An entropy based approach for risk facto

An Entropy Based Approach for Risk Factor Analysis in a Software Development Project Pradnya Purandare Assistant Professor & Research Scholar, Symbiosis Centre for Information Technolo

An Entropy Based Approach for Risk Factor Analysis

in a Software Development Project

Pradnya Purandare

Assistant Professor & Research Scholar, Symbiosis Centre for Information Technology,

Symbiosis International University, Pune, Maharashtra, India

Abstract

Software development projects are mostly encountered by

risks The risks emanates from different risk factors which are

embedded in various activities of the project development

There is no direct method of estimating the influence of each

of the risk factors singularly or jointly for the actual Risk

taking place Nevertheless the project management takes

recourse to subjective judgment in assigning a percentage

value of the influence of each of the risk factors in the

software project since the success or failure or over run of the

project is inseparably associated with risk The traditional

approach for risk estimation follows the procedure of

“guesstimate”-subjectively assigning probability of

occurrence of risk caused by a certain risk factor No doubt

this approach is subjective; however, these parameters can

further be taken for viewing project risk from another

perspective and possibly improvement in the metric of risk

assessment The proposed method in this paper attempted to

use the Shannon’s Entropy concept to measure the amount of

information for estimating the software project risk from

various risk factors Thus, each risk factor at a particular stage

of development is identified and assigned a probability of

causing a disruption This enables arriving in the entropy field

for further analysis

Keywords: Risk Factors in Software Projects, Shannon’s

Entropy

Introduction

Software development projects are usually designed to

progress in stages and each stage involves multiple activities

These activities are prone to risks Several research papers on

Risk Management in software projects have addressed the risk

factors associated with the project [1] These factors if not

identified properly become responsible for the success or

failure of the project Various techniques of risk identification

[2] and categorization [6-9] have been dealt with analyzing

the remedial approach as well However, the very fact that

risk by nature is uncertain leaves the software projects to

some element of chance

Software project risk management identifies, assesses controls

and mitigates the risk factors which impact project success

adversely The risk management can reduce risks Risk

assessment & measuring alone can provide the data to help

project decisions objectively Focus of early literature studies

have been on software project risk assessment and control To

date, yet there is lack of wide acceptance of particular

measure method of software project risk Although the relationship between software project performance and risks involved in it is iteratively examined, application of risk knowledge to mitigation is yet area to be explored since still remains some level of confusion among project and technical managers The conventional risk measurement method works with each risk factor’s loss as well as its probability of occurrence, which usually are assessed by experts subjectively Therefore, it indicates very high influence of artificial factors Also, it is difficult to realize the objective and effective measurement The literature studies indicate emphasis on risk factors, methods, processes, and uncertainties influencing project success [3-12] Especially the previous study with focus on Software Risk Management Principles, Practices and the Software project risks and their effect on outcomes, Identifying Software Project Risks with Delphi and other approaches surely puts more light on software project risk & their management [13-16] Though many methods, processes, techniques are researched and are being practiced by the industry but still there is a gap in software risks and project success

This is also an indication of need of research of new techniques in the risk identification and assessment area In view of these reasons, this paper has proposed software development project’s risk measurement method with information entropy, and it significantly reduces the disadvantages of the subjective assessment in terms of occurrence probability and impact degree in previous studies

In rapid digitization of the world, number of software development projects is increasing Also the customers are expecting 3 virtues of development as minimum duration, minimum cost and high quality These 3 virtues are exposed constantly to external & internal constraints of people and requirements changes during the development These all factors introduce risks and uncertainty to projects There are many techniques used to assess the risks But they introduce subjectivity in their assessment Hence there was a strong need of a technique which can be aptly used to assess the risks So the entropy concept can be suitably applied to the software project risks to assess them effectively The ever increasing demands of client to reduce cost, time and increase quality have put more pressure to have reduced risks and to have reduced uncertainties Hence we will check if Entropy can be used for risk assessment [17-21]

