Ompal Singh

Multi up-gradation software reliability growth model with imperfect debugging

Due to demand of new features and highly reliable software system, the software industries are speeding their up-gradations/add-ons in the software. The life of software is very short in the environment of perfect competition. Therefore the software developers have to come up with successive up gradations to survive. The reported bugs from the existing software and Features added to the software at frequent time intervals lead to complexity in the software system and add to the number of faults in the software. The developer of the software can lose on market share if it neglects the reported bugs and up gradation in the software and on the other hand a software company can lose its name and goodwill in the market if the reported bugs and functionalities added to the software lead to an increase in the number of faults in the software. To capture the effect of faults due to existing software and generated in the software due to add-ons at various points in time, we develop a multi up-gradation, multi release software reliability model. This model uniquely identifies the faults left in the software when it is in operational phase during the testing of the new code i.e. developed while adding new features to the existing software. Due to complexity and incomplete understanding of the software, the testing team may not be able to remove/correct the fault perfectly on observation/detection of a failure and the original fault may remain resulting in the phenomenon known as imperfect debugging, or get replaced by another fault causing error generation The model developed is validated on real data sets with software which has been released in the market with new features four times.

Consumer behaviour-based innovation diffusion modelling using stochastic differential equation incorporating change in adoption rate

Bass innovation and diffusion model and many of its extended forms have been reported in marketing literature and applied successfully for predicting adoption curve of products from different segments of market. All these models assume that an adopter buys the product only once in his lifetime, however, this may not be true, because a consumer might buy the product more than once for his utility (repeat purchasing). Also, there can occur a situation that the consumer leaves the system without buying the product (balking). In this paper, we propose a diffusion model based on Ito’s type of stochastic differential equation with repeat purchasing and balking. It also incorporates the change-point concept, where the rate of product adoption per remaining potential adopter might change due to shift in marketing/promotional strategy, entry/exit of some of the competitors in the market. The applicability of the proposed model is illustrated using new product sales data.

A multi-attribute approach for release time and reliability trend analysis of a software

In a Software Development Life Cycle the testing phase is given a lot of importance. But testing cannot be done indefinitely due to many reasons ranging from marketing considerations to increase in cost. Hence it is pertinent to find the optimal release time during testing phase. Firms routinely face the challenging decision of when to stop testing and release the product in the market. It has been observed that the pace of introduction of new software is much higher in recent years in comparison to any time in the past. Thus to get the competitive edge it is critical to know about the optimal entry time. Too late an entry is likely to lead to significant loss of opportunity. On the other hand early introduction of a product might hinder its growth due to lack of receptiveness of users towards new technology. Many release time problems with optimization criteria like cost minimization, reliability maximization and budgetary constraints etc. have been discussed in the literature. The release time problem discussed in this paper depends on the combined effect of cost and the Failure Intensity function; therefore we formulated an optimal release planning problem based on multi-attribute utility theory. A numerical illustration is provided towards the end of the paper. Furthermore, a trend line for the reliability of software has also been plotted to show the behaviour of reliability.

Release time problem with multiple constraints

Quality of software system generally depends on how much time testing takes and what testing methodologies are used. One attribute of quality is reliability which can be increased by removing more faults from the software and this can be done by spending more time on testing. However, spending more time on testing will increase cost of the software development process. On the other hand, if testing time is too short, testing cost of software may be reduced but it will increase the chance of getting unreliable software and customers may not take higher risk of buying unreliable software. Highly competitive market conditions have forced developers to offer highly reliable products to the users. Software warranty is one such indicator used by the users to judge its reliability with the perception that a longer warranty period indicates higher reliability. Software warranty is a tool which provides assurance about the quality. Warranty cost may be reduced by providing more reliable product. Therefore software reliability, testing, warranty period and cost needs to be considered jointly. In this paper, we propose a new method to estimate the optimal software release time of a software with warranty under imperfect debugging environment by using Multi Attribute Utility Theory. More precisely, three significant attributes, namely Reliability, Cost and Detection rate indicator are used to determine the optimal release time of software under warranty. The proposed new decision model based on multi-attribute utility analysis is tested on the real world data set.

An innovation diffusion model for consumer durables with three parameters

Strategic innovation diffusion converts newly created knowledge into increasing a firm’s value primarily through innovative product offerings. In this paper, we present a time-based adoption pattern with pricing and promotional expenditure as a three-dimensional innovation diffusion model (3D-IDM). In our proposed 3D-IDM, we assume that value of the product plays a crucial role of being the major driver of diffusion, and is classified into the following three main factors: (1) continuation time of the product in the market – representing goodwill of the product; (2) price of the product – indicating consumers’ buying behaviour; and (3) marketing efforts of the firm. A special form of the Cobb–Douglas production function is used to design the three-dimensional framework. An empirical study is performed on number of consumer-durable sales data to validate and compare the proposed model. Various performance measures are treated uniquely using the Mahalanobis distance-based approach (DBA) to determine the rel...

