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Department of Operational Research, University of Delhi Page 193
Chapter 6
Two-Dimensional Model for Successive Generations of
Technology
Understanding and analyzing the rate of adoption of a new technology in the
marketplace is of principal significance for any organization to assess the suitability
of technology investment that can enhance the profitability and its market share in
long run. Successful new product introductions contribute substantially to long-term
financial success and are an effective strategy to increase primary demand. One major
way to increase the market presence is by improving the customer perspective about
the organization through periodic introduction of new products. Technological
breakthroughs are happening rapidly and these innovations often take form as new
products. Companies make a lot of investment in the research and development or in
technology acquisition and are therefore concerned about their success (Cooper and
Kleinschmidt 1986, Zirger and Maidique 1990, Cohen, Eliashberg and Ho 1996,
Winter and Sundqvist 2010). The concept of performance of a new technology
generation over its lifecycle has been explained by using the well known S-curve or
Sigmoid diffusion curve(Looy, Zimmermann and Ranga 2000);(Rodger, Pendharkar
and Bhatt 1996).
The diffusion of innovation refers to the tendency of new products, practices, or ideas
to spread among people. Diffusion models, like any other mathematical models are
simplification of reality. However they constitute a wide range of useful tools, in both
academic and business context. As describe in chaper1 (section 1.16.1) Bass model is
one of the pioneer mathematical model for diffusion of the product in the market.
This Chapter is based on the following research paper entitled:
1. Kapur, P. K., Aggarwal, A. G., Garmabaki, A. H. S., and Tandon, A. (2012), " Modelling
Innovation Diffusion by Incorporating Time & Price for Successive Generations of
Technologies," International Journal of Technology Transfer and Commercialization,
Communicated.
Chapter5 Two-Dimensional Model for Successive Generations of Technology
Department of Operational Research, University of Delhi Page 194
Norton and Bass (1987) proposed a model considering different generations of a
technology. Examples are the series of generations of mobile telephones and personal
computers. In the Norton–Bass model, each generation of the technology attracts
incremental population segments of potential adopters; in addition, later generations
may attract potential adopters of earlier generations. This modeling approach
effectively succeeded the models on technological substitution, where one technology
replaced its predecessor. Speece and MacLachlan (1995) demonstrated applicability
of the Norton–Bass model and forecasted the adoption of successive generations of
gallon milk containers. Mahajan and Muller (1996) extended the Norton–Bass model
to allow adopters of early generations to skip generations, for example, an adopter of
the first generation could replace it with third generation technology and second by
fourth, etc. They validated their model using generations of IBM mainframe
computers. Islam and Meade (1997) demonstrated that the assumption of constant
coefficients of innovation and imitation ( p and q ) over successive generations could
be relaxed. In a study of multi-national mobile telephone adoption, they demonstrated
that the coefficient of imitation ( q ) tended to increase from generation to generation.
Sohn and Ahn (2003) used the Norton–Bass(1987) model to demonstrate a cost–
benefit analysis of introducing a new generation of information technology. The
model proposed by Jiang (2010) is an extended multi generational diffusion model
that uniquely differentiates between the existence of switchers and substituters.
Norton-Bass model acknowledges the existence of substitution and switchers but does
not differentiate between the two mathematically.
6.1. Modeling Innovation Diffusion by incorporating Time & Price for
Successive Generations of Technologies
In this section, we propose a model that embeds a broader theoretical framework to
account for the interactions between different dimensions of adoption i.e. time and
price factors. Incorporating the dynamics of continuation time of the product in the
market and the price has allowed us to model the diffusion process in two-
dimensional framework. Technological adoptions and the role of other dimensions are
explicitly taken into consideration using the Cobb-Douglas production function. For
PhD Thesis Some Contributions to Multi-Release Problems in Software Reliability and Successive Generations of Technologies
Department of Operational Research, University of Delhi Page 195
many technology products customer interactions through word-of-mouth can reduce
the product-uncertainty and can play an effective role in the acceptance of the new
product. The other marketing-mix variable viz price also play important role in
diffusion of a technology product. A potential individual would become a purchaser
after satisfying himself of the utility of the product vis-à-vis the unit price. The model
proposed in this chapter is for successive generations of product. It decomposes the
total sales into first time purchasers, switchers and substitutes. Substitution and
switching are the two main factors of multi generational modeling. These assumptions
are intuitively consistent with the view that attitudes change towards technology as it
evolves from one generation to the next generation. The proposed model has been
compared with an established model. The result are encouraging and the findings are
consistent with the idea that attitudes of purchasers towards new generations change
from the previous one and it is imperative to identify a trend.
