## Wednesday, November 27, 2013

### 09. Obsolescence Factor: Definition and Calculation P- 07. Informetrics & Scientometrics

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# 09. Obsolescence factor: Definition and Calculation

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## Objectives

To know the meaning, definition, and concept of obsolescence factors. To identify the methodology and steps to calculate obsolescence factors.

## Summary

Theoretical framework for obsolesce factor, utility factor and half-life is explained. An attempt has been made to compute the obsolescence factors , utility factor, half-life and also it has been shon how to fit an exponential distribution function for the synchronous citation data. The analysis of citations received by two chemistry journals viz. Indian Journal of Chemistry and Asian journal of Chemistry, is discussed. It has been observed that these two journals have received 30,142 references for 3,027 articles at the rate of 9.95 references per article for 5 year data. The finding of the study are: The value Annual Ageing Factor (AAF) = "a” as calculated from the graph is found to be    A A F =0.948687The value of half life as observed from the graph is 15 years and calculated value is = 13.15865 years which is almost near to the observed value. The value of Utility factor (U) was found to be U = 19.48831 andthe value of the mean (m) is = 18.98392 which confirms the exponential nature of the distribution and also justify the correctness of the average value of ‘a’. Citation frequency distribution in chemical science journals follows exponential patter. The Corrected Obsolescence Factor (a) was found to be = 0.504389. Further it has been concluded that the obsolescence studies are helpful in discarding older materials in libraries; decisions regarding back volumes of periodicals; predicting the future use of literature; serving as a tool to measure the citable or usable documents in the field of chemical science.

## 1. Introduction

‘Obsolete’ generally means out of date or no longer in use. The process of becoming obsolete is known as obsolescence. It is also often referred to as ‘phenomenon of replacement.’ The term obsolescence was used for the first time by Gross and Gross in 1927. They analyzed the references in the 1926 volume of theJournal of Chemical Literature and observed that the number of references fell to one-half in fifteen years. Obsolescence is thus a characteristic of scientific and technical literature.  Thus, obsolescence means decreasing value of functional and physical assets or value of a product or facility from technological changes rather than deterioration. Every newborn grows old and eventually dies. This is universally accepted as truth. So, perplexity sets in when sometimes it is reported that "life expectancies may not always decrease as organisms grow older". It was reported in Science and quoted in the Times of India dated 30 th Oct. 1992 that the results of certain experiments on fruit flies indicated that once a fly was past a certain age, its life expectancy may increase with age. Is this consistent with the universal truth stated in the first line above? Such seeming anomalies may be reconciled only through a detailed study of the phenomenon of aging.
The concept obsolescence is of obvious interest to information theoreticians who concern themselves with the development of career and librarians who administer growing collection in finite spaces. Such librarians look to research on obsolescence to help them decide which item to keep and which to store or discard in order to make room for new acquisitions. Increased periodical costs have made imperative to cancel some subscriptions and librarians have turned once again to obsolescence research in hope that the concept can be employed to forecast   future as well as to describe the current or past use.

## 2. Meaning and Definition

Obsolescence means the decreasing value of functional and physical assets from technological change rather than deterioration. It is characterized by terminology and metaphors that link inevitable organic (aging or decay) or scientific phenomenon (half life) to the phenomenon of changing use or published literature over a period of time. In other words, obsolescence is decline in the usage of literature over a period of time. When the use of document ceases, it is termed as obsolete.

## Types of Obsolescence

Actually obsolescence implies a relation between time and use but the effect of time are revealed in different ways. The impact of time on use of document can be studied in two ways: namely synchronous studies and dia-chrounus studies (Line, 1970). Synchronous studies are made on records of uses or references at one point in time and compress the uses against the age of distribution of the materials used or cited. With respect to obsolescence studies majority of the studies have used citations, records of consultations or loans.
In synchronous study the citations are counted back ward i.e. references in an journal articles is examined to find out how many references have been cited for that particular year. Like, year wise references are analysed. Half life annual aging factor and utility factors are studied with this type of study. The half life of journal article is the time during which half of all the currently active literature was used. The median of an age distribution in other words is half life.

