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IJQRM 21,1

32 Received October 2002 Revised January 2003

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NEW RESEARCH

A new forecasting model for the diffusion of ISO 9000 standard certifications in European countries Fiorenzo Franceschini, Maurizio Galetto and Giovanni Giannı` Dipartimento di Sistemi di Produzione ed Economia dell’Azienda, Politecnico di Torino, Torino, Italy Keywords Quality, ISO 9000 series, International standards, Diffusion, Logistics, Modelling Abstract ISO 9000 standards for quality system management are involving a higher and higher number of enterprises and organizations. This paper presents a detailed analysis of certification diffusion in Italy and in some European countries with similar economic structures. Benchmarking and evolution forecasts are based on the “logistic model”, traditionally used for studying biological growth phenomena. The presentation is supported by many empirical data, which show that, in many countries, the phenomenon is going to be close to saturation. Finally, some considerations about new developments, after the present “certification era”, are proposed.

Introduction The demand for ISO 9000 quality standard certifications is continuously increasing and involving a higher and higher number of enterprises and organizations, both public (no-profit) and private (ISO 9000, 1994, 2000). The

International Journal of Quality & Reliability Management Vol. 21 No. 1, 2004 pp. 32-50 q Emerald Group Publishing Limited 0265-671X DOI 10.1108/02656710410511687

The authors wish to thank the Agencies and Organizations that gently supplied the data utilized in the present research: ISO, EUROSTAT, Organization for Economic Co-Operation and Development Statistics Directorate (OECD) (Luxemburg), European Co-Operation for Accreditation (EA), SINCERT (Italian National System for the Accreditation of Certification and Inspection Bodies) (Italy), Italian Institute for Foreign Trade (ICE) (Italy), ISTAT (Italy), UK National Statistics (UK), Standards and Technical Regulations Directorate (UK), The United Kingdom Accreditation Service (UKAS), Centraal Bureau voor de Statistiek (CBS) (The Netherlands), The Dutch Council for Accreditation (RVA) (The Netherlands), TGA Accreditation Body and DQS GmbH (Germany), Deutsche BundesBank (Germany), Statistisches Bundesamt (Germany), The German Accreditation Council (DAR), Sweden Board for Accreditation and Conformity Assessment (SWEDAC), Sweden Statistics (SCB), Asociation Espanola de Normalizacion y Certificacion (AENOR), Instituto Nacional de Estadistica (Spain), Entidad Nacional de Acreditation (ENAC) (Spain), Association Francaise de Normalisation (AFNOR), Comite Francaise d.Accreditation (COFRAC), Ministere de l’economies (France), Mouvement DES Enterprises de France, (MEDEF), Ministry of Economic Affairs Division Accreditation (BELCERT) (Belgium), National Bank of Belgium, Central Balance Sheet Office (Belgium).

latest ISO survey (ISO, 2001) gives an updated photograph about the state of development of this process in several countries in the world. In general, there are many reasons that “push” an enterprise toward quality certification, both exogenous and endogenous. Sometimes, certification is explicitly required by customers; in other cases it is necessary in order to concur as a contractor in national or international tenders, otherwise, it is simply used to show a real advantage on competitors (Anderson et al., 1999). In addition, quality certification can become the tool by which a company operates a more organic management of its resources, on line with the continuous market changes (Mann and Kehoe, 1994; Weston, 1995; Zhu and Scheuermann, 1999). Without exploring further the reasons for getting a certification, it is interesting to analyze the diffusion of ISO 9000 certifications over time. The phenomenon is extremely complex as a result of a large variety of factors that can influence the strategies of an organization: economic/entrepreneurial structure, merchandise sector, incentives and pushes by central Governments, and so on. Many authors tried to analyze the effects of ISO 9000 certifications over performances and quality improvement in order to obtain effective competitive advantage (Rayner and Porter, 1991; Withers et al., 1997; Beattie and Sohal, 1999). In detail, Withers et al. (2000) used the eight dimensions of quality (Garvin, 1987) to evaluate the impacts of ISO 9000 certification on companies’ product quality. Many results indicated that quality seems to improve as a result of ISO 9000 certification, and it can also be argued that the reason for seeking certification can influence the degree to which quality is improved (Withers et al., 2000). Despite some authors tried to make an interpretation of ISO 9000 registrations and define a new perspective for their implementation (Ebrahimpour et al., 1997; Docking and Dowen, 1999), an exhaustive analysis of ISO 9000 diffusion is still lacking. In order to describe the certification diffusion process, in the present paper a detailed analysis of certification growth in Italy and in some other European countries is reported. A particular attention is devoted to those countries where the phenomenon is close to arrive at a saturation level. The methodology utilized for the analysis can be easily extended to other countries where the certification growth is still far from a stable and definitive level. Finally, some indications about new developments after the present “certification era” are reported. The ISO survey is the starting point of the analysis (ISO, 2001). Available data concur to trace a synthesis of what has happened and what is in progress all over the world. One of the purposes of this research is to make country/regional/local governments sensible to the dynamics and times of certification, especially when certification is interpreted as a tool for stimulating enterprises competitiveness.

