# STATISTICS AND SIX SIGMA

## PROCESSES OPTIMISATION

#### The application of statistical techniques to productive processes

The application of statistical techniques to productive processes and services allows to minimise the costs and to improve the quality in a systematically and sustainably way. Through the development of specific focused projects, the 6 Sigma program allows important improvements, that means breakthroughs, and optimises the processes and services with noticeable advantages for the efficiency and reduction of waste.

### Statistical Process Control (SPC)

The SPC’s aim is to keep stable the productive process and to evaluate it in relation to the specification’s requirements, which are applicable to finished or semi-finished products. The SPC is essential to guarantee the client’s expectation satisfaction and to reduce the production costs due to the failures created during the different process’ phases. The SPC is a mandatory requirement in the sectors in which there are quality critical conditions (Automotive, Medical, Aerospace, etc.)

### Control cards

The control cards are the most suitable instrument to evaluate and keep the productive process stability, and together with the analysis of process capability, are an essential technique in the SPC. The control cards allow to distinguish the cases in which the process variability is due to “special” causes, that need to be removed to avoid the process goes out of control, from the cases in which no interventions are required because the variability is the natural process’ one. To be effective the control cards must be selected according to the to-be-analysable process parameters and their control limits need to be defined in a rigorous way.

### Process Capability

The Process capability is the ability to create products in compliance with specification requirements. The Process Capability is measured through specific indicators, CP and CPK, which allow to estimate the product percentage that will be out of the specification limits, and which lead to defects in the short or long term. Together with the control cards, the evaluation of process capability performed by the CP and CPK values calculation, is a crucial instrument for the SPC.

### ANOVA

The ANOVA (Analysis of Variance) is a statistical technique able to define if the differences among data groups are casual or substantial, that means due to factors able to affect the data. The ANOVA is a wide-range application: from the analysis of several treatments (chemical, physical, etc.), to the evaluation of productive processes or services.

### Sampling plans

The sampling plans define the statistical inference-based criteria through which it is possible to perform the spot checks applicable in every field (approval/evaluation of batches of products or semi-finished products, of productive processes or services) The sampling plans application allows to also evaluate the risks and benefits of every kind of sampling in a rigorous and objective way.

### Design of Experiments

The Design of Experiments (DOE) is a statistical technique able to optimise processes and services according to the required achievable goals through the setting and the statistical analysis of a series of well-structured tests/experiments. The DOE is effectively usable in different fields and applications, both industrial and of different kinds.

### Statistical Tests

The Statistical Tests allow to evaluate if the differences among data groups concerning batches, samples, productive processes, or services, must be considered casual or due to real variations. Through these tests it is possible to define if the observed trends correspond to improvements, worsening, or “real” or apparent variations in a unique and objective way.

### FMEA

The FMEA (Failure Modes and Effects Analysis) is a technique which allows to analyse a project or a productive process to identify possible weaknesses and, consequently, to perform improvement actions. With the FMEA it is possible to assign the intervention priorities on the project or process through an evaluation developed into a dedicated team. When the FMEA is performed on a project, it is called DFMEA (Design FMEA); while if it is applied to a productive process is called PFMEA (Process FMEA).

### Measurement system analysis (repeatability, reproducibility, R&R gage, accuracy)

The measurement system analysis is performed to determine the measurement error, which has different components. Through the R&R gage analysis is possible to determine the repeatability (that means the variability only due to the error inside the instrument or in the measurement system) and the reproducibility (that means the variability due to factors like the operator, the environmental changes, etc.). Besides these quantities, to determine the whole measurement accuracy, it is necessary to calculate the bias, that is the variance of the measured values average from the real value.

### 6 Sigma method

The 6 Sigma method is applied both to productive processes, and to services. Its aim is to achieve significant improvements, which are not reachable through common actions, that lead to a gradual improvement. This method involves statistical technique and focused projects, structured in 5 phases: Define, Measure, Analyse, Improve e Control (DMAIC).