Spc statistical process control

What is statistical process?

Statistical processing stands for statistical process control.Statistical processing does not refer to a particular technique, algorithm or procedure.Statistical processing is an optimization philosophy concerned with continuous process improvements, using a collection of tools (statistics) for:

a- data and process analysis

b- making inferences about process behavior

c- decision making.

Statistical processing is a key component of overall quality initiatives. Ultimately, statistical process seeks to maximize profit by improving product quality, improving productivity, streamlining process, reducing waste, reducing emissions, improving customer service, etc.

Tools for the statistical process

Tools commonly used in statistical processing include

Flow charts Performance charts Pareto chart and analysis Cause-effect charts Frequency histograms Control charts Process capability studies Acceptance sampling plans Scatter charts Each tool is simple to implement These tools are generally used to complement, rather than as stand-alone techniques

Organization charts

Have no statistical basis are excellent visualization tools Demonstration of flow charts Work progress Flow of material or information with a sequence of operations Flow charts are useful in an initial process analysis Flow charts should be supplemented by process flow charts or flow charts Processes (detailed) if available Everyone involved in the project should draw a flowchart of the process that is studied to reveal the various views of how the process works.

Flowchart of an example of a procedure to ensure data quality.

Operation Charts

Performance charts are simply diagrams of process characteristics versus time or in chronological sequence. They have no statistical basis, but are useful in revealing

Trends Relationships between variables

Performance graphs can be used to study relationships between variables. For example, in the above chart, the relationship between the 2 variables is difficult to discern. To facilitate this, the appropriate scaling for the diagrams must be chosen. If each mapped variable has its own y-axis scale, the above performance graph then becomes,

Now, the relationship between the two becomes very enlightening. This method will obviously fail when there are more than two variables. However, if the variables are standardized before plotting, only a single common axis is necessary, and the results are just as clearly as the above.

Vilfredo Pareto (1848-1923) discovered that:

80% of the abundance in Italy were carried out by 20% of the population; 20% of customers considered 80% of sales; 20% of parts considered 80% cost, etc. These observations were confirmed by Juran (1960) and led to what is known as the Pareto principle.

The Pareto principle indicates that:

»Not all the causes of a particular phenomenon occur with the same frequency or with the same impact»

Such characteristics can be highlighted using Pareto Charts.

Pareto charts and analysis

Pareto charts demonstrate the most frequently occurring factors Pareto chart analysis helps make the best use of limited resources by pointing out the most important problems to address

For example:

Products may suffer from various defects, but defects occur in different frequencies Only a few account for most of the defects present Various defects incur different costs

So a product line can experience a range of defects (A, B, C…

J). Plotting the contribution of the percentage of each type to sum the number of failures, give a bar-trace in the following diagram. Then if each of these contributions is added sequentially, a cumulative line diagram is obtained. These two diagrams together make up the Pareto chart.

Pareto chart example

From the information on the graph, the manufacturer could for example,

focus on reducing defects A, B and C since they make up 75% of all defects focus on eliminating defect E, if defect E causes 40% monetary loss

The Cause-and-effect diagrams:

They are also called:

Ishikawa diagrams (Dr. Kaoru Ishikawa, 1943) Fishbone diagrams Cause-effect diagrams do not have a statistical basis, but are excellent aids for problem solving and trouble-shooting Cause-and-effect diagrams can reveal important relationships between several possible variables and causes provide additional insight into process behavior

Example of a Cause-effect diagram

Frequency histogram

The frequency histogram is a very effective graphical and easily interpreted method for summarizing data The frequency histogram is a fundamental statistical tool of the statistical process It

provides information about:

The mean (mean) of the data The variation present in the data The pattern of the variation

If the process is within specification

Frequency Drawing Histograms

In drawing histograms of frequency, consider the following rules:

Intervals must be equally spaced Select intervals for convenient values The number of intervals is generally between 6 to 20 Small amounts of data require few intervals

10 intervals are sufficient for 50 to 200 readings

Processes that are not in a state of statistical control:

demonstrates excessive variations display variations that change over time

Control Charts

They are used to detect whether a process is statistically stable. Control charts distinguish between variations

That normally expects from due process occasion or common causes that change over time due to assignable or special causes.

Variations due to common causes

have little effect on the process is inherent to the process due to: the nature of the system the way the system is managed the way the process is organized and operated The can only be removed by making process modifications changing the process is the responsibility of higher management

Cleats variations due to special causes are:

localized in nature Exceptions to the system Considered normalities Often specific to: Certain operator Certain machine Certain batch of material, etc. Investigation and removal of variations due to special causes are key to process improvement.

Note: Sometimes the delineation between common and special causes may not be very clear

The principles behind the use of control charts are very simple and are based on the combined use of

Performance graphs Hypothesis testing

The process is:

Sample the process at regular intervals trace the statistics (or some measure of performance), eg, Average Range Variable Number of defects, etc. Check (graphically) if the process is under statistical control If the process is not under statistical control, do something about it

Various charts are used depending on the nature of the commonly used planned charts of the data are:

For continuous data (of the variables): Shewhart sample mean (c- graph) Shewhart sample range (R - graph) Shewhart sample (X - graph) Cumulative sum (CUSUM) Average loaded exponential graph Moving (EWMA) Charts Move-means and range For (attributes and countable) the data described: Proportion of defective sample (p - graph) Number of defectives sample (np - graph) Sample number of defects (c - graph) Number of the sample of defects per unit (u - graph s - graph)

Control chart calipers make assumptions about the plotted statistic, namely

is independent, that is. A value is not influenced by its last value and will not affect future values It is normally distributed, that is, the data has a normal function of the probability density

Normal Probability Density Function

The assumptions of normality and independence allow predictions to be made about the data.

The normal distribution N (m, s 2) has several distinct characteristics:

The normal distribution is flared and is symmetric The middle, m, is located in the center The probabilities that a point, x, lies some distance beyond the middle is: Band (x> m + 1.96 s) = band (x> m - 1.96s) = 0.025 Band (x> m + 3.09 s) = band (x> m 3.09s) = 0.001

S is the standard deviation of the data

Control charts: interpretation

The control charts are normal distributions with an added dimension of time.

Control charts are performance charts with superimposed normal distributions

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Graphs to test hypotheses

Control charts provide the graphical means to test hypotheses about the data being monitored.

Consider Shewhart's commonly used chart as an example.

Shewhart's X Chart with Control and Warning Limits

The probability of a sample having a particular value is given by its location on the graph. Assuming that the plotted statistic is normally distributed, the probability of a value lying beyond:

Warning limits are about 0.025 or 2.5% chance Control limits are about 0.001 or 0.1% chance, this is rare and indicates that Variation is due to an assignable cause Process is out of statistical control

The rules of operation

They are the rules that are used to indicate situations outside of statistical control.

Typical rules of operation for Shewhart X charts with warning and control limits are:

one point lying beyond the control limits 2 consecutive points lying beyond the warning limits (0.025 × 0.025 × 100 = 0.06% chance of occurring) 7 or more consecutive points lying on one side of the middle (0.5 7 × 100 = 0.8% chance to occur and indicates a change in the middle of the process) 5 or 6 consecutive points going in the same direction (indicates a trend) Other rules of operation can be formulated using similar principles