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A I I E Transactions New Insights into the Life Cycle Approach
New Insights into the Life Cycle Approach
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Volumen:
5
Idioma:
english
Revista:
A I I E Transactions
DOI:
10.1080/05695557308974895
Date:
June, 1973
Archivo:
PDF, 393 KB
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This article was downloaded by: [UQ Library] On: 05 November 2014, At: 14:45 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 3741 Mortimer Street, London W1T 3JH, UK A I I E Transactions Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/uiie19 New Insights into the Life Cycle Approach Peter S. Eisenhut a a IBM System Products Division , Published online: 09 Jul 2007. To cite this article: Peter S. Eisenhut (1973) New Insights into the Life Cycle Approach, A I I E Transactions, 5:2, 150155, DOI: 10.1080/05695557308974895 To link to this article: http://dx.doi.org/10.1080/05695557308974895 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sublicensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/ter; msandconditions New Insights into the Life Cycle Approach PETER S. EISENHUT SENIOR MEMBER,AIIE Downloaded by [UQ Library] at 14:45 05 November 2014 IBM System Products Division Abstract: Life cycle or logistics curves have been used in government and industry in recent years to predict project oriented manpower. A plausible theory is advanced to justify the use of these curves. Assumptions about project characteristics are used to derive a form of life cycle curve which appears to have general application. One possible application is described. A life cycle curve is so called because it describes the chronology of some particular activity from beginning to end. In particular, this discussion pertains to curves having the general bell shape shown in Fig. 1, or, equivalently, the cumulative area under this curve which takes on the general S shape shown in Fig. 2. The S curve is sometimes referred to as a growth curve or achievement curve. The bell curve may be viewed as taking its shape as the result of some interaction or combination of increasing factors and decreasing factors. During the first part of the curve, the increasing factors dominate and the curve goes up. During the later part of the curve, the decreasing factors dominate and the curve goes down. The relative peakedness and skewness of the curve varies according to the interaction and relative strengths of the two types of factors. Why talk about life cycle curves? First, many real world situations exist which can be described by a life cycle curve. Some of these will be discussed later. Second, if curve equations can be found which fit historical life cycle data appropriate to particular real world situations, then these equations can be used to predict the future in those situations by extrapolation. Third, an understanding of the curve appropriate to a particular situation can result in better planning and control. For example, if the parameters of the curve can be related to factors which exist in the real world situation, then one can simulate the effects of planned changes in the real world. Thus, the life cycle curve has relevance. Time 'Received January 1972; revised April 1973. Fig. 1. Life cycle curve AIIE TRANSACIIONS,Volume 5, No. 2 3. The dollars expended on particular research and development projects such as those related to ecology or automotive safety which are of particular interest to society. 4. Effort expended on a special police investigation or an industrial task force. 5. Even marriage has been humorously described by a life cycle (2) Think of other events possibly described by life cycle curves. In each of the examples there will be factors causing the curve to increase and other factors causing it to decrease. Think of what some of these factors might be. How would you describe the effect of some of these factors mathematically? Time Downloaded by [UQ Library] at 14:45 05 November 2014 1 1 i I Fig. 2. S shape growth curve. Various Applications I Consolidation Former students of marketing may be familiar with what can be called the product market life cycle. A plot of units sold versus time is likely to have the bell shape referred to earlier. Such a curve is probably influenced by the following increase causing and decrease causing factors. Increase causing: 1. Advertising and promotion 2. Product availability 3. Customer need 4. Price ieduction 5. Product improvement Development and Service to Buyerr to Insure Satisfactory Use I I I Decrease causing: 1. 2. 3. 4. Competitive products Market saturation Obsolescence Price increase Time (Curve Represents Hypothetical Expectations of Growth) (Ref 1) Fig. 3. Typical growth curve Figure 3 shows a typical cumulative growth curve (1). The rate of growth would have the bell shape. The limiting factors to the growth of the firm may include items not mentioned such as government constraints, organization structure, and changing organizational goals. The market analyst may be able to determine other factors relevant to particular situations. An understanding of these factors, the relationship between them, and their effect on the market curve, can lead to the ability to simulate decisions involving facility planning, timing of product introduction, and pricing. A life cycle curve could possibly describe situations as diverse as the following: 1. The economic strength of an era of civilization. 