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The paper starts with a description of the certification process in general terms. Then, from the analysis of empirical data we discuss about the strict analogy between the diffusion of certifications and the bio-systems population growth. On the basis of this association, we propose a general forecasting model to explain the diffusion of certifications in Italy and in some other European countries. The paper proceeds analyzing the tight link between the number of certifications and the entrepreneurial structure of each country. At the end, some cues about the future of ISO 9000 standard quality certifications are argued. The model Data analysis of the countries which firstly started certification process highlights a behavior very similar to that of a bio-population growth in a limited resource habitat, or to a diffusion process of new technologies (Pearl, 1978; Cherruault, 1983; Edelstein-Kesher, 1988; Murray, 1993; Stoneman, 1995). Quality certification diffusion began when some companies, with the aim of distinguishing themselves in the business competition, manifested a wish to give an external and formal evidence of their organizational efforts towards quality practice. Achieving success in a more and more careful market, their number has progressively grown up with a trend almost exponential. This dissemination was promoted by central governments and by quality national system bodies, reducing administrative features and supporting the diffusion of the certification bodies in the countries. As a result of these joint actions an increasing attention of the enterprises towards the certification was manifested: inside of the organization itself, in order to increase the resource involvement; outside, to give their own customers the evidence of excellence achievement. But the increasing process does not go on without end. Caught up the interest apex, the driving push slowly begins to attenuate under the effect of some concomitant factors: the reduction of the competitive gap between certified and not certified companies, and the limited number of enterprises potentially interested to certification. So, the growth tends slowly to a gradual saturation. Figure 1 shows the evolution of the number of certifications in some European countries (SINCERT, 2001; ISO, 2001). The curves highlight the different evolutionary stage of each country. The diffusion process is very close to the behavior of the so-called logistic systems, firstly introduced by the Belgian mathematician Pierre Verhulst (1838) in order to describe the phenomena related to a bio-population growth. Under a set of well defined conditions (see the Appendix), the “modified-logistic-curve” for a “certus-population” (i.e. the ISO 9000 standards certified companies, hereinafter called “certus-population”) is the following: N ðtÞ ¼

N 0 K  N 0; N 0 þ ðK  N 0 Þe r0 t

where the parameters have the following meaning:

ð1Þ

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Figure 1. The evolution of certifications in the main European countries since October 1992 . .

. .

N(t) is the number of ISO 9000 standards certified companies over time; r0 is the population growth rate in the absence of intra-specific competition; N0 represents the translation value to assure the condition N ð0Þ ¼ 0; N ð1Þ ¼ ð K  N 0 Þ is the certus-population saturation level, that is the total number of companies that will be interested in the certification process.

