3.1 CONTROL CHARTS

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Basic plots of statistical variation to show trends. Uses basic values like,

- average

- standards deviation

- range

the uses for control charts,

- these give a measure of performance, and therefore we can estimate the benefits of process parameter adjustment.

- process capability can be determined

- process specifications can be made greater than process capability

- can indicate when a process is out of control, and be used to reject a batch of product.

3.1.1 Sampling

values used for control charts should be numerical, and express some desired quality.

selecting groups of parts for samples are commonly done 2 ways.

INSTANT-TIME METHOD - at predictable times pick consecutive samples from a machine. This tends to reduce sample variance, and is best used when looking for process setting problems.

PERIOD-OF-TIME METHOD - Samples are selected from parts so that they have not been presented consecutively. This is best used when looking at overall quality when the process has a great deal of variability.

Samples should be homogenous, from same machine, operator, etc. to avoid multi-modal distributions.

Suggest sample group size can be based on the size of the production batch

3.1.2 Creating the Charts

The central line is an average of `g' historical values.

The control limits are +/-3 s of the historical values

At start-up these values are not valid, but over time it is easy to develop a tight set of values.

For the non-technical operators there are a couple of techniques used.

- to simplify calculation of the control limits we can approximate s with

3.1.3 Maintaining the Charts

Over time sR and sX should decrease.

If some known problems occurred that created out of control points, we can often eliminate them from the data and recreate the chart for more accurate control limits.

If we recalculate values from the beginning there is no problem, but if we are using the numerical approximation (using constants from table B)

3.1.4 The s-Chart

Instead of an R-chart we can use an s-chart to measure variance

This chart will reduce the effect of extreme values that will occur with R charts. And, as the number of samples grows, so does the chance of extreme values to throw off the R-chart.

the approximate technique is,

3.1.5 Interpreting the Control Charts

We consider a point that lies outside of the 3s control limits to be very unlikely, therefore the process is `out of control'

In some cases a process may have points within the control limits, but in highly unlikely trends that indicate a process is out of control

3.1.6 Using the Charts for Process Control

1. change or jump in level (X)

- indicates a discontinuity in the process, could be caused by material, new operator, etc.

- e.g. measurement gauge has slipped.

2. Change or jump in level (R)

- indicates a change in process accuracy, caused by failure of small parts, material, etc.

- e.g. measurement gauge has stretched

3. trend, or steady change in level (X and R)

- indicates a gradual change in the process caused by wear, aging, etc.

- e.g. a tool is aging

4. Cycles

- indicates time variance in process

- e.g. shift change, day-night temp changes, etc.

5. Mixed Data

- indicates multimodal distributions caused by mixed material batches, alternate operators, etc.

- e.g. steel from scrap dealer, and from steelco is used.

6. Error

- readings are incorrect because of misreadings, transcription error, etc.

- e.g. a new operator measured the wrong dimension

3.1.7 Practice Problems

#1 Draw the detailed X, R, and s charts for the data below.

#2 What problems can be seen in this control chart?

#3. Draw the Pareto diagram for the data below. The data indicates the number of reported errors made when taking fast food orders by telephone