2. The U.S. troop level in the Vietnam War. June 1973, AIIE TRANSACTIONS . Manpower Prediction The life cycle approach can predict the manpower required over the life cycle of an engineering or research type project. A project is viewed here as a collection of problems and activities, undefined at the outset, associated with reaching one particular goal or objective. An indepth understanding of the nature of projects, and justification for the use of life cycle curves is provided by Norden (3). A life cycle curve used to predict this "indirect" manpower is in some ways analogous to a learning curve used to predict "direct" manpower. Both curves are useful for making predictions under large degrees of uncertainty when detailed approaches such as time study or PERT planning are not possible. 151 The general shape of the life cycle curve in Fig. 1 can be explained in a general way. At the start of a project, no one knows what must be done and there is no action. This initiates search activity. Through learning, problems are recognized and action initiated at an incieased rate; the curve goes up. Then, as problems are solved and solutions implemented, more effort is spent on followup activity. As followup results in progress towards the objective, less new work is defined and the curve starts to decline. As the followup activity increases, the curve is extended to the right. The followup activity is reduced as satisfactory solutions to problems are verified and the curve goes to zero. This explanation is admittedly somewhat incomplete. Many factors affect the shape of the curve. Some of these are discussed more fully later. Downloaded by [UQ Library] at 14:45 05 November 2014 Life Cycle Curves Described by Probability Curves One can see at this point that a life cycle has attributes resembling a probability density function. Both are unimodal continuous curves. If all the points on the life cycle curve were divided by a constant such that the area under the curve equals 1, and if the curve is assumed to start at a value of zero, then all the conditions of a probability density function are met. This suggests a technique for modeling life cycle curves. For a description of some general probability function which may be appropriate, the reader should consult a text (4). Studies done by this author have indicated that the Beta density function can be made to fit normalized engineering manpower data with some accuracy. However, it is found that regardless of the parameter values selected, there is some mismatch between the shape of the data curve and the shape of the Beta curve. "Johnson distributions" are more flexible than the Beta in that they can be made to conform to a greater variety of shapes while employing the same number of parameters and for this reason are superior. However, it appears that the difficulty associated with selecting two shape and one scale parameters may limit the usefulness of fitting either of these probability functions. It appears as though the parameter values would differ for each situation. On the other hand, reasonable success in describing engineering manpower has been observed with Weibull density functions. It has been possible to derive this function based on pertinent assumptions about the environment. For this reason, its two shape parameters have some meaning in the real world. A special case of the Weibull function, the Raleigh function having only one shape parameter, was investigated by Norden (3). He found a reasonable degree of success in applying this curve to R and D project manpower. A Simple Model  The Weibull Curve Basic Assumptions Assume that a project consists of a set of problems (tasks) which must be recognized (defined) and then solved (executed). Assume that the rate of expending effort for solution, implementation, and followup activity is proportional to the product of two factors. The first is a learning factor and the second is a project status factor. Equation [I] describes this relationship. where MP(t) = rate of expending effort t = time L' = learning factor Y, = goal Y(t) = status at time t . The first factor or learning factorl' represents the ability to recognize problems and define tasks or activities. This factor increases with time. In this simple model, learning is assumed to be independent of the project status. The reciprocal of L' may be viewed as a delay time for recognition. The reciprocal of L' is assumed to follow the classical learning curve as described by Eq. [2]. where D = delay time b, B = constants Project Time, t Fig. 4. Recognition delay vs. project time. Whenever time t is doubled, delay time D is reduced by the fraction, 1  %. The shape of the curve of D as