The logistic model is also widely utilized to model the diffusion process of new technologies (Stoneman, 1995). Forecast of the Italian certus-population growth In this section, we will try to describe the diffusion of quality certifications by means of the logistic model. The empirical data allow making a forecast about certification growth for those countries where the phenomenon has yet to arrive at the saturation level. Looking, for example, at the certification growth in Italy (see Figure 1 and Table I), we can observe that the evolution is close to the end of the preliminary exponential growth. In this situation it is interesting to

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36 Table I. Numbers of ISO 9000 standard certifications in Italy from year 1991 up to 2001

Year 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 Source: SINCERT (2001)

Number of certifications 161 348 810 1,589 3,033 5,097 8,513 13,690 21,069 30,895 40,000

provide a forecast of the total number of enterprises that will be involved in the certification process (saturation level), and when it will happen (saturation time). A first consideration, that comes out from this preliminary data analysis, is that the number of certified enterprises is much smaller than the total number of potential ones. As well as for Italy, British and Dutch growths confirm this assertion (see Figure 1 and Tables II and III). Referring to the logistic model, the saturation level value N ð1Þ is only a limited fraction of the number of potentially interested companies. The analysis of ISO survey data shows that the certus-population growth appreciably depends on the economic and productive structure of each country (ISO, 2001). With the aim of identifying some common evolutionary aspects of certus-populations, it is useful to consider in a deeper detail the entrepreneurial mix of each country. In accordance with a typical enterprise classification, Table IV shows the Italian entrepreneurial macro-composition from 1995 to 2000. From these values, we observe the dominant presence of sole traders category. A substantial balancing of the ratio over time of the four macro-categories – corporations, partnerships, sole traders and others – emerges too. This aspect is not only true for Italy, but also for the other European countries considered in this analysis (see Table II). With the aim of defining a common way for reading the certus-population evolution, we suggest to compare the number of certified enterprises with the total number of corporations. These last represent the category with the larger number of certified enterprises, constituting the natural catchment for the certification issues. Table V shows the percentage rate of Italian companies that achieved the ISO 9000 standard quality certification (SINCERT, 2001). In order to carry out a homogenous comparison among the various European countries, we applied the modified logistic model (equation (1)) on the percentage rate of certified companies (see Tables III and V). Figure 2 shows

The Netherlands (2000) n % Germany (1999) n %

Spain (2001) n %

France (2001) n %

Sole traders 578,505 35.6 272,285 47.0 2,037,230 70.6 1,651,265 62.4 1,182,352 48.4 Partnerships 358,330 22.1 122,375 21.1 357,009 12.4 105,876 4.0 38,859 1.6 Corporations (CC) 657,215 40.5 162,445 28.0 442,036 15.3 796,790 30.1 943,191 38.6 Others 28,970 1.8 22,150 3.8 49,993 1.7 91,386 3.5 278,960 11.4 Sources: Eurostat (2002), UK National Statistics (2001) (UK), Centraal Bureau voor de Statistiek (CBS) (2000) (The Netherlands), Deutsche BundesBank (Germany), Statistisches Bundesamt (1999) (Germany), Instituto Nacional de Estadistica (2001) (Spain) and Ministere de l’economie de France (2001) (France)

UK (2001) n %

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Table II. Entrepreneurial macro-structures of UK, The Netherlands, Germany, Spian and France

Table III. Certus-population growth rate of UK, The Netherlands, Germany, Spain and France and related percentage on total corporation companies (CC)