In diachronous study the successive observations at different time are made by counting the citations in forward direction i.e. counting the citations that an article or journal published in 2005 is going to get in year 2006, 2007…etc. This type of study is helps in determining the rate at which the citations decline in future. Many  studies have been undertaken in this field. Some of the notable studies in the field are Gros and Gross (1927),  Burton and Kessler (1960), Kent and Others (1979), Jain (1966), Brookes (1970), Line (1970, 1974)Ravichandra Rao (1971), Sangam (1989), Moed (1998), Gupta (1997,1998), etc.

While studying and reviewing the studies in the field of obsolescence, it is observed that very few studies have been done. Though new indicators and methods are being developed and applied to study the obsolescence, the case studies are found to be very less. In the present study an attempt has been made to identify the obsolescence factors and pattern in the field of chemical science.

## Theoretical framework for the Obsolecence factors

Burton and Kebler (1960) were the first to use the term ‘half-life’ as applied to documents in 1960. It is defined as ‘the time during which one-half of all the currently active literature published.’ It is the period of time needed to account for one-half all the citations received by a group of publications. The concept of half-life is always discussed in the context of diachronous studies. More precisely, Line and Sandison (1974) refer to diachronous studies in those that follow the use of particular items through successive observations at different points in time, whereas synchronous studies are concerned with the plotting the age distribution of material used at one point of time. However, there is no reason to suppose that the half-life for some subject is the same as the median citation age in that subject. Half-life in the context of synchronous data is referred to as median age of the citations / references. The use of literature may decline much faster with data of ephemeral relevance, if it is in the form of reports, thesis, advance communication or pre-print and in the context of advancing technology. However, the use of literature may decline slowly when it is descriptive (e.g., taxonomic botany) and critical (e.g., literary criticism).

Brookes (1970) in one of his articles argued that if growth rates of literature and contributors are equal then the obsolescence rate remains constant. In this sense growth and obsolescence are related. Ravichandra Rao and Meera (1991) studied the relationship between growth and obsolescence of literature, particularly in mathematics. Gupta (1999) studied the relationship between growth rates and obsolescence rates and half-life of theoretical population genetics literature. He observed that the lognormal distribution fits very well to the age distribution of citations over a period of time.