a function of time is shown in Fig. 4. AIIE TRANSACIIONS,Volume 5, No. 2 I 1 Downloaded by [UQ Library] at 14:45 05 November 2014 I The second or status factor [Yg Y(t)] may be viewed as the number of remaining problems. This factor decreases with time. Yg is the goal or the total number of problems to be solved and Y(t) is the status or the number of problems already solved. In this simple method, it is assumed that all Yg problems exist at the start of the project and the number of problems are always decreasing. That is, additional problems are not added over time; it is assumed that the goal Yg remains fixed. If the learning factor were constant the life cycle curve would be an exponentially decreasing curve. In effect, without learning, each problem would have a probability of recognition which did not change from one time interval to the next. In other words, a constant percentage of the remaining problems would be recognized at each time interval. Combining the two factors, one recognizes an increasing proportion of the remaining problems. The effort required to solve and followup is then assumed proportional to the number of recognized problems. Solvina the Differential Eauation Based on the previously mentio~ledassumptions, Eq. [I] can be restated as a differential, Eq. [4]. where C = Constant of proportionality Y'(t) = Rate of change in status proportional to MP(t). A solution to the differential equation is: This equation gives the cumulative effort at time t, for a project which requires a total of K manperiods. Equation [6] has the desired S shape shown in Fig. 1 for P values 2 1. This equation is recognized as K times the Weibull probability distribution function (4). If the cumulative manpower is determined from Eq. [6], then the number of men for a point in time is determined from the first derivative of Eq. [6]. This equation has the desired bell shape shown in Fig. 1. ' CMP1(t) = MP(t) = K ~ a f exp (  a f ) where CMP(t) = Cumu1ati~eeffort expanded by time t a Y K = Total effort expended. a Y B P = b + l . a = C + PB. June 1973, AIIE TRANSACTIONS [7] Evaluation The parameters a, P, and K must be evaluated for any real application. First, look at the parameter P and recall its relation to the learning curve shown in Fig. 4, P = b + 1 The higher the value of P, the greater the rate of learning (1  %). A P value of 1 means no learning. A value of P = 2 is equivalent to a 50% learning curve. P = 3 will be more like a 40% curve. (Refer to Eq. 131). Industrial practitioners, especially those in the aircraft industry, have generally been concerned with "learning curves" with slopes in the neighborhood of SO%, (% = 0.80). Such curves have generally been applied to product cost or labor productivity (5). It may, therefore, appear unusual to talk about curves steeper than 50% (% = 0.50). However, such fast rates of learning have been found to exist in true learning situations. E. B. Cochran cites a psychology experiment performed by H. Ebbinghaus (6). Rates of learning for the data represented by Cochran varied between 35% and 44%. It is expected that the parameter P i n this model will be in the neighborhood of 2 (50% learning curve). In Nordens equation the P value is seen to be fixed at a value of 2. . MP(t) = 2Kat exp (at2), %is solution is verified by substituting Eq. [5] in Eq. [4] . Assuming manperiods of effort proportional to the number of s o h 4 pr~blemsand conb;i.rPing constants: . [81 Norden has At Eq. [8] to actual manpower data and found a better fit than "logistics" equations of the same general shape (7). Notice that when P = 2, a special form of the Weibull distribution, the Raleigh distribution, results. However, Eq. [7] is more flexible as it allows a greater variety of shapes. Figure 5 illustrates the relative effects of changes in P. Let us now look at the coefficient a. It is possible to determine a in terms of P and Tp. T is the time at which the $;wve peaks. This is done by t&ing the derivative of Eq. f7] with respect to time, setting it equal to zero, and solving fix a. constant (P  1 ) c P  C/B a= 191 P P P .   Equation 193 implies that P and 2"'' are related. The time when the curve peaks and the required P value will depend upon the urgency of the project. The degree of Application of Weibull Curve Downloaded by [UQ Library] at 14:45 05 November 2014 Ti me Fig. 5. Effect on Weibull Curve of increased P. A proposed application of the Weibull model pertains t o semiconductor manufacturing. Manufacturing engineering manpower is predicted by product for the purpose of long range planning (two to ten years in the future). In this application, engineering projects are identifiable to product technologies. The engineering required to establish and debug each manufacturing process for a product follows a life cycle pattern. In addition special projects may be speeified for such things as cost enhancements on established products and manufacturing plant changes. These projects also follow life cycle patterns. The WeibuII model equations in the previous section are used to predict manpower for each