0.00 December 1986 0a December 1987 December 1988 0a 0.00 0a 0.00 0a 0.00 0a 0.00 0.04 8a 0.00 1a 0.00 December 1989 58a a a a December 1990 144 0.09 217 0.05 15 0.00 0.15 234a 0.05 59a 0.01 December 1991 14,000 2.13 250a 0.44 790a 0.18 159a 0.02 1,049 0.11 December 1992 18,577 2.83 716a Sepember 1993 28,096 4.28 1,502 0.92 1,534 0.35 320 0.04 1,586 0.17 December 1993 1,849a 1.14 2,087a 0.47 394a 0.05 June 1994 36,825 5.60 2,718 1.67 3,470 0.79 586 0.07 3,359 0.36 0.10 December 1994 781a March 1995 44,110 6.71 4,198 2.58 5,875 1.33 942 0.12 4,278 0.45 December 1995 52,595 8.00 5,284 3.25 10,236 2.32 1,492 0.19 5,536 0.59 December 1996 53,099 8.08 7,986 4.92 12,979 2.94 2,496 0.31 8,079 0.86 December 1997 56,696 8.63 10,380 6.39 20,656 4.67 4,268 0.54 11,920 1.26 December 1998 58,963 8.97 10,570 6.51 24,055 5.44 6,412 0.80 14,194 1.50 December 1999 61,800 9.40 10,620 6.54 30,150 6.82 8,699 1.09 16,028 1.70 December 2000 63,725 9.70 11,036 6.79 32,500 7.35 12,576 1.58 17,170 1.82 1.95 December 2001 15,568a Notes: Data refer to ISO survey, with the exception of the marked ones (a). These last have been harmonized with those from each national accreditation and certification body Sources: ISO (2001), UK Standards and Technical Regulations Directorate (2001) (UK), The United Kingdom Accreditation Service (UKAS) (2002) (UK), The Dutch Council for Accreditation (RVA) (2002) (The Netherlands), TGA Accreditation Body e DQS GmbH (2002) (Germany), Asociation Espanola de Normalizacion y Certificacion (AENOR) (2002) (Spain) and Association Francaise de Normalisation (AFNOR) (2002) (France)

Year

38

The Netherlands Germany Spain France Rate on Rate on Rate on Rate on Rate on Number of total CC Number of total CC Number of total CC Number of total CC Number of total CC certifications (%) certifications (%) certifications (%) certifications (%) certifications (%)

UK

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Total

Corporations

Percentage

Partnerships

Percentage

Sole traders

Percentage

Others

Percentage

1995 3,578,931 386,531 10.8 751,188 21.0 2,361,689 66.0 79,523 2.2 1996 3,806,838 401,044 10.5 785,462 20.6 2,539,871 66.7 80,461 2.1 1997 4,704,107 416,197 8.8 806,234 17.1 3,399,814 72.2 81,862 1.7 1998 4,727,504 435,727 9.2 832,364 17.6 3,375,206 71.4 84,207 1.8 1999 4,774,264 459,728 9.6 849,426 17.8 3,377,230 70.7 87,880 1.8 2000 4,840,366 490,427 10.1 867,007 17.9 3,389,839 70.0 93,093 1.9 Sources: Italian Institute for Statistics (ISTAT) (2002), Italian Institute for Foreign Trade (2002) and Italian Ministry of Productive Activities (2001)

Year

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Table IV. Italian entrepreneurial classification

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40 Table V. Quality certification growth in Italy with reference to the total number of corporation companies

Figure 2. Forecast of the Italian ISO 9000 standard certus-population growth elaborated by a modified logistic model until 2010

Number of corporation companies

Year

Number of certifications

Percentage rate

1991 161 298,811a 319,241a 1992 348 339,671a 1993 810 360,101a 1994 1,589 386,531 1995 3,033 401,044 1996 5,097 416,197 1997 8,513 435,727 1998 13,690 459,728 1999 21,069 490,427 2000 30,895 503,111a 2001 40,000 a Note: Data related to years 1991, 1992, 1993, 1994, 2001 have been extrapolated Sources: SINCERT (2001) and Italian Ministry of Productive Activities (2001)

0.05 0.11 0.24 0.44 0.78 1.27 2.05 3.14 4.58 6.30 7.95

the estimated curve, obtained for the Italian certus-population growth. The curve has been derived by applying to the empirical data a first-order nonlinear regression fit (Seber and Wild, 1989). Table VI reports the estimated values of the model parameters, while Table VII illustrates the details of the expected Italian certus-population growth until 2010. The estimated average asymptotic value N ð1Þ of the fraction of certified companies is approximately 13 percent of the total number of corporation companies. Starting from the first half of 2004, the whole amount will be contained within a ^ 10 percent tolerance interval around the asymptotic value

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Table VI. Parameter values and Logistic model parameters Estimated values Lower confidence limit Upper confidence limit confidence limits (risk coefficient: a ¼ 5 0.063 0.058 0.067 N0 (%) percent) for the modified K (%) 13.07 12.66 13.48 logistic model (equation r0 (year2 1) 0.53 0.52 0.54 (1)) applied to the Italian Note: Years are numbered since 1990 data