The prime objective is to conduct risk assessment of software development projects The Software Project Risk management area has been studied & analyzed thoroughly by researchers & practitioners The primary work in this area has done by Barry

Boehm and researchers in identifying critical risk factors

which make impact on the project success or failures Then

Risk management standards & methodologies adopted are

PMI, Prince II, and ISO etc Lot of Risk management tools,

software’s are used by industries And to the dismay in spite

of all these efforts in the area of risk assessment &

management, more than 35% projects are successful

contributing to one of the top reasons being risk assessment &

management Also the existing risk assessment techniques

have their own subjectivity issues So we thought of

introducing, studying & analyzing the entropy concept to

assess risks and to check if it can be suitable and make risk

assessment efficient [17-21, 23]

The Risk Evaluation System of Software Project Risk

The Establishment of Index System

According to the risk factors that are existing in the software

project, the paper analyses all links that affect certainty, safety

of the project from internal and external project risk aspects

[13-15, 22]

To calculate the importance of the software project risk

indicators in evaluation system decision-making data is

obtained through research which constructs the decision

matrix

R={rij}mxn

Where, m is the total number of projects considered and n is

the total number of attributes rij is the risk factor at ith project

and jth attribute





 m

i

rij

rij

0

The normalized matrix is R=(rij) mxn

Calculate the information entropy of index, the specific

calculation formula is (1)







j

rij rij

n

Ei

1

ln ln

1

(2)

Where i=1, 2, …, m

Calculate the weights of indicators, the specific formula is:









 n

k

Ek

Ei

wi

1

) 1

(

1

(3)

Where, E represents the entropy weight

Weight vector of indicators is w=(w1,w2, wn)

Here, weight can be defined as the importance of that risk

indicator in entropy calculation

According to the above steps, we can draw evaluation weights

of software project risk indicators

Methodology:

Step 1: Software Projects Risk factor wise original data is

gathered

Step 2: Calculate Pij, decision matrix is standardized normalized

Step 3: Calculate the Entropy Weight Ej Step 4: Table4 for FINAL SCORES Step 5: Decision on Risk Ranks

Analysis

We applied the above Entropy method to software project’s dataset It is consisting of risk factor values Above entire process of Entropy method was applied to these projects a w could arrive at risk ranks It yields us in understanding the uncertainty levels very clearly through these projects

Software Project Risk Uncertainty degree based on Entropy Process [13-14, 22]

Entropy Process

1 To gather Original Data with Project Risk factor impacts

2 To calculate Pij

3 To calculate the Entropy Weight Ej

4 To calculate attribute weightt wi

5 To calculate the FINAL Risk SCORES Step 1: Gather Original Data with Software Development Project Risk factors

 Enter each project details as risk variable values per project

 To take sum(Xij) of that each attribute across all project

Step 2: Calculate Pij: decision matrix is standardized normalized

 Each project’s each attribute’s value is calculated as Pij=Xij / Sum(xij) from previous table1

 Mathematical Expression: Pij=Xij / sum(xij) rij=rij / sum (rij)

Step 3: Calculate the Entropy Weight Ej

 Each project’s each attribute’s value is calculated as Pij=P ij * Log(Pij) from previous table2’s corresponding values

 Then sum (P ij * Log(Pij)) is calculated for each attribute variable value across projects

 Then for each attribute variable, single Ej value is calculated as per below given mathematical expression

 N is the total number of projects considered to calculate the entropy

 Mathematical Expression Ej=-1 / log n * sum (P ij * Log(Pij)) wher i=1 to n

Step 4: attribute wt wi calc

 Calculate 1-Ej from Ej values of Step3 Table

 Calculate sum(1 – Ek) i.e K=1 to m from Ej values per attribute k=1 to m of Step3 Table