In the analysis of obsolescence, Brookes (1970) argued that the geometric distribution expresses the idea that when a reference is made to particular periodical of age t years (1-a) at-1 . ‘a (< 1)’ is a parameter – the annual aging factor; it is assumed to be constant over all values of t. Let  U  =  1 + a2 + a+ a4 + …. + at + ….   i.e., U  = 1/(1-a).  Similarly if U(t)  =  at + at+1 +  at+1  at+2 +  ……   =  at (U(0), then   U(t)/U(0)   =  at. Using this relation, by graphical method, we can compute half-life as well as ‘a’. If we assume that the literature is growing exponentially at an annual rate of g, we then have R(T)  = R(0)egT, where R(T) is the number of references made to the literature during the year T.  We also have
U(0)  =  R(0)/(1-a0)  and U(T)   =   R(T)/(1-aT
Where a0 and   aT are the annual aging factors corresponding to the years 0 and T respectively. Under the assumption that utility remains constant (U(0) = U(T)) , we have R(0)/(1-a0)  =  R(T) )/(1-aT). By substituting the value of R(T), we get a relationship value between the growth and the obsolescence:
egT  =  (1-aT)/(1- a0)
However, Egghe and Ravichandra Rao (1992) showed that the obsolescence factors (aging factors) ‘a’ is not a constant, but merely a function of time. They have also shown that the function ‘a’ has a minimum which is obtained at a time t later than the time at which the maximum of the number of citations is reached.
Egghe (1993) developed a model to study the influence of growth on obsolescence. He obtained different results for the synchronous and diachronus studies. He argued that for an increase of growth implies an increase of obsolescence for the synchronous case and for the diachronous case, it is quite the opposite. In order to derive the relationship, he also assumed the exponential models for growth as well as for obsolescence. In another paper, for the diachronous aging distribution and based on a decreasing exponential model, Egghe (2000) derived first citation distribution. In his study he assumed the distribution of the total number of citations received conforms to a classical Lotka’s function (16). The first citation distribution is given by
f (t1)  = g (1- a t1)a-1
where g is the fraction of papers that eventually get cited; t1 is the time of the citation, ‘a’ is the aging rate and a is Lotka’s exponent.  Egghe and Ravichandra Rao (2002) in their study in 2002 observed that the cumulative distribution of the age of the most recent references is the dual variant of the first citation distribution. This model is different from the first citation distribution. In another study, Egghe and Rao (2001) have shown the general relation between the first citation distribution and the general citation age distribution; if Lotka’s exponent a = 2, both these distributions are the same. In the same study, they have argued that the distribution of nth citation is similar to that of the first citation distribution. Egghe, Rao and Rousseau (1995) studied the influence of production on utilization function. Assuming an increasing exponential function for production and a decreasing one for aging, these authors have shown that in the synchronous case, the greater the increase in production, the greater the obsolescence; however, for the diachronous case it is quite the opposite. This proof is different from the earlier one derived by Egghe.
The study of obsolescence, in practical terms, is related to changes in the use of documents over time. Line and Sandison (1974), Jain (1966a, 1966b), Kent and others (1979) in their Pittsburgh study, and FussIer and Simon (1969) attempt to prove the hypothesis that use declines over time. Line and Sandison, however, argued that this hypothesis is to be tested first and should not be made a starting assumption. Brookes (1970) claims that the decline of use over time conforms closely to a negative exponential distribution. He hypothesizes that the number of references to an issue is a function of its age~, and he assumes the function to be a geometric distribution:
p(t) = (1-a)at            0 ≤ t ≤     and  0 ≤ a ≤ 1.
p(t) is the probability mass function of reference to an issue of the journal of age tyears; if references are made to a given periodical during its first year of life, then aR references can be expected during its second year, a2R references can be expected during its third year, and so on. Under the assumption that a is constant for all values of t and for a < 1, the series at converges to the sum  as t . Therefore, the total number of refe­rences that will be made to it during its infinite life time is
U(o)  =
If the periodical is years old, then the number of further references to it can be computed by:

U(o) is called the total utility of a periodical which has just been published. Brookes (1970) suggests a graphical method for computing a. The function  is called the utility factor of the periodicals. Under the assumption that the literature is growing exponentially at an annual rate of growth g, we have:
R(T) = Regt
where R(T) is the number of articles at time T and R is the number of articles at time T=OBrookes (1970) and also Line (1970) have discussed the computational aspects of half-life, utility factor, etc. in their articles.  Below a worked out example has been given in this regard.

## An Worked out Example

We considered synchronous approach to collect the data for obsolescence analysis. The citation appended to the articles published in the following two journals
1. Indian Journal of Experimental Biology (CSIR), New Delhi
2. Asian Journal of Chemistry” New Delhi.
were  considered as source data. We have collected the dta for five years (2001-2005). For computation of obsolescence rate, the graphical method as explained by Brookes may be  used. The data is given in Table 2. Table 1 gives the summary of the data.
Below, an attempt has been made to fit the exponential distribution, to compute the ageing factor, utility factor and half-life.
Table-1: Average Citation Rate of Journals

 Year Asians Journal  of Chemistry Indian Journal of Exp.Biology Articles References Citation ate Articles References Citation Rate 2001 276 1409 5.11 378 4735 12.53 2002 271 1583 5.66 314 4494 14.31 2003 302 1783 5.90 278 3772 13.57 2004 295 1878 6.37 297 3009 10.13 2005 351 2470 7.04 265 5059 19.09 Total 1495 9073 6.02 1534 22069 13.926

Some Observation:   Out of 30142 references 38% are received for the publications of the last 10 years; 69.57% for the last two decade; 93 % for the last four decade, 99.10% citations are received for the last 6 decades and only 0.9% are for the other decades which are 269 in number. The half of the citations has been produced up to the age of 13 years (15180). Maximum number of references has been observed in the year 2000 (1562 i.e. 5.08%) followed by 1998 (1530), 1996 (1510) and 1997 (1501).This shows that scholars are using current information for their research purposes. More than 117 articles are from the age more than 71 to 105 years.