Year

Progressive year (reference year 1990)

Empirical percentage rate (%)

Estimated percentage rate (%)

Lower confidence limit (%)

Upper confidence limit (%)

1990 0 0 0.00 0.00 0.00 1991 1 0.05 0.04 0.04 0.05 1992 2 0.11 0.12 0.11 0.12 1993 3 0.24 0.24 0.23 0.24 1994 4 0.44 0.44 0.42 0.45 1995 5 0.78 0.78 0.74 0.78 1996 6 1.27 1.30 1.25 1.29 1997 7 2.05 2.10 2.03 2.07 1998 8 3.14 3.23 3.14 3.18 1999 9 4.58 4.69 4.57 4.62 2000 10 6.3 6.37 6.24 6.29 2001 11 7.95 8.07 7.93 8.00 2002 12 9.57 9.39 9.56 2003 13 10.74 10.51 10.82 2004 14 11.57 11.29 11.74 2005 15 12.12 11.80 12.37 2006 16 12.47 12.12 12.77 2007 17 12.69 12.32 13.02 2008 18 12.82 12.43 13.18 2009 19 12.89 12.50 13.28 2010 20 12.94 12.54 13.33 Notes: The estimated average asymptotic value is equal to 13 percent of the total number of corporation companies. Starting from the first half of 2004, the certus-population will be contained inside of a tolerance interval of ^ 10 percent of the asymptotic value (13 percent)

Table VII. Results obtained by implementing the modified logistic model (equation (1)) with the Italian data

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(13 percent). This point will mark the conclusion of the evolutionary process (see Figure 2). According to the EA classification scheme (SINCERT, 2001), a deeper analysis of the Italian certification growth has been performed for each merchandise sector. The study has clearly evidenced a different involvement of the various sectors. Referring to the percentage rate of certified companies over the total number of corporation companies, the first three places are respectively held by sectors 19 (electrical and optical equipment), 14 (rubber and plastic products) and 37 (education). On the other hand, if we consider the average annual certification growth rate in the last three years, the first three positions are respectively held by sectors 29c (repair of personal goods and household goods), 31 (transport, storage and communication) and 29b (repair of cycles, motor-cycles and motor vehicles).

The situation in other European countries Italian results have been compared with those of other European countries characterized by a similar economic and entrepreneurial structure. Among these, particular attention has been directed to UK, The Netherlands, Germany, Spain and France. Table II shows the entrepreneurial macro-structure of each country, while Table III illustrates the certus-population growth rate over time. Table VIII shows the pooled results of the analyzed European countries, obtained by the modified logistic model (eqiuation (1)). The Tables provide the parameters r0, N0 and K and the forecasts for the asymptotic saturation values of each country (for the next five years). Figures 3-7 report the empirical points, the fitted certus-population growth rate, and their respective confidence intervals (95 percent). Data related to the Italian, British, Dutch and German situations show many analogies, but also some meaningful differences. First of all, certus-population growth is not synchronized in the different countries. The starting times and the diffusion dynamics depend on the local political and economic conditions. The common element is the shape of the evolution growth that is very well fitted by a logistic model. A second relevant aspect is that the asymptotic value (saturation level) is a very small fraction of the total number of corporation companies present in each country. Certification penetration is a very “limited” phenomenon. The set of factors that pushes or inhibits the certification process finds a synthesis in a saturation value close to the 10 percent of the corporation companies there operating. This number, in analogy with the bio-population behavior, can be considered a kind of native property of the certification process, for well-defined context conditions typical of some European countries.