6.1.1. Modeling of the Two-Dimensional adoption process
In the chapter, we propose a mathematical structure which incorporates time and price
factors. For representation of the effect of these factors on the adoption process
simultaneously, we use the Cobb-Douglas production function (Cobb and Douglas
1928), as described in chapter 1 section 1.10.
The mathematical form of the production function is given as:
1t p (6.1)
Where is total production (the monetary value of all goods produced in a year) and
t, p are labor input and capital input respectively. Also is elasticity of labor. This
value is constant and determined by the available technology. In this paper t, p
represent time and price, respectively and is the degree of the impact of time to the
adoption process. By this technique, we are able to consider the effect of several
factors simultaneously and the impact of each factor on adoption process depends on
the value of elasticity parameter .
Chapter5 Two-Dimensional Model for Successive Generations of Technology
Department of Operational Research, University of Delhi Page 196
Figure 6.1: Cobb–Douglas Function Behavior
6.1.2. Bass model in Two-Dimensional framework
For modeling the innovation diffusion, usually an S-shaped function is used as the
basis of the diffusion equations. These diffusion equations generally have two kinds
of parameters: One measures the upper asymptote of the curve, i.e. the eventual level
or penetration of innovation’s diffusion, and the other measures the rate of adoption in
the social system. The other parameters due to marketing efforts are most of the cases
ignored. The two-dimensional innovation diffusion model proposed in this chapter
represents the adoption decision of an adopter that explicitly depends on the value of
the product introduced in the market. Value of the product can be determined by the
time for which the product is in the market and purchase price.
To formulate the functional relationship between the product continuation time in the
market and the price of the product is given by Cobb-Douglas production function.
Bass model for diffusion of innovation assumes that the potential adopter of a new
product can either be an innovator or an imitator depending upon how he/she makes
the purchase decision. The Bass model has been applied to a variety of new product
types introduced during past almost four decades. In spite of apparent limitations of
the model including that of non-inclusion of explanatory variables like price etc., most
of these applications have been successful (Bass, Krishnan and Jain 1994); (Mahajan
and Muller 1996); (Wilson and Norton 1989).
PhD Thesis Some Contributions to Multi-Release Problems in Software Reliability and Successive Generations of Technologies
Department of Operational Research, University of Delhi Page 197
Recently Kapur, Singh, Chanda and Basirzadeh (2010) modified Bass(1969) model
into two dimensional frameworks.
Customers will buy a product according to their varied needs and expenditure
capacity. Thus, price plays a major role in the overall success of the product. A
potential individual would become a purchaser after satisfying himself of the utility of
the product vis-à-vis the unit price. Thus a target customer’s motivation towards a
new product will depend on its price. In their two-dimensional innovation diffusion
model it was assumed that value of the product as the major driver of diffusion and
can be classified into the following two main factors:
The factors which are related to the goodwill of the product, such as the
continuation time of the product in the market.
The factors which are responsive to the consumer buying decision, such as price.
The proposed innovation diffusion model depends on the above two factors. To
incorporate the effect of above two factors in the consumer decision making process,
measure of diffusion (i.e. time, for one-dimension) was extended in two dimensional
frames by means of value of the product in the model. Mathematical equation in Two-
Dimensional framework for the model of adoption due to innovation and imitation
can be expressed as:
1
1
, ,
1.
1
i i
i i
p q t p
t p t p
p q t pi
i
eN N F N
qe
p
(6.2)
Where
,t pN are the cumulative number of adopters in time t and price p.
N is the initial market size.
ip and iq are the innovation and imitation coefficients respectively.
p is the price
represent the effect of product valuation to the innovation diffusion model.
Chapter5 Two-Dimensional Model for Successive Generations of Technology
Department of Operational Research, University of Delhi Page 198
When 1 , adoption take place due to goodwill of the product and price has no
effect on the overall adoption.
When 0 , adoption take place due to the pricing effect of the product and
goodwill has no effect on the overall adoption.
The two dimensional adoption processes are dependent on unit price and time can be
viewed from the figure below:
Figure 2: Two Dimensional Adoption Process.