Table-2: Citation Frequency Distribution of Journals

 Year Age (x) Citations Cumulative Citations Tail % of Citations % Cumulative Citations 2005 0 15 15 30142 0.049764 0.049764 2004 1 191 206 30127 0.633667 0.683432 2003 2 410 616 29936 1.360228 2.04366 2002 3 761 1377 29526 2.524716 4.568376 2001 4 1221 2598 28765 4.050826 8.619202 2000 5 1562 4160 27544 5.182138 13.80134 1999 6 1497 5657 25982 4.966492 18.76783 1998 7 1530 7187 24485 5.075974 23.84381 1997 8 1501 8688 22955 4.979762 28.82357 1996 9 1510 10198 21454 5.009621 33.83319 1995 10 1276 11474 19944 4.233296 38.06649 1994 11 1306 12780 18668 4.332825 42.39931 1993 12 1278 14058 17362 4.239931 46.63924 1992 13 1122 15180 16084 3.722381 50.36162 1991 14 1070 16250 14962 3.549864 53.91149 1990 15 971 17221 13892 3.221419 57.1329 1989 16 882 18103 12921 2.92615 60.05905 1988 17 757 18860 12039 2.511446 62.5705 1987 18 734 19594 11282 2.43514 65.00564 1986 19 716 20310 10548 2.375423 67.38106 1985 20 662 20972 9832 2.196271 69.57733 1984 21 723 21695 9170 2.398646 71.97598 1983 22 595 22290 8447 1.97399 73.94997 1982 23 553 22843 7852 1.834649 75.78462 1981 24 529 23372 7299 1.755026 77.53965 1980 25 475 23847 6770 1.575874 79.11552 1979 26 479 24326 6295 1.589145 80.70466 1978 27 444 24770 5816 1.473028 82.17769 1977 28 396 25166 5372 1.313781 83.49147 1976 29 333 25499 4976 1.104771 84.59624 1975 30 359 25858 4643 1.191029 85.78727 1974 31 386 26244 4284 1.280605 87.06788 1973 32 311 26555 3898 1.031783 88.09966 1972 33 272 26827 3587 0.902395 89.00206 1971 34 254 27081 3315 0.842678 89.84473 1970 35 284 27365 3061 0.942207 90.78694 1969 36 239 27604 2777 0.792914 91.57986 1968 37 230 27834 2538 0.763055 92.34291 1967 38 178 28012 2308 0.590538 92.93345 1966 39 189 28201 2130 0.627032 93.56048 1965 40 143 28344 1941 0.474421 94.0349 1964 41 135 28479 1798 0.44788 94.48278 1963 42 100 28579 1663 0.331763 94.81454 1962 43 127 28706 1563 0.421339 95.23588 1961 44 159 28865 1436 0.527503 95.76339 1960 45 91 28956 1277 0.301904 96.06529 1959 46 104 29060 1186 0.345034 96.41032 1958 47 101 29161 1082 0.335081 96.74541 1957 48 100 29261 981 0.331763 97.07717 1956 49 80 29341 881 0.26541 97.34258 1955 50 64 29405 801 0.212328 97.55491 1954 51 66 29471 737 0.218964 97.77387 1953 52 72 29543 671 0.238869 98.01274 1952 53 65 29608 599 0.215646 98.22839 1951 54 53 29661 534 0.175834 98.40422 1950 55 44 29705 481 0.145976 98.5502 1949 56 49 29754 437 0.162564 98.71276 1948 57 47 29801 388 0.155929 98.86869 1947 58 27 29828 341 0.089576 98.95826 1946 59 27 29855 314 0.089576 99.04784 1945 60 18 29873 287 0.059717 99.10756 1944 61 20 29893 269 0.066353 99.17391 1943 62 12 29905 249 0.039812 99.21372 1942 63 22 29927 237 0.072988 99.28671 1941 64 14 29941 215 0.046447 99.33316 1940 65 20 29961 201 0.066353 99.39951 1939 66 12 29973 181 0.039812 99.43932 1938 67 19 29992 169 0.063035 99.50236 1937 68 16 30008 150 0.053082 99.55544 1936 69 7 30015 134 0.023223 99.57866 1935 70 10 30025 127 0.033176 99.61184 71 117 30142 117 0.388163 100 Total 30142 100