The Netherlands 95 percent confidence interval Value

Germany 95 percent confidence interval Value

Spain 95 percent confidence interval Value

France 95 percent confidence interval Value

(0.56; 0.81) year 2005 (9.05; 9.88)

0.68

9.47

6.91

0.88

(6.62; 7.20)

(0.76; 1.00) year 2005 8.07

0.68

(7.35; 8.79)

(0.57; 0.78) year 2005

2.91

0.55

(2.59; 3.23)

(0.51; 0.60) year 2006

(0.53; 0.70) year 2005 (1.87; 2.16)

0.62

2.01

0.080 (0.008; 0.152) 0.016 (0.004; 0.027) 0.023 (0.005; 0.041) 0.004 (0.002; 0.006) 0.012 (0.005; 0.019) 9.55 (9.08; 10.01) 6.93 (6.63; 7.23) 8.12 (7.36; 8.89) 3.01 (2.63; 3.40) 2.03 (1.87; 2.19)

Value

UK 95 percent confidence interval

Notes: The Table shows the model parameter values and their respective 95 percent confidence intervals. The forecasts for next five years of the asymptotic saturation values, as a percentage of corporation companies, are also reported

N0 (%) 0.063 (0.058; 0.067) K (%) 13.07 (12.66; 13.48) r0 (year2 1) 0.53 (0.52; 0.54) year 2006 Forecasts for next five years (% CC) 12.45 (12.12; 12.77)

Italy 95 percent confidence interval Parameter Value

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Table VIII. Regression results obtained by the modified logistic model (equation (1)), for Italy, UK The Netherlands, Germany, Spain and Italy

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Figure 3. UK certifications growth (since 1986)

Figure 4. The Netherlands certifications growth (since 1988)

Conclusions The paper presents an analysis of ISO 9000 standard quality certification growth in some European countries. In detail, the research suggests a model to describe the certification diffusion process related to each specific economic-entrepreneurial macro-structure. The model allows providing a

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Figure 5. Germany certifications growth (since 1988)

Figure 6. Spain certifications growth (since 1988)

forecast of new certifications growth, together with the time required to reach the saturation level. The central idea of the proposal is based on the close analogy between certification diffusion and bio-population growth. The certus-population

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Figure 7. France certifications growth (since 1988)

growth of Italy and of some other European countries has been deeply analyzed. Being the phenomenon close to the saturation in many countries, some questions come out about the future of quality certification. Will the certification market go on? Will certified enterprises continue to be interested on it? Can be foreseen new certification approaches? If yes, towards what new aspects of quality? Hazarding a hypothesis, we think that the new focus on the certification will shift from the inside of enterprises (internal quality systems), to the actual beneficiaries of their performances. In line with this new view, enterprises will be evaluated on the basis of how and what they are able to perform with reference to their own stakeholders. So, no more general principles and quality rules to be observed. Then, the new “tool” could become, why not, the certification of stakeholder satisfaction?

References Anderson, S.W., Daly, J.D. and Johnson, M.F. (1999), “Why firms seek ISO 9000 certification: regulatory compliance or competitive advantage?”, Production and Operations Management, Vol. 8 No. 1, pp. 28-43. Asociation Espanola de Normalizacion y Certificacion (AENOR) (2002), private communication (updated to January 31, 2002). Association Francaise de Normalisation (AFNOR) (2002), private communication (updated to January 31, 2002).

