# Statistical Methods for Manufacturing Process Improvement...

## Information | Understanding | Best Practice.

There are a range of statistical methods which can be used in manufacturing process improvement. In many instances, the statistics need not be complex, in fact one of the primary benefits of implementing statistical analysis, is not the statistical methods themselves, but more that fact that engineering and management focus is placed on a process which by itself results in an improved process understanding, drives a greater attention to detail and improved level of control and thereby results in reduced process variability and improved output quality.**What are the widely applied statistical methods for manufacturing process improvement?**

These are a range of statistical process control (SPC) methods such as attribute and variable charts, individual and moving range charts, moving average and moving range charts, exponentially weighted moving range charts (EWMA), run charts, pre-control charts. Other popular statistical methods are Cu-sum and Pareto Analysis.

A relatively simple, yet quite powerful method of process control is the scatter diagram.

Many organizations perform process capability analysis (Cp, Cpk, Pp, Ppk.) as part of an effort to determine the capability of a manufacturing process to consistently output product within the required specifications. Another widely applied statistical technique is gage R&R, which seeks to answer the question, “how much of the total engineering tolerance is consumed by error in the method of measurement”, i.e. what is the repeatability and reproducibility of the method of measurement.

**Looking at a sample of these statistical methods.**

**Attribute and variable charts**

Attribute control charts deal with data in which the characteristic of the data is discrete in nature, e.g. number of defects per product, use of a go/ no go gauge, colours, etc., basically you have a Pass/Reject decision.

Variable control charts deal with actual measurements over a continuous scale, e.g. mm’s, kg’s, Amps,…

To develop the control chart, you first need to determine the specific quality attribute or performance characteristic you want to understand and control. Then decide on a method of measurement. Once you know what you want to measure, you can then determine if the control chart will be an attribute or variable chart. Next determine the appropriate sample size, this will be based relative to the manufacturing process volume. Finally, how are you going to collect and record the measurements.

Once the above is determined, you are now in a position to start to construct the control charts. First make the measurements, then from the results obtained, you can calculate the mean and standard deviation of the process. From these you can obtain the control chart centerline and control limits. The upper and lower control limits are usually set at +/- 3 standard deviations. Then you can record the measurements results which you obtain on an ongoing basis onto the control chart and commence interpretation of the results.

**Scatter Diagrams**

Scatter diagrams are used to analyze the relationship between two variables to determine if there is any form of relationship between them. If a relationship is identified, then one variable can be controlled by varying the other variable.

For example, in a milling process, say the speed of the drill impacts the smoothness of the final cut. Therefore, the finish required, can be controlled by means of varying the drill speed.

**Gage (Gauge) R&R**

A gage repeatability and reproducibility analysis is performed to ensure we have confidence in data which has been obtained from some form of inspection or testing activity. We perform gage R & R in order to minimize or eliminate measurement error on product acceptance decisions, to ensure decisions taken during process capability analysis is based on accurate facts, or to ensure that the measurements we are recording during an SPC charting activity are true and accurate. Gage R&R is also applied when introducing new equipment into a manufacturing process or for making comparisons between the acceptability for use of different types of test equipment.

**Pareto Charts**

Pareto charts are basically bar graphs which rate in order of criticality the important causes or reasons for problems which may be seen in a manufacturing process. Effectively, the pareto chart provides a clear approach to determining what needs to be addressed first, then what will be the second problem to be addressed, etc.

**Comment:**

It is possible to “over analyze” the optimum method of statistical analysis to be applied and individuals are discouraged by the perceived complexity of the various statistical analysis tools. Often the single biggest benefit of implementing statistical analysis in a manufacturing process is the focus it places on the process itself and the increased understanding by all involved which derives from consistently collecting and recording process measures.

Where statistical methods are in place and as user confidence in the analytical methods develop, then it may be appropriate to research the more specific statistical methods available, with a view to closer matching the particular process control requirements to the best available statistical process controls available.

## SPC & Statistical Methods for Process Improvement.

- Process Capability. Variability Reduction. Statistical Process Control.
- Pre-Control. R&R Studies.
- Process capability indices Cp, Cpk, Cpm, Capability ratio.
- Performance indices Pp and Ppk.
- Variable Control Charts.
- Attribute Charts.
- Pareto Charts.
- Individual – X Charts.
- Histograms / Process Capability Analysis.
- Scatter Diagrams.
- Etc. … Etc. …
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