Figure No. 2: Cumulative Citation frequency Distribution

## Test of Exponentially of Citation Distribution

The data of column 5 of table-3 are plotted as frequency polygon 'AA' in figure 3. The curve AA looks like a negative exponential distribution. The data indicates a roughly declining trend in the frequency citations as against the cited ages. The points are concentrated at one end and the curve tapers off gradually to years at the other end while an initial build-up occurs from the first entry (t = 0). With the help of table 3 the values of  and σ are calculated; Mean =17.06234; Variance =159.2974; SD =12.62131; also, in order to test the exponentially of the distribution, another test i.e. Kolmogorov-Smirnov Test (K-S Test), is applied. The observed value of cumulative citation frequencies are calculated and presented in column 6 of Table-3. The calculation of the estimated values: -

F(x)=l-eϴx  ...................(1)
Where x = 0,1,2,3,4,5,.......
and

The estimated values using (10 are presented in column 7 (represented as E(x) in Table-3. To test the exponentiality of the distribution, K-S test is used. According to this test, the maximum deviation in observed and estimated values, 'D' is calculated as follows: D = |F(x)-En(x)|. At the 0.01 level of significance, the K-S statistics is equal to 1.63/ n1/2. If 'D' is greater than K-S statistics; than the distribution does not fit the theoretical distribution at this level of significance. In this case n =71, hence K-S statistics for the 0.01 level should be 1.63/701/2 =0.1948 and the value of 'D' should not exceed this. The examination of the data of column 6, 7 and 8 of table-3 reveals that 'D' value does not exceed the 0.1948 limits, Theeta value 0.058609 and  D value is 0.193445 and hence it confirms statistically that the distribution of the data follows negative exponential distribution.
Table-3: Citation Frequency Distribution of Journals and Parameter values