Beattie, K.R. and Sohal, A.S. (1999), “Implementing ISO 9000: a study of its benefits among Australian organizations”, Total Quality Management, Vol. 10 No. 1, pp. 95-106. Centraal Bureau voor de Statistiek (CBS) (2000), “Bedrijven naar grootte, naar rechtsvorm en naar regio vanaf 1993-2000”, available at: www.cbs.nl (and private communication (updated to January 31, 2002)). Cherruault, Y. (1983), Biomathematiques, PUF, Paris. Comite Francaise d’Accreditation (2002), available at: www.cofrac.fr (updated to January 31, 2002). Deutsche BundesBank (2001), “Monthly report December”, available at: www.bundesbank.de (and private communication (updated to January 31, 2002)). Docking, D.S. and Dowen, R.J. (1999), “Market interpretation of ISO 9000 registration”, The Journal of Financial Research, Vol. XXII No. 2, pp. 147-60. (The) Dutch Council for Accreditation (RVA) (2002), available at: www.rva.nl (and private communication (updated to January 31, 2002)). Ebrahimpour, M., Withers, B.E. and Hikmet, N. (1997), “Experiences of US- and foreign-owned firms: a new perspective on ISO 9000 implementation”, International Journal of Production Research, Vol. 35 No. 2, pp. 569-76. Edelstein-Kesher, L. (1988), Mathematical Models in Biology, Birkhaeuser, New York, NY. Eurostat (2002), available at: www.eurostat.eu (and private communication (updated to January 31, 2002)). Garvin, D.A. (1987), “Competing on the eight dimensions of quality”, Harvard Business Review, Vol. 65 No. 6, pp. 101-9. Instituto Nacional de Estadistica (2001), available at: www.ine.es (and private communication (updated to January 31, 2002)). Italian Institute for Foreign Trade (2002), “Le nuove guide Paese”, available at: www.ice.it (and private communication (updated to January 31, 2002)). ISO (2001), The ISO Survey of ISO 9000 and ISO 14000 Certificates: Tenth Cycle, 2000, ISO, Geneva. ISO 9000 (1994), Quality Management and Quality Assurance Standards – Guidelines for Selection and Use, ISO, Geneva. ISO 9000 (2000), Quality Management Systems – Requirements, ISO, Geneva. Italian Institute for Statistics (ISTAT) (2002), available at: www.istat.it (and private communication (updated to January 31, 2002)). Italian Ministry of Productive Activities (2001), available at: www.minindustria.it (and private communication (updated to January 31, 2002)). Mann, R. and Kehoe, D. (1994), “An evaluation of the effects of quality improvement activities on business performance”, International Journal of Quality & Reliability Management, Vol. 11 No. 4, pp. 29-44. Ministere de l’economie de France (2001), available at: www.minefi.gouv.fr (and private communication (updated to January 31, 2002)). Ministry of Economic Affairs, Division Accreditation Belgium (BELCERT) (2002), Private communication (updated to January 31, 2002)). Murray, J.D. (1993), Mathematical Biology, Springer-Verlag, Berlin, Heidelberg and New York, NY.

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Mouvement des Enterprises de France (2001), “Situation des enterprises”, available at: www.medef.fr (updated to January 31, 2002). Pearl, R. (1978), The Biology of Population Growth, History of Ecology Series, Ayer Co. Pub., New York, NY. Rayner, P. and Porter, I.J. (1991), “BS 5759/ISO 9000 – the experience of small and medium sized firms”, International Journal of Quality & Reliability Management, Vol. 8 No. 6, pp. 16-28. Seber, G.A.F. and Wild, C.J. (1989), Nonlinear Regression, Wiley Series in Probability and Mathematical Statistics, New York, NY. SINCERT (2001), “Database query”, available at: www.sincert.it (and private communication (updated to January 31, 2002)). Statistisches Bundesamt (1999), “Steuerpflichtige und deren Lieferungen und Leistungen 1999 nach Wirtschaftsabschnitten und Rechtsformen”, available at: www.destatis.de (and private communication (updated to January 31, 2002)). Stoneman, P. (1995), Handbook of the Economics of Innovation and Technological Change, Blackwell Handbooks in Economics, Oxford. Sweden Board for Accreditation and Conformity Assessment (2002), available at: www.swedac.se (and private communication (updated to January 31, 2002)). TGA Accreditation Body e DQS GmbH (2002), available at: www.tga-gmbh.de (and private communication (updated to January 31, 2002)). (The) United Kingdom Accreditation Service (UKAS) (2002), available at: www.ukas.com (and private communication (updated to January 31, 2002)). UK National Statistics (2001), “Size analysis of UK businesses”, available at: www.statistics.gov.uk (and private communication (updated to January 31, 2002)). UK Standards and Technical Regulations Directorate (2001), private communication (updated to January 31, 2002). Weston, F.C. (1995), “What do managers really think of the ISO 9000 registration process?”, Quality Progress, Vol. 28 No. 10, pp. 67-73. Withers, B.E., Ebrahimpour, M. and Hikmet, N. (2000), “Does ISO 9000 certification affect the dimensions of quality used for competitive advantage?”, European Management Journal, Vol. 18 No. 4, pp. 431-43. Withers, B.E., Ebrahimpour, M. and Hikmet, N. (1997), “An exploration of the impact of TQM and JIT on ISO 9000 registered companies”, International Journal of Production Economics, Vol. 53 No. 2, pp. 209-16. Zhu, S. and Scheuermann, L. (1999), “A comparison of quality programmes: total quality management and ISO 9000”, Total Quality Management, Vol. 10 No. 2, pp. 291-7.