 Mathematical Expression wi=(1-Ej) / sum(1-Ek) where k=1 to m

Step 5: Table for FINAL ENTROPY, Risk SCORES

 To calculate with zi(w)' sum, Sum(rij) is referred here

from corresponding each value from the Table2 as Pij

Wi value is available per attribute from the Step4 i.e

From Table4

 Each attributes sum is calculated, it is the Rank Score

of Risk Entropy calculated finally

 Based on these Ranks scores decision of entropy levels

and risk levels can be taken

 Mathematical Expression zi(w)=sum(rij) * wj where

j=1 to m

Application Example of Entropy on Software Projects

Risk Assessment

The Establishment of Index System

We have tried to experiment the above entropy method to

calculate uncertainty degree of risks of software projects The

dataset is of software development projects available in public

domain The dataset consists of risk factor impact values of

the software projects We have converted the risk factor’s linguistic levels numerical values for further calculations [7]

Table 1 Attributes

Here we have gathered the original project data with Risk factor values, which were converted from linguistic to numerical values All these risk factors are pre-defined by that cocomo-sdr dataset Risk factors for the parameters RELY, DATA CPLX, RUSE, DOCU, TIME, STOR, PVOL, ACAP, APEX, PCAP, PLEX, LTEX, PCON, TOOL, SITE, SCED, PREC, FLEX, RESL, TEAM are taken into consideration in the dataset The project ID shows the12 projects of the dataset for these risk factor parameters The tables show the above risk factor parameters as v1 to v22 [13-15, 22]

In this step, each project’s details are mentioned as the risk variable values per project Then we have taken sum (Xij) of that each attribute across all projects

Table 1: Attributes of Software Projects Risk factor wise original data

Project ID v1 v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12 v13 v14 v15 v16 v17 v18 v19 v20 v21 v22

1 1 1 0 0.95 0.91 1.29 1.05 1 0.85 0.81 0.76 0.91 0.91 0.81 0.9 1.09 1 6.2 3.04 5.65 2.19 7.8

2 1.1 1 0.87 0.95 0.91 1.29 1.17 1 1 1 0.76 0.85 0.91 0.81 0.9 1.22 1 0 3.04 5.65 0 7.8

3 1.1 1.28 0.87 0.95 0.91 1.29 1.17 1 1 1 0.88 0.85 0.84 0.81 0.9 1.22 1 0 3.04 5.65 2.19 7.8

4 1.1 1.14 0.87 0.95 0.91 1 1 1.15 0.85 0.88 0.88 0.85 0.91 1.29 1 0.93 1 0 2.03 2.83 2.19 4.68

5 0.92 1 1.34 1.15 1.23 1.11 1 1 0.85 1 0.88 1 1 0.9 1 0.93 1 3.72 3.04 5.65 2.19 4.68

6 0.92 0.9 1 1 1 1 1 0.87 0.71 1 0.76 0.91 0.91 0.9 1.17 0.8 1 0 4.05 0 0 3.12

7 0.92 0.9 0.87 0.95 0.91 1 1 0.87 0.71 1 0.76 0.85 0.84 0.81 1.17 0.93 1 0 0 0 3.29 3.12 Project ID v1 v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12 v13 v14 v15 v16 v17 v18 v19 v20 v21 v22

8 0.92 0.9 0.73 0.95 0.81 1.29 1.17 0.87 1.19 1 0.88 1 1 0.81 1 0.86 1 3.72 5.07 0 3.29 6.24

9 0.82 1 0.87 0.95 0.91 1 1 0.87 1.19 0.88 0.88 0.91 0.91 0.81 1 0.93 1 6.2 5.07 4.24 5.48 6.24

10 0.82 1.14 1 1 1 1.29 1.17 0.87 1.19 0.88 0.76 0.85 0.91 0.81 1 1 1 3.72 5.07 0 4.38 6.24

11 0.92 1 1 1 1 1 1 0.87 0.71 1 0.88 1 0.91 0.81 0.78 0.86 1 2.48 3.04 0 2.19 6.24

12 0.92 0.9 1.17 1.07 1.11 1 1 0.87 1.19 0.88 0.88 1 0.91 0.81 0.78 0.86 1 4.96 3.04 4.24 2.19 4.68 sum(Xij) 11.46 12.16 10.59 11.87 11.61 13.56 12.73 11.24 11.44 11.33 9.96 10.98 10.96 10.38 11.6 11.63 12 31 39.53 33.91 29.58 68.64

