**Introduction**

The
acceptance and adoption of free and open source software (FOSS) is
widespread and expanding exponentially across many industries. The
use of FOSS is an attractive option today for many organisations and
enterprises including for development, deployment, operations and
strategy. Most organisations that use SW/I.T. today are certainly
using FOSS in some form or the other, though the manner and extent to
which FOSS gets used would vary greatly across organisations. There
is no way of objectively assessing and stating the difference in the
‘FOSS Maturity’ or ‘FOSS Friendliness’ of organisations in a
quantified and objectively verifiable manner. The present work has
come up with a “**FOSS
Adoption Index (FAI) Model”**
that objectively computes a number using data gathered through online
questionnaire.

**The
FAI Model and Approach **

Our Model
uses multiple ‘levels’ depending on the type and extent of FOSS
–use data that an organisation may have with it. In the simplest
case of the model, there may be just one level where a series of
questions would be answered by the organisation which is used to
compute a single index. A 2-level model would however collect more
refined or fine-grain primary data from the organisation at level-2,
whose computation would produce secondary data which would be used
for computation at level-1 (which is above level-2) to produce the
single index. If the organisation has data that can be further
drilled down, then a 3-level model could be used where the primary
data would be used at the 3^{rd}
and the lowest level. Etc. At each level, values of the indices are
computed by assigning weights to the different criteria at that
level, the criteria themselves being coarsest at level-1, and
becoming finer as one goes down to the levels below.

The following definitions are used in building the model –

__Criteria
(Level-1)__
used in defining the FAI are indicated by the subscript ‘ i’, i =
1 to N^{(l)}
The set of N^{(l)}
level-1 criteria capture the most important factors or attributes
that impact on the value of the FOSS Adoption Index (FAI) in an
organisation belonging to the class ‘l’, and their selection is a
vital part of the model building exercise. For each level-1 criteria
‘i’ for a class ‘l’ of organisation, the ‘level-1 criteria
scores’ (*S*_{i}^{(l)}
are calculated using the data collected from organisations of that
class through a survey, and a weighted sum of these scores (*S*_{i}^{(l)})
defines the *FAI*^{(l)},
as explained below.

__Criteria
(level-2)__
indicated by the subscript ‘j’, j = 1 to M_{i,}
are the finer elements to which each level-1 criterion ‘i’ is
broken down for greater clarity and precision in data gathering.
Selection of appropriate level-2 criteria for a given level-1
criterion is an important part of model design that impacts on the
eventual usefulness of the model. ‘Level-2 criteria scores’
(*s*_{ij}^{(l)})
are obtained from the data collected, whose weighted sum gives *S*_{i}^{(l)}
as explained below.

__Model
Parameters__*α*_{i}^{(l)}
, *β*_{ij}^{(l)}
for a given class ‘l’, are the weights defined that eventually
impacts on the contribution of a particular criterion on the FAI
value of the organisaiton. The FAI, weights α_{i}^{(l)}β_{ij}^{(l)}
, and scores for level-1 criteria *S*_{i}^{(l)}
are defined through the following operations (shown for two levels) :

(3.1)

(3.2)

With
these definitions, the 2-level model looks as follows:

Data from online survey of the organization

In this study, the scores s_{ij}^{(l)
}obtained through survey
questionnaire have been assigned a range of 0 to 10, which makes
S_{i}^{(l)}
as well as FAI also to have the same range; a low value of FAI^{(l)}
(closer to zero) implying very little adoption of FOSS in the
organisation belonging to class ‘l’, and a high value (closer to
ten) meaning high levels of FOSS adoption and FOSS friendliness in
that organisation.

The key
aspect of this modelling exercise however is the proper choice of the
criteria at multiple levels that would cover all the areas of an
organisation. The other key aspect is correct assignments of values
to the model parameters α_{i}^{(l)},
β_{ij}^{(l)
}
and are discussed below.

A criterion captures the factors or attributes that impact on the value of the FOSS Adoption Index (FAI) in an organisation. Those factors that most significantly affect the adoption of FOSS in an organisation should be selected as the ‘level -1 criteria’ and those factors that further helps in measuring a ‘level-1 criteria’ in more details should be selected as ‘level-2 criteria’. In large and complex organisations, it may be necessary to drill down to still finer scales of granularity by defining ‘level-3 criterion’ etc. Our model is open and extendable in this sense, with the definition of the Index for a 3-level model given as below:

(3.3)

Where
are
the weights associated with level-3 of organisation '*l*'
and *s*_{ijk}^{(l)}
are the scores obtained through the survey. What
ultimately decides the number of levels to which one might want to
drill down is the ability to gather meaningful data at finer and
finer levels from within the organisation.

**Choice
of weights at multiple levels**

Choice
of weights or model parameters *α*_{i}^{(l)},
*β*_{ij}^{(l)}etc
associated with each level is another critical decision needed for
working with our model. The logic of such choice that works at one
level also works at other levels of the model, and we may illustrate
it with a level-1 situation. Taking the example of the criterion
“FOSS Policies and Guideline” once again, the value of its score
contributes to the final Adoption Index value through a weighted
summation – the score *S*_{i}^{(l)}appears
as multiplied with its weight *α*_{i}^{(l)},
and not by itself. In other words, the extent of contribution that
this particular score makes to the final Index value is also
determined by the associated weight value – a low weight value
reducing its contribution and a high weight value enhancing the same.

**Calculation
of level-2 scores ‘****s**_{ij}^{(l)}**’**

For
a level-2 model, the calculation of level-2 score **‘****s**_{ij}^{(l)}**’
**
is the most crucial exercise and has to be carefully done. For
measuring the usage and adoption of FOSS at level-2 a series of
questions are framed that cover the particular criteria. Each
question is assigned a score and a summation of the scores for all
the questions pertaining to a particular level-2 criterion gives the
score **‘****s**_{ij}^{(l)}**’.
**This
score along with the weight assigned β_{ij}^{(l)}are
used for calculating the S_{i}^{(l)}
and FAI^{(l)}
and can be seen in equation 3.1 and 3.2.