 Year Age Citations % Cumulative F(x) E(x) D x f(x) xf(x) x2f(x) Observed 2005 0 15 0 0 0.000498 0 0.000498 2004 1 191 191 191 0.006337 0.056924 0.050588 2003 2 410 820 1640 0.013602 0.110608 0.097006 2002 3 761 2283 6849 0.025247 0.161236 0.135989 2001 4 1221 4884 19536 0.040508 0.208982 0.168474 2000 5 1562 7810 39050 0.051821 0.25401 0.202189 1999 6 1497 8982 53892 0.049665 0.296475 0.24681 1998 7 1530 10710 74970 0.05076 0.336522 0.285763 1997 8 1501 12008 96064 0.049798 0.37429 0.324493 1996 9 1510 13590 122310 0.050096 0.409908 0.359812 1995 10 1276 12760 127600 0.042333 0.443499 0.401166 1994 11 1306 14366 158026 0.043328 0.475177 0.431849 1993 12 1278 15336 184032 0.042399 0.505052 0.462653 1992 13 1122 14586 189618 0.037224 0.533227 0.496003 1991 14 1070 14980 209720 0.035499 0.559798 0.524299 1990 15 971 14565 218475 0.032214 0.584856 0.552642 1989 16 882 14112 225792 0.029261 0.608487 0.579226 1988 17 757 12869 218773 0.025114 0.630774 0.60566 1987 18 734 13212 237816 0.024351 0.651792 0.627441 1986 19 716 13604 258476 0.023754 0.671613 0.647859 1985 20 662 13240 264800 0.021963 0.690307 0.668344 1984 21 723 15183 318843 0.023986 0.707936 0.683949 1983 22 595 13090 287980 0.01974 0.724561 0.704821 1982 23 553 12719 292537 0.018346 0.74024 0.721894 1981 24 529 12696 304704 0.01755 0.755027 0.737477 1980 25 475 11875 296875 0.015759 0.768972 0.753213 1979 26 479 12454 323804 0.015891 0.782123 0.766231 1978 27 444 11988 323676 0.01473 0.794525 0.779795 1977 28 396 11088 310464 0.013138 0.806222 0.793084 1976 29 333 9657 280053 0.011048 0.817252 0.806205 1975 30 359 10770 323100 0.01191 0.827655 0.815745 1974 31 386 11966 370946 0.012806 0.837466 0.82466 1973 32 311 9952 318464 0.010318 0.846718 0.8364 1972 33 272 8976 296208 0.009024 0.855443 0.846419 1971 34 254 8636 293624 0.008427 0.863672 0.855245 1970 35 284 9940 347900 0.009422 0.871433 0.86201 1969 36 239 8604 309744 0.007929 0.878751 0.870822 1968 37 230 8510 314870 0.007631 0.885653 0.878023 1967 38 178 6764 257032 0.005905 0.892162 0.886257 1966 39 189 7371 287469 0.00627 0.898301 0.89203 1965 40 143 5720 228800 0.004744 0.90409 0.899346 1964 41 135 5535 226935 0.004479 0.90955 0.905071 1963 42 100 4200 176400 0.003318 0.914698 0.911381 1962 43 127 5461 234823 0.004213 0.919554 0.915341 1961 44 159 6996 307824 0.005275 0.924133 0.918858 1960 45 91 4095 184275 0.003019 0.928452 0.925433 1959 46 104 4784 220064 0.00345 0.932525 0.929075 1958 47 101 4747 223109 0.003351 0.936366 0.933015 1957 48 100 4800 230400 0.003318 0.939988 0.936671 1956 49 80 3920 192080 0.002654 0.943404 0.94075 1955 50 64 3200 160000 0.002123 0.946626 0.944503 1954 51 66 3366 171666 0.00219 0.949664 0.947475 1953 52 72 3744 194688 0.002389 0.95253 0.950141 1952 53 65 3445 182585 0.002156 0.955232 0.953075 1951 54 53 2862 154548 0.001758 0.95778 0.956022 1950 55 44 2420 133100 0.00146 0.960183 0.958724 1949 56 49 2744 153664 0.001626 0.96245 0.960824 1948 57 47 2679 152703 0.001559 0.964588 0.963028 1947 58 27 1566 90828 0.000896 0.966603 0.965708 1946 59 27 1593 93987 0.000896 0.968504 0.967609 1945 60 18 1080 64800 0.000597 0.970297 0.9697 1944 61 20 1220 74420 0.000664 0.971988 0.971325 1943 62 12 744 46128 0.000398 0.973583 0.973185 1942 63 22 1386 87318 0.00073 0.975086 0.974357 1941 64 14 896 57344 0.000464 0.976505 0.97604 1940 65 20 1300 84500 0.000664 0.977842 0.977179 1939 66 12 792 52272 0.000398 0.979103 0.978705 1938 67 19 1273 85291 0.00063 0.980293 0.979663 1937 68 16 1088 73984 0.000531 0.981415 0.980884 1936 69 7 483 33327 0.000232 0.982473 0.98224 1935 70 10 700 49000 0.000332 0.98347 0.983139 71 117 8307 589797 0.003882 0.984411 0.98053 Total 30142 514293 13576583 0.983139