Further reading Enterprise Register Statistics Sweden (2000), available at: www.scb.se (and private communication (updated to January 31, 2002)). Entidad Nacional de Acreditation (2002), available at: www.enac.es (updated to January 31, 2002)). European Co-Operation for Accreditation (2002), available at: www.european-accreditation.org (and private communication (updated to January 31, 2002)). National Bank of Belgium, Central Balance Sheet Office (2000), “Annual account 2001”, available at: www.nbb.be/BA/E/homee.htm (updated to January 31, 2002).

OECD Statistics Directorate (2002), “Structural-ANalysis (STAN) database query”, available at: www.oecd.org/statistics (and private communication (updated to January 31, 2002)). Appendix A logistic model is based on the hypothesis that the population growth rate r declines with the population density. At low densities (N!0) the population growth rate is maximal and equal to r0. Parameter r0 can be interpreted as the population growth rate in the absence of intra-specific competition. The population growth rate reaches the zero value when N ¼ K. The population growth rate can be described as:   N ; ðA1Þ r ¼ r0 1  K where K is the upper limit of population growth and is called carrying capacity. It is usually interpreted as the amount of resources expressed in the number of bio-organisms that can be supported by these resources. The dynamics of the population is described by the following differential equation:   dN N ¼ rN ¼ r0 N 1  ; ðA2Þ dt K which has the solution: N ðtÞ ¼

N 0 K ; N 0 þ ðK  N 0 Þe r0 t

ðA3Þ

where N0 represents the number of bio-organisms at time t ¼ 0. Parameter r0 /K can be interpreted as the indicator of the competitive level of the evolutionary environment, while r0 represents the maximum possible rate of population growth which is the net effect of reproduction and mortality. In absence of competition the population growth is described by an exponential model with parameter r0. For the certification process, the parameter r0 stands for the maximum rate of population growth of the certified companies, while K is the carrying capacity of certified enterprises. It takes into account the interaction effect among enterprises. This close analogy between the two growth mechanisms has a meaning under the following hypotheses: . first of all, the model considers only the total number of certified enterprises, paying no attention to their specific dimension and to their commodity sector; . for certus-populations K parameter (saturation level) is affected by market competition and by the economic policies pursued by the Central Governments; . parameter r0 is influenced by national incentives, by the presence of local governments’ encouragement and by the number of certification bodies; . we suppose there are not events or external interferences that can change the natural evolution of the certus-population (for example, international/national changes, competitive pressure, regulatory/legislation changes); . while the number of elements of a bio-population is Nð0Þ – 0 when t ¼ 0, for a certus-population the initial value is N ð0Þ ¼ 0 (at the certification launch, the certification number is zero). Taking into account this last consideration, the model (equation (A3)) can be modified so as to impose the passage through the origin:

Diffusion of ISO 9000

49

IJQRM 21,1

  dðN þ N 0 Þ ðN þ N 0 Þ ¼ ð N þ N 0 Þr 0  1  with N0 . 0; dt K

ðA4Þ

with the following initial condition N ð0Þ ¼ 0. Solving equation (A4) we obtain:

50

N ðtÞ ¼

N 0 K  N 0; N 0 þ ðK  N 0 Þe r0 t

ðA5Þ

where: . .

.

N0 represents the translation value to assure the conditionN ð0Þ ¼ 0; Nð1Þ ¼ ð K  N 0 Þ is the certus-population saturation level, that is the asymptotic plateau level of N ðt Þ; rð0Þ ¼ N 0 r0 ½1  ðN 0 =KÞ identifies the certus-population growth rate at the launch. This represents the slope of the curve just at the right side of the origin in the plane (N, t). Larger is the emphasis on the certification process by quality national bodies, greater will be its value.
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