FICCI CE

Accuracy & Precision

FICCI CE

Accuracy - Measurement of central tendency

Accuracy is defined as closeness of agreement between observed values and known reference standard.

Accuracy can be measured by measuring central tendency of the process.

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Accuracy

There are three popular measures of accuracy:-

• Mean

• Mode

• Median

The most commonly used measure of accuracy is mean ( simple arithmetic mean). Hence for the purpose of Six Sigma we confine our study on Mean only.

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Measurement of accuracy

Mean - it is the arithmetic average of the measurements.

To find the mean, all the measurements X1, X2, X3, ……, Xn

are added and their sum is divided by the number of

measurements, n. Mathematically it is represented as:-

Mean X = ( X1 + X2 + X3 +……+ Xn)

n

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Measurement of dispersion - Precision

Precision is the measure of dispersion between several individual observations

of relevant quality characteristics. Precision describes consistency of the process. Precision can be measured through :-

1. Range: Range is the difference between the largest and smallest measurement in a given set of observations.

2. Standard Deviation: Standard deviation in general terms is a measure of mean variation of values from the central tendency.

Standard deviation is more reliable method of measuring precision, hence for the purpose of Six Sigma, we will confine our study on Standard deviation.

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Measurement of precision

Mean Deviation of values from central tendency can also be used to measure dispersion. However, there is one difficulty in the use of this measure, that the algebraic sum of all deviations is zero.

Standard deviation is calculated as root mean square of the deviations of observations from the mean which henceforth will be represented by abbreviation SD.

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Calculation of standard deviation

Variance, V =(X1

2 + X22 +….+Xn

2) - n ( X ) 2

(n - 1)

Standard Deviation, SD =

V

Standard deviation can be calculated by the following formula :- If X1, X2 ,X3…………Xn are individual observations And X is the arithmetic mean

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Example to calculate standard deviation

Sl. X X (Square)

1 10 100

2 11 121

3 12 144

4 13 169

5 14 196

Total 60 730

Calculate standard deviation of 10, 11, 12, 13 , 14

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Calculation of Standard Deviation

Variance, V =(X1

2 + X22 +….+Xn

2) - n ( X )2

(n - 1)

X = 60

5= 12

= 730 - 5 x (12) 2

(5 - 1)

= 2.5

SD = =1.5811 2.5

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Accurate and PrecisionPicturization of accuracy & precision

Accuracy & precision of a process can be best explained by using the analogy of a rifle firing at a

target.

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Accuracy and precision

With the center of the target taken to be the true value of the characteristic being measured and by the rifle shots representing the measured values, there are four combinations of accuracy and precision as depicted in the following slides.

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Inaccurate and imprecise

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Accurate and imprecise

+

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Precise but inaccurate

+

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Accurate and precise

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Objectives of accuracy & precision

As observed from the Picturization in the preceding slides, the objective of moving towards world class quality is to continuously achieve greater consistency of the processes by aiming for consistently higher levels of accuracy & precision