## i) Annual Ageing Factor (=AAF)

Based on the negative exponential function over time or obsolescence annual aging factor is the ratio of percentage of non-used (or used) documents in successive years. In case of citations this may be measured in proportion to number of citations received in library context.
The AAF = "a" has been calculated graphically, following the procedure suggested by Brookes.
The data of column 5 of table-3 are plotted on semi-log paper and are shown in figure 3.
1. On axis 'X' (linear scale), the values of citation ages, that is, of 't'
2. in years are taken, starting with the year 2005 (t = 0), as the base year, the values were taken from t = 0 to t = 71;
3. On the 'Y' axis, on to left hand side, the values of cumulative citations from "Tail" that is, 30142 for 2005, are taken on log scale,
4. The resultant line by joining maximum point on a straight time, 'XY' is plotted;
5. For convenience sake, a parallel line to 'XY' is drawn from the point 'T' (t) =10,000; on this line T(t) for t =1 gives the value of  T(l) = a1 = a the Annual Aging Factor;
6. The value of 'a' from this line, directly reads from the graph in figure ' 28' is equal to '0.94' approximately;
7. vi)  The scale on the left hand is graduated to find out different values of 'a' directly from graph, from 1.0 to 0.1;
8. The time 'OA' reads the values of t = 0 to t = 20; and value for 'A' on the line at the extreme right is 0.1.
9. viii)   Taking this value to the left hand side, another line    O 'A' is drawn parallel to 'XY'.
10. Similarly, the parallel lines could be drawn to head the value for the values more than 70 years.
11.  It could be observed from these lines that only one straight line is not possible for the whole data. There may be a few more lines depending upon the nature of literature of a specific subject at a particular time.
The values of 'a' thus should be calculated by using the following formula:
T(t) = at
The value as read directly from the graph for t = 1, is found to be 0.94
The value of using parallel 'OA'
a= 0.77
6 log (a) = log (0.77)
by solving this equation we get,
log a = log (0.77) /6
= - 0.04356
a = e - 0.957374
Therefore,
a = 0.957374
The average value of 'a' can be taken as,
a =0.94 + 0.957374 /2
= 0.948687
Therefore   A A F = 0. 0948687

t= Age of Citations in Years
Figure No. 3 Semi log Curves for T (t) and t
ii) Half-life: The time calculated/ expected during which half the use of individual articles constituting a literature has been or expected to be made. The half-life can be determined from the graph in such a way that relation ah= 0.5 will hold well. The value as observed from the graph is 15 years. As calculated from the above relation, h = 13.15865 years which is almost near to the observed value. The half-life for the value of 'a' of chemical science journals literature can be calculated as follows,
Log (0.948687)h = log 0..5
h   log  0.948687 = h log 0.5
we get the equation as
-0.69315/- 0.05268
h = 13.15865
iii) Utility factor (U)
Utility factor can be calculated by using the relationship, u - 1/1 -a
U=l/(l-a)
=1/1-0.948
U = 19.48831
iv) Mean: The value of the mean (m) can be calculated from the value of AAF by using following formula,
1/m= loge a = loge 1/a  and a = 0.948
loge a = loge 1/0.948
1/m = 0.052676
m= 18.98392
Both values (frequency table value 17.06234 and 18.98392) being almost the same, confirm the exponential nature of the distribution and also justify the correctness of the average value of 'a' and this finding proves that Citation frequency distribution in chemical science journals follows exponential pattern.
v) Corrected Obsolescence Factor (a)
The corrected obsolescence factor is the factor by which the active life of an individual article on a set of documents tends to delay annually.
It has been calculated by using the following formulae,
ά  = (0.5)1/m = (0.5) 0.052676
ά = 0.1.037187
U-m =19.48831-18.98392= 0.504389

## nference

1. Indian J Experimental Biology has received 22069 references for 1534 articles at the average of 13.926 citations per article while Asian Journal of Chemistry has received 9073 references for 1495 articles at the average of 6.02 references per article Over all, these two journals have received 30,142 references for 3,027 articles at the rate of 9.95 references per article for 5 year data.
2. The Annual Ageing Factor (AAF) = "a” as calculated from the graph is found to be    A A F =0. 0948687
3. The value of half life as observed from the graph is 15 years. As calculated from the above relation, h = 13.15865 years which is almost near to the observed value.
4. The value of Utility factor (U) is U = 19.48831
5. The value of the mean (m) is = 18.98392 which confirms the exponential nature of the distribution and also justify the correctness of the average value of ‘a’.
6. Citation frequency distribution in chemical science journals follows exponential patter.
7. The Corrected Obsolescence Factor (a) was found to be = 0.504389

Findings of the Obsolescence factors are useful in understanding the researchers to what extent they can go back to obtain the required published information in their particular field of interest. In the evolution of life there is a theory called “use and disuse” which means the one always in use continuous to exist where as the one which is not in use perishes gradually. Similarly in the field of literature also the publication may go on decreasing with the advancement of age.

The obsolescence studies are helpful in discarding older materials in libraries; decisions regarding back volumes of periodicals; predicting the future use of literature; serving as a tool to measure the citable or usable documents in the field of chemical science. Results of this study cannot be generalized with other subjects and subfields.
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