• 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.



1.1.1 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





1.1.2 Creating the Charts


• The central line is an average of ‘g’ historical values.



• The control limits are +/-3 σ 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 σ with





1.1.3 Maintaining the Charts


• Over time σR and σX 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)





1.1.4 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,






1.1.5 Interpreting the Control Charts


• We consider a point that lies outside of the 3σ 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





1.1.6 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


1.1.7 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