# The Manager's Toolkit - Part 7: Studying capability

## Capability Studies

Capability Studies can analyse if a production process is capable of producing parts to the tolerance required.

The Histogram (Histograms - see Toolkit No.6) can be extended into a Capability Study for the process. This is a method for seeing if a production process is capable of producing parts to the tolerance required.

If enough samples are taken and if the cell size is decreased then the histogram begins to look like Figure 1.

## Figure 1: The Normal Distribution

This is known as the 'normal distribution' or bell-curve. This normal distribution describes how many things vary, it shows how height varies in the population, how intelligence varies in the population, and how a process produces parts. The graph shows the number of people or parts with a given intelligence or size.

We know that it is physically impossible to produce every successive part from a process to exactly the same dimensions. If enough measurements are taken then the normal curve will begin to appear. The greatest number of parts is near the centre of the curve with small numbers of parts being produced over the edges.

This normal distribution is predictable and can be fully described by just two numbers:

Mean - This is the average of all the individual values. It is the centre of the distribution and gives the 'where' value. It is written as X.

Standard Deviation - This is the 'spread' of the values and is related to the variability of the process. It is calculated by a simple formula, (it is even marked on many calculators) and is written as s.

The standard deviation is such that the limits X +/-s contains 68% of the samples, the limits X +/- 2s contains 95.44% of the samples and  +/- 3s contains 99.73% of all the samples.

If the average is 10 and the standard deviation is one, then 68% of the samples will have a value in the range of 10 +/- 1 (between 9 and 11) and 95.44% of the samples will have a value in the range of 10 +/-2.

The value +/-3s or 6s is a special value and is termed the 'process spread' or process variability. The spread can be described by Cp where:

Cp = Specified Tolerance
6s

If Cp is less than 1.33 then the process is not regarded as being capable of reliably producing in-tolerance parts.

The location can also be described by Cpk where Cpk is the smaller of:

Cpk = Upper Tolerance Limit - Mean
3s

or

Cpk = Mean - Lower Tolerance Limit
3s

If Cpk is less than 1.33 then the process is not regarded as being capable of reliably producing in-tolerance parts.

## Ease of information

A capability study can give valuable information about a process quickly and easily as shown in the examples:

## Using the information

Capability studies are vital in the purchasing machines and in setting realistic and achievable tolerances.

If a supplier tells you that a saw will cut to +/- 0.1mm then ask what the Cp and Cpk values are. If he doesn't understand then cut 50 pieces, measure the lengths, calculate the mean and standard deviation (from your calculator) and then work out Cp and Cpk based on +/- 0.1 mm. If they are not greater than 1.33 then the machine will not cut to +/- 0.1 mm.

Capability studies will tell you if a machine is operating properly and if you can ever expect to get good results from it. Capability studies lead on naturally to Statistical Process Control but that is a longer story.