Table 2 Attributes

Here, we have calculated Pij to create a decision matrix which is standardized & normalized

Each project’s, each attribute’s value is calculated as

Pij=Xij / Sum(xij) from previous table1,

as Pij=Xij / sum(xij),

rij=rij / sum (rij)

Table 2: Attributes calculate Pij

Project ID v1 v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12 v13 v14 v15 v16 v17 v18 v19 v20 v21 v22

1 0.087 0.082 0 0.080 0.078 0.095 0.082 0.088 0.074 0.071 0.076 0.082 0.083 0.078 0.077 0.093 0.083 0.2 0.076 0.166 0.074 0.113

2 0.095 0.0822 0.082 0.080 0.0783 0.095 0.091 0.088 0.087 0.088 0.076 0.077 0.083 0.078 0.077 0.104 0.083 0 0.076 0.166 0 0.113

3 0.095 0.105 0.082 0.080 0.078 0.095 0.091 0.088 0.087 0.088 0.088 0.077 0.076 0.078 0.077 0.104 0.083 0 0.076 0.166 0.0740 0.113

4 0.095 0.093 0.082 0.080 0.078 0.073 0.078 0.102 0.074 0.077 0.088 0.077 0.083 0.124 0.086 0.079 0.083 0 0.051 0.083 0.074 0.068

5 0.08 0.082 0.126 0.096 0.105 0.081 0.078 0.088 0.074 0.088 0.088 0.091 0.091 0.086 0.086 0.079 0.083 0.12 0.076 0.166 0.074 0.068

6 0.08 0.074 0.094 0.084 0.086 0.073 0.078 0.077 0.062 0.088 0.076 0.082 0.083 0.086 0.10 0.068 0.083 0 0.102 0 0 0.045

7 0.080 0.074 0.082 0.08 0.078 0.073 0.078 0.077 0.062 0.088 0.076 0.077 0.076 0.078 0.10 0.079 0.083 0 0 0 0.111 0.045

8 0.080 0.074 0.068 0.08 0.069 0.095 0.091 0.077 0.104 0.088 0.088 0.091 0.091 0.078 0.086 0.073 0.083 0.12 0.128 0 0.111 0.09

9 0.071 0.082 0.082 0.08 0.078 0.073 0.078 0.077 0.104 0.077 0.088 0.082 0.083 0.078 0.086 0.079 0.083 0.2 0.128 0.125 0.185 0.090

10 0.071 0.0937 0.094 0.084 0.086 0.095 0.091 0.077 0.104 0.077 0.076 0.077 0.083 0.078 0.086 0.085 0.083 0.12 0.128 0 0.148 0.090 Project ID v1 v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12 v13 v14 v15 v16 v17 v18 v19 v20 v21 v22

11 0.08 0.082 0.094 0.084 0.086 0.073 0.078 0.077 0.062 0.088 0.088 0.091 0.083 0.078 0.067 0.073 0.083 0.08 0.076 0 0.074 0.09

12 0.08 0.074 0.11 0.09 0.095 0.073 0.078 0.077 0.104 0.077 0.088 0.091 0.083 0.078 0.067 0.073 0.083 0.16 0.076 0.125 0.074 0.068 sum(rij) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Table 3 Attributes

Here, we have calculated the Entropy Weight Ej Each project’s each attribute’s value is calculated as Pij=P ij * Log(Pij) from previous table2’s corresponding values Then sum (P ij * Log(Pij)) is calculated for each attribute variable value across projects Then for each attribute variable, single Ej value is calculated as per below given mathematical expression N is the total number of projects considered to calculate the entropy with Ej

Table 3: Attributes for Entropy Weight Ej

Project ID v1 v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12 v13 v14 v15 v16 v17 v18 v19 v20 v21 v22

