Week 7/8

Question 1

Define Central Tendency and Dispersion

Answer 1

Central tendency:
Mean is the normal type of average used and is denoted by µ for population or lot and Xbar the average of a sample. If the sample is truly random and is large then the sample mean and population mean should be very similar

Dispersion:
Dispersion how close are all the results to the mean is very important in quality control.

Question 2

What is the difference between a machine capability study and a process capability study?

Answer 2

Variability of machine or process compared to allowed variability
Machine – short-term, inherent, machine ‘only’ source of variation
Process – longer term including usual common sources of variation

Question 3

What do the following symbols mean?

σ, μ, Cpk, Cm, Xbar

Answer 3

σ - Standard deviation
μ - mean of population or lot
Xbar - Average of the sample

CPK - Capability process index

If you also want to study the position of the process in relation to the tolerance limits, you use the Cpk index, which describes the process capability corrected for position. It is not much use having a high Cp index if the process setting is way off centre in relation to the middle of the tolerance range.

A high Cpk index means, then, that you have a good process with a small spread in relation to the tolerance width, and also that it is well centred within that width. If Cpk is equal to Cp, the process is set to produce exactly in the middle of the tolerance range

Cm (capability machine)

The Cm index describes machine capability; it is the number of times the spread of the machine fits into the tolerance width. The higher the value of Cm, the better the machine.

Example: if Cm = 2.5, the spread fits 2½ times into the tolerance width, while Cm = 1 means that the spread is equal to the tolerance width.

Note that even if the spread is off-centre, it is still the same size (Cm index). The figure takes no account of where the spread is positioned in relation to the upper and lower tolerance limits, but simply expresses the relationship between the width of the spread and the tolerance width