# Linearity and Resolution

Apart from accuracy and precision, there are more factors that determine the soundness of a measurement system. Two of these important factors are as follows:

Resolution: Resolution is the ability to see fine details in a system. This ability also gives the system, the ability to distinguish different readings from one another.

A good example would be that of the system that records late coming employees. If the measurement system designed to monitor employees coming late measures it only in hours i.e. uses the wrong resolution, then any employee who is up to 59 minutes late will appear to be on time. This is because the system will display 0 till the 60th minute is reached. In effect the organization will lose its ability to distinguish between employees coming on time and those that come late.

A good thumb rule is to build an extra decimal place in the system. If you need data up to 2 decimal places, build a system that records data up to 3 decimal places. Wrong resolution can seriously hamper the process and lead to wrong decisions.

Linearity: A system is said to be linear if proportional changes in input measurements produce proportional changes in output measurement. This means that if I know for a fact that an employee coming 10 minutes late would lead to a 2% loss of productivity in his daily output, then the same employee if he comes 30 minutes late should ideally lead to a 6% loss in his daily productivity.

The method used to find out linearity is fairly simple. Any given measurement is considered, the input variables are varied in a controlled manner and the resultant output is recorded. It is essential that at least 10 measurements be taken throughout the possible range of measurement. These points are then charted on a graph and an attempt is made to fit a line through these points. The degree to which all the points lie on this line of best fit is the degree of linearity of a system.

The degree to which the points lie away from the line of best fit is called the bias of the measurement system. For instance, if a machine shows a more accurate measurement at the centre of its operating range than at the upper or lower ends then the equipment is biased.

Common reasons for measurements not being linear are as follows:

• Worn out equipment
• Calibration required at the upper and lower ends of the operating range
• Internal design problems especially in the case of electronic measurement

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Six Sigma - Measure Phase