1 1 1 0 0.95 0.91 1.29 1.05 1 0.85 0.81 0.76 0.91 0.91 0.81 0.9 1.09 1 6.2 3.04 5.65 2.19 7.8

2 1.1 1 0.87 0.95 0.91 1.29 1.17 1 1 1 0.76 0.85 0.91 0.81 0.9 1.22 1 0 3.04 5.65 0 7.8

3 1.1 1.28 0.87 0.95 0.91 1.29 1.17 1 1 1 0.88 0.85 0.84 0.81 0.9 1.22 1 0 3.04 5.65 2.19 7.8

4 1.1 1.14 0.87 0.95 0.91 1 1 1.15 0.85 0.88 0.88 0.85 0.91 1.29 1 0.93 1 0 2.03 2.83 2.19 4.68

5 0.92 1 1.34 1.15 1.23 1.11 1 1 0.85 1 0.88 1 1 0.9 1 0.93 1 3.72 3.04 5.65 2.19 4.68

6 0.92 0.9 1 1 1 1 1 0.87 0.71 1 0.76 0.91 0.91 0.9 1.17 0.8 1 0 4.05 0 0 3.12

7 0.92 0.9 0.87 0.95 0.91 1 1 0.87 0.71 1 0.76 0.85 0.84 0.81 1.17 0.93 1 0 0 0 3.29 3.12

8 0.92 0.9 0.73 0.95 0.81 1.29 1.17 0.87 1.19 1 0.88 1 1 0.81 1 0.86 1 3.72 5.07 0 3.29 6.24

9 0.82 1 0.87 0.95 0.91 1 1 0.87 1.19 0.88 0.88 0.91 0.91 0.81 1 0.93 1 6.2 5.07 4.24 5.48 6.24

10 0.82 1.14 1 1 1 1.29 1.17 0.87 1.19 0.88 0.76 0.85 0.91 0.81 1 1 1 3.72 5.07 0 4.38 6.24

11 0.92 1 1 1 1 1 1 0.87 0.71 1 0.88 1 0.91 0.81 0.78 0.86 1 2.48 3.04 0 2.19 6.24

12 0.92 0.9 1.17 1.07 1.11 1 1 0.87 1.19 0.88 0.88 1 0.91 0.81 0.78 0.86 1 4.96 3.04 4.24 2.19 4.68 sum(Xij) 11.46 12.16 10.59 11.87 11.61 13.56 12.73 11.24 11.44 11.33 9.96 10.98 10.96 10.38 11.6 11.63 12 31 39.53 33.91 29.58 68.64

Table 4 Attributes

Here, we have calculated the attribute wt wi by from table3 values of Ej & Ek

To calculate wi=(1-Ej) / sum(1-Ek) where k=1 to m

Table 4 shows wi calculation for example a few risk parameter’s wi calculation based on CPLX, DOCU, STOR, ACAP, PCAP,LTEX, TOOL, SCED For remaining all risk parameters same method is used to calculate wi

Table 4: Attribute weight wi

1-Ek

sum(1-Ek)

Hence, wi= 0.002820076 0.00350 0.05751 0.00102 0.00337 0.004263 0.00153 0.00244 0.01154

Table 5 Attributes

Here, we have to calculate FINAL ENTROPY and Risk SCORES with zi(w)' sum Each attributes sum is calculated, it is the Rank Score of Risk Entropy calculated finally Based on these Ranks scores decision of entropy levels and risk levels can be taken

as zi(w)=sum(rij) * wj where j=1 to m Decision Making: More the Score indicates more Entropy value means less of risk, less score means more risk

Table 5: Attributes for FINAL Risk SCORES

Project ID v1 v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12 v13 v14 v15 v16 v17 v18 v19 v20 v21 v22

1 0.00024 0.00028 0 8.22584 0.00026 0.00040 0.00012 0.00021 0.00085 0.0001 0.00011 0.00011 6.10392 0.00046 0.00033 0.00048 0 0.06669 0.00550 0.05372 0.01037 0.00268