6.1.3. Proposed Model development
The proposed model considers three market conditions. It discusses the nature of
adoption when there is only a single product in the market and innovation gets
diffused in the population with time along with the effect of the price. In the second
situation, after a finite period of time a new product is launched in the market. The
new product competes with the existing product in the market and the two parallel
innovations exist in the market. Earlier, many models have been developed in the
literature to discuss this situation but in our model we have used a two dimensional
framework where both introduction time of the new innovation and also the price of
the product is taken into account to capture the adoption process. Finally, we study the
market situation when three generation of the product competes together
simultaneously in the two dimensional framework.
PhD Thesis Some Contributions to Multi-Release Problems in Software Reliability and Successive Generations of Technologies
Department of Operational Research, University of Delhi Page 199
6.1.4. Assumptions of proposed model
The model is based on the following assumptions:
,( )j
i t pN is total number of adopters of thi generation when j number of
generations have been launched in the market at time t with price p.
Each generation of the product creates its own market potentialiN . Thus iN is the
eventual number of adopters of the thi generation if the next generation is not
introduced.
Let i be the introduction time of the
thi generation.
Let j be a fraction of those who substitute previous generations with the j
th
generation.
Once adopters adopt a new technology, she/he doesn't revert to earlier generation
technology.
When a new generation of a technology is introduced in the market, there would
be three types of purchasers. Those who are switching from the earlier generation,
(ii) those who adopt the new technology instead of the earlier one (substitutions),
(iii) potential customers who would only adopt the new technology.
Each adopter (New Purchasers) can purchase exactly one product unit and she/he
makes no further purchases of the product generations that they have adopted.
Also, each adopter after having made the first purchase may make a repeat
purchase of exactly one unit in the successive generation or they may skip the next
generation and wait for more advanced one.
A consumer's choice in each time period can be independent of her/his choice in
previous periods and depends on the utility of the new product.
Like the first time purchasers, switching purchasers (i.e. buyers who have also
purchased from previous generations) can also be influenced by the word-of-
mouth effect and as well as the marketing-effort made by the firm. All the two
kinds of the purchasers may be modeled according to the Bass model.
The model for different market situations can be built as follows:
Chapter5 Two-Dimensional Model for Successive Generations of Technology
Department of Operational Research, University of Delhi Page 200
6.1.4.1. The Formulation of Proposed Model
Case 1:
When there is only first generation (base product) in the market, the cumulative
number of adoption can be given by the model proposed by (Kapur, Singh, Chanda
and Basirzadeh 2010):
0
1
1 , 1 1 ,( ) ( )t p t pN N F (6.3)
Where 0 0t t and
(1 )1 1 0
0 (1 )1 1 0
( ).
1 ,( ).1
1
1( )
1 ( ).
p q t p
t pp q t p
eF
qe
p
(6.4)
In this case, note that there is no effect of other generation on diffusion of product.
Case 2: When two generations are in the market
Bass (1969) in his model framework assumed a constant potential market for
diffusion through the social network but in successive generation of technology
scenario is different. After introducing second generation in the market, there would
be a sizable portion of this population who are yet to purchase. So, when they have
the option to choose, they will go with the product having maximum utility. In this
situation, satisfied adopters can influence others, with positive word-of-mouth. Due to
the influence of promotional effort and word-of-mouth some potential buyers of
earlier generation technology who otherwise would adopt the older generation may
decide to purchase the new generation instead and some of adopters of first generation
upgrade their product and eventually become the potential repeat purchasers of the
later generation. Let fraction of the adopters of first generation who switch to the
second generation technology be 21,2 ,( )t pSw and
21,2 ,( )t pSub
be the fraction of
adopters of first generation who substituted their idea with new generation. Hence, the
number of adopters of first generation after second generation decreases and the
PhD Thesis Some Contributions to Multi-Release Problems in Software Reliability and Successive Generations of Technologies
Department of Operational Research, University of Delhi Page 201
population of second generation increases. Thus in two generation market scenario,
cumulative number of adopters for two generations may be given as:
1 2
2
1 , 1 1 , 1,2 ,( ) ( ) ( )t p t p t pN N F Sub (6.5)
2 2 2
2
2 , 2 2 , 1,2 , 1,2 ,( ) ( ) ( ) ( )t p t p t p t pN N F Sub Sw
Where j jt t and ,( ) , 1,2, 1..2ji t pF i j is the cumulative adoption function
with model parameters ip and
iq , respectively.
