Page 164 - DMGT501_OPERATIONS_MANAGEMENT

Operations Management

Notes d
Mean deviation from mean = where ‘d’ is deviation from mean.
n
dk
Mean deviation from mode = where ‘dk’ is deviation from mode.
n
dm
Mean deviation from median = where ‘dm‘ is deviation from median.
n
Significance of Mean Deviation: As the mean deviation is not affected very much by the
extreme values as is the case with Standard deviation, the Mean deviation is useful for
many studies in economic field, e.g., computing the personnel distribution of wealth in a
community or a nation.
4. Coefficient of Variation: As standard deviation is analogous to some absolute error being
based on the deviations of observations from the central value which may be looked upon
as the true value, a measure of relative dispersion is comparable to a measure of relative
error. Such a measure, to be of any use should be free from any units for the sake of
comparability. The most commonly used measure of this type is the co-efficient of variation
given by
c.v = 100 × /X
where is the standard deviation and X is the mean. The pth percentile of a variable refers
to the value below which p% of the observation lie. For example, the median is the 50th
percentile.
The percentiles can be obtained by drawing a graph of the cumulative frequencies in ‘y’ axis
against the end of the class interval upto which the frequencies are cumulated in x axis and
reading off the ‘X’ value corresponding to any desired percentile value.

6.4 Chance and Assignable Causes of Variations

However, best the methods of transformation (for conversion from Inputs to Outputs) be, no
two pieces of output produced even under the most modern machines would be identical.
Variation is inevitable.

Variation consists of two parts:
1. Chance causes: This is the variation which is natural or inherent in the process.

2. Assignable causes: This variation is unnatural or external due to assignable causes that can
be traced.

Variations resulting from the assignable causes which can be traced, show some pattern and
follow the statistical laws, i.e., laws of distribution normal, poisson, hyper-exponential, etc.

Example: Number of machines under breakdown, variation in alloy steels sheets rolled/
forged.

The pattern of distribution can be predicted from the samples of size ‘n’ taken out of the population
(N). The process is said to be under statistical control if the process need not necessarily yield
products confirming to specifications as the process under statistical control produces results
which conform to the control limits. The main objective of quality control is to present defects
during production.

158 LOVELY PROFESSIONAL UNIVERSITY