2 0.00027 0.00028 0.00472 8.22584 0.00026 0.00040 0.00014 0.00021 0.001 0.00013 0.00011 0.00011 6.10392 0.00046 0.00033 0.00054 0 0 0.0055 0.05372 0 0.00268

3 0.00027 0.00036 0.00472 8.22584 0.00026 0.0004 0.00014 0.00021 0.001 0.00013 0.00012 0.00011 5.63439 0.00046 0.00033 0.00054 0 0 0.0055 0.05372 0.01037 0.00268

4 0.00027 0.00032 0.00472 8.22584 0.00026 0.00031 0.00012 0.00025 0.00085 0.00011 0.00012 0.00011 6.10392 0.00074 0.00037 0.00041 0 0 0.00367 0.02691 0.01037 0.0016

5 0.00022 0.00028 0.00727 9.9576 0.00035 0.00034 0.00012 0.00021 0.00085 0.00013 0.00012 0.00012 6.70761 0.00051 0.00037 0.00041 0 0.04001 0.0055 0.05372 0.01037 0.0016

6 0.00022 0.00025 0.00543 8.65878 0.00029 0.00031 0.00012 0.00018 0.00071 0.00013 0.00011 0.00011 6.10392 0.00051 0.00044 0.00035 0 0 0.00733 0 0 0.00107

7 0.00022 0.00025 0.00472 8.22584 0.00026 0.00031 0.00012 0.00018 0.00071 0.00013 0.00011 0.00011 5.63439 0.00046 0.00044 0.00041 0 0 0 0 0.01558 0.00107

8 0.00022 0.00025 0.00396 8.22584 0.00023 0.00040 0.00014 0.00018 0.0012 0.00013 0.00012 0.00012 6.70761 0.00046 0.00037 0.00038 0 0.04001 0.00918 0 0.01558 0.00214

9 0.00020 0.00028 0.00472 8.22584 0.00026 0.00031 0.00012 0.00018 0.00120 0.00011 0.00012 0.00011 6.10392 0.00046 0.00037 0.00041 0 0.06669 0.00918 0.04031 0.02595 0.00214

10 0.0002 0.00032 0.00543 8.65878 0.00029 0.0004 0.00014 0.00018 0.0012 0.00011 0.00011 0.00011 6.10392 0.00046 0.00037 0.00044 0 0.04001 0.00918 0 0.02074 0.00214 Project ID v1 v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12 v13 v14 v15 v16 v17 v18 v19 v20 v21 v22

11 0.00022 0.00028 0.00543 8.65878 0.00029 0.00031 0.00012 0.00018 0.00071 0.00013 0.00012 0.00012 6.10392 0.00046 0.00029 0.0003849 0 0.02667 0.00550 0 0.01037 0.00214

12 0.00022 0.00025 0.00635 9.26489 0.00032 0.00031 0.00012 0.00018 0.0012 0.00011 0.00012 0.00012 6.10392 0.00046 0.00029 0.00038 0 0.05335 0.0055 0.04031 0.01037 0.00160 FINAL

SCORE :

SUM

0.00282 0.0035 0.05751 0.00102 0.00337 0.00426 0.00153 0.00244 0.01154 0.00152 0.00146 0.00141 0.00073 0.00595 0.00437 0.0052 0 0.33345 0.07164 0.32246 0.14012 0.02359

RANK

RISK

Risk Rank

Decision Making: More the Score indicates ore Entropy value

means less of risk, less score means more risk

Conclusion

The application of Entropy to Software Project risks definitely

helps in understanding the uncertainty level & degree of risks

in those software projects Hence, entropy techniques shows

promising way to assess the risk uncertainty degree ahead,

and we will take further research work in the area of software

project risks based on information entropy technique

Acknowledgements

My sincere thanks to Phd Guide Dr Prasenjit Sen, Professor

Symbiosis International University, Pune, India for the

invaluable inputs and guidance on introduction of Shannon’s

Entropy concept to software project risk management

research

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