(1 )
(1 )
( ).
,( ).
1( )
1 ( ).
i i j
ji i j
p q t p
i t pp q t pi
i
eF
qe
p
(6.6)
In the Eq. (6.5), 21,2 ,( )t pSub and
21,2 ,( )t pSw are the fractions of potential and actual
adopters of an earlier generation (first in this case) who buy the second generation.
The mathematical form can be given as follows:
2
21 1
2
1,2 ,
2 1 1 , 1 3,
0( )
. . ( ) ( )t p
t p P
tSub
N F F t
(6.7)
2
221
2
1,2 ,
1 1 2 , 3,
0( )
. ( ). ( )t p
t pP
tSw
N F F t
(6.8)
Where2
1 2 1 .
Case 3: When three generations of product are in the market place.
When a firm introduces its third generation product without withdrawing any of the
earlier generations, potential adopter of both the first and second generation come
under the influence of innovation and imitation effects of the latest one. As a result,
31,3 ,( )t pSub , 32,3 ,( )t pSub , are groups of potential adopters who substitute first and
Chapter5 Two-Dimensional Model for Successive Generations of Technology
Department of Operational Research, University of Delhi Page 202
second generation with the third one based on the substitution effect caused by
introduction of third generation in the market. This group otherwise would have
adopted the first and second generation technology. Similarly some of customers of
first generation substitute to second generation technology as 21,2 ,( )t pSub (as
discussed in earlier section). Finally, let 21,2 ,( )t pSw and
32,3 ,( )t pSw be the group of
people who adopted first and second generation and make decision for switching to
second and third generation, respectively. Thus in three generation market scenario,
cumulative number of adoption can be given as:
1 2 3
3
1 , 1 1 , 1,2 , 1,3 ,( ) ( ) ( ) ( )t p t p t p t pN N F Sub Sub
2 3 2 2
3
2 , 2 2 , 2,3 , 1,2 , 1,2 ,( ) ( ) ( ) ( ) ( )t p t p t p t p t pN N F Sub Sub Sw (6.9)
3 3 3 3
3
3 , 3 3 , 1,3 , 2,3 , 2,3 ,( ) ( ) ( ) ( ) ( )t p t p t p t p t pN N F Sub Sub Sw
Where j jt t and ,( ) , 1..3, j 1..3ji t pF i is the cumulative adoption function
with model parameters ip and
iq , respectively.
(1 )
(1 )
( ).
,( ).
1( )
1 ( ).
i i j
ji i j
p q t p
i t pp q t pi
i
eF
qe
p
In the above equations,21,2 ,( )t pSub ,
31,3 ,( )t pSub and 32,3 ,( )t pSub are fractions of
the potential and actual adopters of an earlier generation (first and second in this case)
who buy the second, third generation. The mathematical form may be given as
follows:
3
31 1
3
1,3 ,
3 1 1 , 1 3 4,
0( )
. . ( ) ( )t p
t p P
tSub
N F F t
(6.10)
3
32 2
3
2,3 ,
3 2 2 , 2 3 4,
0( )
. . ( ) ( )t p
t p P
tSub
N F F t
(6.11)
PhD Thesis Some Contributions to Multi-Release Problems in Software Reliability and Successive Generations of Technologies
Department of Operational Research, University of Delhi Page 203
Where .j
i j i
Adoptions of generation i may also come from adopters of earlier generations who
switch to it (i.e., adopters of (i - 1) th
generation). The mathematical form may be
given by:
3
332
3
2,3 ,
2 2 3 , 3 4,
0( )
. ( ). ( )t p
t pP
tSw
N F F t
(6.12)
21,2 ,( )t pSub and 21,2 ,( )t pSw have been defined in previous case.
6.1.5. DATA
The proposed model has been validated on data collected from Dynamic Random
Access Memory (DRAM) computer chips, This company selects data of world-wide
dynamic random access memory (DRAM) shipments of six generations taken for a
period 1974 to 1992(Victor and Ausubel 2001). Estimation done on first three
generation as data set1( DS-1) and generations third and fourth as data set2(DS-2).
DS1 is related to 4K, 16K, 64K and Ds2 related to 64K and 256K chip generation of
DRAM, respectively.