SOFTWARE RELIABILITY GROWTH AND INNOVATION DIFFUSION MODELS: AN INTERFACE

The objective of this paper is to show an interface between modelling, allocation problems and control problems in software reliability and marketing. It has been brought out that in models which exist in software reliability and defined implicitly/explicitly for errors of two types; it is the dependency factor among errors that gives rise to S-Shaped growth curve. It is further shown that this dependency on the line of categorization of errors, adopters can be of several types/categories. Such categorization, though implicit in nature, not brought out in literature, further strengthens the fact that modeling any software phenomenon should incorporate errors of different severity rather explicitly. We have also provided a general model which can account for imperfect debugging and error generation in software reliability. The approach followed is rather implicit in nature but provides good closed form solutions. Such solutions were being alternatively looked for in innovation diffusion models namely the Bass Model, which can account for repeat purchase and growing market size. Besides we also show how problem of resource allocation and control in the two fields can be analyzed similarly. The analogy as brought out in this paper is interesting and may further lead to enriching the two areas of current research.

A stochastic formulation of successive software releases with faults severity

Software companies are coming with multiple add-ons to survive in the pure competitive environment. Each succeeding up-gradation offers some performance enhancement and distinguishing itself from the past release. If the size of the software system is large, the number of faults detected during the testing phase becomes large, and the number of faults, which are removed through each debugging, becomes small compared to initial fault content at the beginning of the testing phase. In such a situation, we can model the software fault detection process as a stochastic process with continuous state space. In this paper, we propose a multi-release software reliability growth model based on Itôs type of differential equation. The model categorizes Faults in two categories: simple and hard with respect to time which they take for isolation and removal after their observation. The model developed is validated on real data set.

Unified approach for modeling innovation adoption and optimal model selection for the diffusion process

Purpose - – Mathematical modeling of innovation diffusion is a constantly evolving field within marketing science. The diffusion process explains the dispersion of an innovation among potential buyers. Prior research on innovation diffusion has been based on modeling varied aspects of real life situations in marketing. One such aspect is studying the adoption process depending on the awareness and motivation level among the customers. Awareness is having knowledge of an innovation, whereas motivation is about the perception of an individual. In line with these aspects, the purpose of this paper is to propose a unified modeling framework for the adoption process based on the awareness and motivation about the product. Design/methodology/approach - – When the market is well informed about the product, there are some people who are motivated and some, who have adopted the product earlier and shall now influence others in their buying behavior. It is very much similar to queuing system in which some units are waiting in a queue for the service, service for some units are being processed and some units have already been served. This analogous behavior between two approaches has motivated the use of infinite server queuing theory in modeling adoption of the product. Thereafter, the authors have proposed a unification scheme to model different market scenarios. Findings - – From analyzing the values of comparison criteria, it was not clear that which among them is performing best. Thus there was a need for an approach which can judiciously find the optimal model. For this very purpose the authors applied distance-based approach which was capable of computing the optimal model based on the distance of attribute value from the optimal. The analysis performed on two real life sales data sets depict that model in which awareness is following logistic pattern and motivation and adoption are following a constant pattern is ranked one. Research limitations/implications - – The idea has been validated on product. It would be interesting to know how the methodology works on service. Originality/value - – The modeling framework discussed in this paper can be helpful to know from the available set of alternative, which among them is performing better in capturing the spread of the product in the market. The proposed framework offer some managerial guidance by highlighting the unusual aspects of diffusion process and also present an approach to judge the best among a set of different models.

A software up-gradation model with testing effort and two types of imperfect debugging

Recent advances in the software world have seen the rise of various Software Reliability Growth Models (SRGMs). These SRGMs take into account various factors and associate them to reliability to come out with a new approach. Some of them consider calendar time as the governing factor while others argued that effort based modeling is more towards reality. In the real industrial scenario, due to the ever growing demands of the customer and stiff contention in the market, developers generally prefer to release the software with multiple versions instead of rolling out all the functionalities at one go. Consequently the customary approach towards software development process as observed in practice is iterative in nature. Moreover, the debugging process is not a perfect event. It has bottlenecks owing to the increasing complexity of software due to up gradations which transcends the limited knowledge of testing team. Thus, it is not a practical approach to go with the assumption of fault removal with certainty after the failure is observed. In a real scenario, it may happen that initially the testing team may not be skilled enough to detect all the faults leading to imperfect debugging, also during debugging it may happen that some faults are added fault causing error generation. Some models successfully capture the influence of imperfect debugging on multiple releases of software. In this present paper, we present a two stage detection/correction based software reliability growth model with testing effort, integrating the concept of two types of imperfect debugging in multiple up gradations of a software. We have taken Exponential and logistic distribution functions for detection and correction process in this paper. The proposed model is successfully tested on a real life software data set.

SOFTWARE RELEASE TIME BASED ON DIFFERENT MULTI-ATTRIBUTE UTILITY FUNCTIONS

The decision to release a software product will become an even more complex and important decision. A decision has strategic value when it has the potential for large prospective financial losses to a software manufacturer or its customers or end-users. A software release decision is a tradeoff between early release to capture the benefits of an earlier market introduction and the deferral of product release to the reliability. If a software product is released too early, the software manufacturer incurs post-release costs of later fixing failures. If a software product is released too late, the additional development cost and the opportunity cost of missing a market window could be substantial. These two attribute reliability and cost need to be combined to determine the optimal release time of software. This paper proposes a new practical method for determining when to stop software testing considering reliability and cost as two factors simultaneously. The proposed new decision model is based on three different weighted combination of utility function in Multi-attribute utility theory.