Post on 29-Dec-2015
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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.
FICCI CE
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.
FICCI CE
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
FICCI CE
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.
FICCI CE
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.
FICCI CE
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
FICCI CE
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
FICCI CE
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
FICCI CE
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.
FICCI CE
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.