment to an observation

**Definition Domains (Discreet or Continuous): **if the observed feature can assume a finite number of states, we say that observation and relative measurement are defined in a **discrete** set (Ex. outcome of a Quality Control [Acceptable, Unacceptable]) otherwise they are defined in a **continuous** set ( Eg measuring temperature, length, etc.)

In the case of infinite definition domains, as our limited measurement tools (can not represent an infinite number of values to be attributed to observation), the attributed value will always be an approximation of the real, more accurate it is our instrument of Measuring then lesser is the difference between measured value and reality, this difference represents an error that we call "measurement error (e)".

Transforming an observation into a single numeric value is called "**random variable**", the "random" attribute refers to the fact that observation is generated by an experiment (or mechanism, or natural phenomenon, etc.) that we are not able to predict the outcome with certainty.

Although we can not predict the outcome with certainty, we can predict how the different measurements will be statistically distributed. This distribution will generally be considered "Normal" (Gauss) based on two theorems: Large Number Act, Central Limit Theorem.

Law of large numbers:establishes the convergence of the average mean value of a certain random variable sample (x1, x2, x3 ...... .xn) to the expected value E (x). In other words, thanks to the law of large numbers, we can trust that the average we calculate from a sufficient number of samples is sufficiently close to the real average; nothing says about the probability distribution laws of such random variables.

Central limit theorem:it answers this problem and sets the conditions for which a random variable tends to Gauss's normal distribution. Well, in the rough terms, the central limit theorem states that the distribution of the sum of a large number of independent and identically distributed random variables tends to be distributed normally, regardless of the distribution of the individual variables

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Some properties that characterize a generic statistical distribution (not necessarily Normal) are:

**Location:** They are indicators that describe and highlight some characteristics of the population distribution. The main position indices are: Media, Median, Moda

**Spread:** Location index values are important for a brief description of a statistical phenomenon but are not sufficient for the overall understanding of the phenomenon as they are unable to provide any information on data dispersion (homogeneity or non-homogeneity). Some dispersion indices are: Range, Variance, Standard Deviation.

**Shape:** The shape measurements are synthetic indexes used to identify the shape of the distribution, among the various forms we remember: symmetry, curtosis.

Suppose now that the object of our observation is the result of a process (or individual characteristics of it) of which we do not know the details (black box). The analytical study of the measurements of the results obtained can give us useful information about the process in order to know its present state, to predict future results and, if necessary, to act on the process to improve it.

A very useful tool for performing an analytical measurement is** SPC (Statistical Process Control)** and its Control Cards.

A key concept underlying the SPC is that a set of measurements, at the same system level, have a variability, within certain limits, which can be associated with **common unspecified causes**. Thus, the presence of deviations from the expected value due to common causes is determined, Focus moves on any **special causes** that drift through the process (measurements beyond certain limits).

The concept of "certain limits" and its enhancement will be discussed in the next readings.

Process Excellence Lead & Founder of Lean Six Sigma Community

Management engineer with 15+ years of experiences in multinational companies, employed in different roles but with common goals: Continuos Improvement, processes standardization &...

Process Excellence Lead & Founder of Lean Six Sigma Community

Management engineer with 15+ years of experiences in multinational companies, employed in different roles but with common goals: Continuos Improvement, processes standardization & optimization.

I'm trainer and consultant about Lean & Six Sigma methodologies, I love to help organizations to improve their performances in terms of times/costs/defects/spaces reductions.

I founded Lean Six Sigma University & Community, two synergic projects developed for creating a common place where learn and divulgate knowledges about Lean and Six Sigma methodologies applied to different ambits.

The application of Lean & Six Sigma methods are not simply methods learned and applied, it is a cultural change.

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