6.1.5.1. Empirical analysis
The parameters of proposed model in the above sets of equation were estimated using
simultaneously nonlinear least squares (NLLS). Srinivasan and Mason (1986) by
software package SAS (SAS 2004). Estimated value of diffusion parameters of DS1
and DS2 are given in Table 6.1.
As expected, Table 6.1 shows all the estimated coefficients are highly significant and
asymptotic standard errors are very low and also α is highly significant for two
datasets.
Chapter5 Two-Dimensional Model for Successive Generations of Technology
Department of Operational Research, University of Delhi Page 204
Table 6.1: Parameter estimates of the two-dimensional proposed model.
Technology Generat
ions Parameters
jN jp jq
j
DRAM Company In
Three Generation(DS-1)
4k 376.36*
(20.41)
0.000026
(8.102E-6)
0.028817
(0.00369) -----
0.476363
(0.0197)
16k 1230.98*
(23.70)
6.526E-7
(5.122E-7)
0.04869
(0.00536)
0.1593
(0.0457)
0.476363
(0.0197)
64k 2639.96*
(23.89)
1.099E-8
(0)
0.064175
(0.00911)
0.0001
(0)
0.476363
(0.0197)
DRAM Company
In
Two Generation(DS-2)
64k 2658.776
(18.329)
1.01E-6
(0)
0.1340
(0.0221) -----
0.6273
(0.0224)
256K 4627.03
(24.03)
0.000023
(9.625E-6)
0.2051
(0.0178)
0.00001
(0)
0.6273
(0.0224)
Asymptotic Standard Errors are in parenthesis; (*)in millions (j = 1,2,3 )
In addition, Table 6.2 shows the values of SSE (Sum of Squares Error), MSE and
Adj-R2
of both the models that were applied on two sets viz; DS-1 and DS-2. To
establish the predictive validity of our model, we compared our model with the one
dimensional model. From Table 6.2 and Figures. 6.2, 6.3 and 6.4, it is clear that at any
point of time the proposed model will give more accurate and better fit to the data in
comparison to same situation in one-dimension model. It is also evident from Table
6.2 that the mean square error (MSE), Sum of Squares Error (SSE) and Adj-R2 of
two-dimensional model of all generations related to DS-1 and DS-2 (except second
generation in DS-1) is much better than one dimensional model.
The three dimensional curves of non cumulative and cumulative adopters on axis
time, price and adopters for expected number of cumulative and non-cumulative
adopters for 4 K, 16 K and 64 K in DRAM datasets are plotted in Figures 6.5, 6.6,
6.7, 6.8, 6.9 and 6.10, respectively.
The proposed model gives a clear view about the decomposition of total sales into
new adoptions and it also gives clear idea about the substitution and switching
PhD Thesis Some Contributions to Multi-Release Problems in Software Reliability and Successive Generations of Technologies
Department of Operational Research, University of Delhi Page 205
behavior of purchasers in two dimensional framework. With this model we tried to
give a proper mathematical interpretation of the following:
1. Cumulative number of adoptions,
2. Substitution and switching behavior of adopters when technology comes in
multiple generations,
3. Influence of introduction of latest technology to the sales figure of earlier
generations,
4. Combined effect of time and price on the cumulative number of adopters for
successive generations of technologies.
Table 6.2: Comparison criterion of one-dimension and proposed model
Technology Generations Model
DRAM Company
In
Three Generation
One-Dimension 2-D Proposed model
SSE MSE Adj-R2 SSE MSE Adj-R
2
4k 94.633 5.4076 0.9995 47.0072 2.7383 0.9998
16k 5072.0 317.0 0.999 8423.2 537.6 0.9983
64k 63720.2 4720.0 0.9968 35327.6 2493.7 0.9983
DRAM Company
In
Two Generation
64k 72578 4147.3 0.997 49013.4 2800.8 0.9979
256k 56383.9 3888.5 0.9991 34707.4 2393.6 0.9994
Chapter5 Two-Dimensional Model for Successive Generations of Technology
Department of Operational Research, University of Delhi Page 206
Figure 6.2: simultaneous estimation of generation 4K, 16K and 64K
Figure 6.3: Simultaneous estimation of generations 64K and 256K.
0.00
500.00
1000.00
1500.00
2000.00
2500.00
3000.00
Cu
mla
tive
Nu
mb
er o
f A
do
up
ter
(in
mill
ion
)
Time
Cum Num of adopters for 4K
Exp Num of adopter for 4K
Cum Num of adopters for 16K
Exp Num of adopter for 16K
Cum Num of adopters for 64K
Exp Num of adopter for 64 K
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Cu
mu
lati
ve N
um
ber
of
Ad
ou
pte
r (i
n m
illio
n)
Time
Cum Num of adopters for 64 K
Exp Num of adopter for 64 K
Cum Num of adopters for 256 K
Exp Num of adopter for 256 K
PhD Thesis Some Contributions to Multi-Release Problems in Software Reliability and Successive Generations of Technologies
Department of Operational Research, University of Delhi Page 207
Figure 6.4: Simultaneous estimation of generation 64K and 256K
Figure 6.5: Estimated adopters of for non-cumulative dataset of 4K DRAM Chipset
0
200
400
600
800
1000
1200
Act
ual
Nu
mb
er o
f A
do
up
ter
(in
mill
ion
)
Time
Actual Num of adopters for 64 K
Exp Actual Num of adopter for 64 K
Actual Num of adopters for 256 K
Exp Actual Num of adopter for 256 K
1.00
4.678.33
12.00
Time 389
2293
4197
6101
price0.45
24.74
49.02
73.30
sale
Chapter5 Two-Dimensional Model for Successive Generations of Technology
Department of Operational Research, University of Delhi Page 208
Figure 6.6: Output of the proposed model for cumulative data of 4K, DRAM.
Figure 6.7: Estimated adopters of for non-cumulative dataset of 16K DRAM .
6.1.6. Managerial Implication:
Cautious product planning is very essential, especially when product is launched in
the market in successive generations. Despite potential advantages of new
1.00
4.67
8.33
12.00
Time6101
8981
11861
14741
Price5
109
212
316
Sale
1.00
4.67
8.33
12.00
Time0
1119
2238
3357
Price0
93
187
280
Sale
PhD Thesis Some Contributions to Multi-Release Problems in Software Reliability and Successive Generations of Technologies
Department of Operational Research, University of Delhi Page 209
technologies, their long-term viability is often unclear. Hence, before adopting an
innovation, decision makers need to answer following questions:
1. What is the target market of the product and its size?
2. How the innovation spreads through its target population?
3. How much is the effect of substitution and switchers on the sales pattern?
4. What and how much is the effect of marketing-mix variables such as price,
product etc on the diffusion of innovations within generations?
Also from managerial perspective, it is crucial to understand what product features to
offer, at what price, so as to help firms maximize their profits and market share, while
ensuring that the firm's customers are satisfied. Due to intense competition in the
market, it is important for a firm to understand and analyze the rate of adoption of
new technology that enhances profitability.
When a new technology is introduced in the market, it not only attracts first time
purchasers but also previous buyers who would upgrade their products. This factor
adds more complexity to the modeling. Innovator, Imitator, Substitution and Switcher
are the four major factors which influence the adoption process. Innovation diffusion
model can be of great help to the managers in understanding such decision making
process. The two dimensional model discussed in this paper helps the marketing
manager to figure out the number of innovators, imitators, substitution and switchers
separately, under the effect of time and price. In earlier research papers only one
aspect of adoption was considered i.e. time, but with the help of Cobb-Douglas
production function, the managers can confidently predict the adoption behavior of
the product that comes in generations, incorporating both time and price (at which
consumers are ready to adopt the product).
Chapter5 Two-Dimensional Model for Successive Generations of Technology
Department of Operational Research, University of Delhi Page 210
Figure 6.8: Output of the proposed model for cumulative dataset of 16K DRAM.
Figure 6.9: Estimated adopters of for non-cumulative dataset of 64 K DRAM.
1.00
4.67
8.33
12.00
Time0
2156
4311
6467
Price0
414
829
1243
Sale
1
7
13
19
Time0
924
1848
2771
Price0
222
444
667
Sale
PhD Thesis Some Contributions to Multi-Release Problems in Software Reliability and Successive Generations of Technologies
Department of Operational Research, University of Delhi Page 211
Figure 6.10: Output of the proposed model for cumulative dataset of 64 K DRAM.
17
1319
Time 0
2065
4130
6195
Price0
879
1758
2638
Sale
Chapter5 Two-Dimensional Model for Successive Generations of Technology
Department of Operational Research, University of Delhi Page 212