project. In this appiication, the first year of the plan is based an budgets built up from a detailed departmental level. The remaining years of the plan are then based on life cycle projection. How are the equation parameters determined? Ef historical data and a current year budget are available, the value of K is calculated from Eq. Ell]. P and are fmnd by iteration (trial and error) until a "best fit"' to the history and budget is found. The criteria used for best fit is to minimize the standard percent deviation between the life cycle curve and the history. The future years are a projection of history and budget (Fig. 6). By being compatible with both historical fact and detailed budgets, the prediction is more plausible. T' urgency of a project will be dictated by factors unique to the environment of a particular project. For example, the urgency of a project to improve a semiconductor process may be related to such things as management goals, funds available, manpower ceilings, desired yield improvement with time, desired volume and revenue build up, expected life of the product, etc. A more urgent project will at any point in time have expended a greater amount of total effort. Rewriting Eq. [6] as Eq. [lo] illustrates this. CMP(t) = K [ 1  exp (constant/~)f] [lo] More urgency requires a higher P and a more rapid expenditure of effort. Referring again to Eqs. [6] and [lo] it can be seen that K represents the total manperiods of effort required to get to the ultimate state, or end result. In other words, the integration of Eq. 171 from zero to infinity is equal to K. This value of K is like a scaling factor which must be related to the overall magnitude or importance of the project. In the case of manufacturing engineering improvements to a semiconductor process, relevant factors may include volume of product through the process, tlie complexity and sophistication of the process and the product, and the extent to which improvement is required or judged economically feasible. If some data already exist for the project or if the cumulative manpower at a time, t , can be determined by some independent estimating technique, then K may be found as follows: M = K [l  exp ( UT,')] [Ill In Eq. [ I 11, M is the known or estimated cumulative manperiods of effort at any time T,. 154 I+ PI."  Time Fig. 6. Life cycle projection of history and budget. If there is no history however, as for future projects, the value of K is computed from preestablished relationships to product process variables. Experience will indicate approximate values for P and the constant referred to in Eq. [ 9 ] . The time of peak value is found to be related to key product dates. For a future project, specification of T, allows calculation P and vice versa. AIIE TRANSACIIONS, Volume 5, No. 2 Downloaded by [UQ Library] at 14:45 05 November 2014 The calculations are done by a program written in APL, a highly flexible language ideal for array and matrix manipulations. Its data terminal orientation and conversational style allows fast turnaround and a high degree of user flexibility. The user sits down at the typewriter, dials a number on the telephone, and types a predefined code. The program then types instruction as to what to do. No knowledge of programming is required. The data for existting projects are stored in the computer via the accounting system so input is minimal. The program does all of the manpower calculation and then summarizes totals by product and plant, and graphically illustrates results. The prediction for each product and for all products are seen to be an aggregate of a number of life cycle curves. The effect of summarizing many life cycle curves peaking at different points in time is usually a fairly level composite curve as suggested in Fig. 7. The APL program allows a form of game playing whereby the timing of all future products and projects can be varied until a desired composite curve is reached. Thus, true planning at a top management level is allowed for. approach is to apply generalized probability curves such as the Beta or Johnson curves. However, pure curve fitting does not offer any theoretical justification for applying a particular life cycle function. A better approach is to derive the appropriate life cycle function based on appropriate assumptions. This provides a theoretical basis as well as a good fit to data. The derivation of the Weibull curve illustrated here has been found applicable to engineering projects to establish or improve semiconductor processes. It is hoped that the reader will pursue other applications. Several aspects of life cycle curves undoubtedly require further study. For example, what is the effect of managerial imposed constraints on the rate of manpower expenditure? Or, what is the effect of modifying the goal during the course of a project? If the reader has unanswered questions, it is hoped that his interest will lead to additional insight into the life cycle approach. References (1) (2) (3) (4) (5) (6) (7) Anderson, Wroe, and Green, Paul, Planning and Boblem Solving in Marketing, IR. D. Irwin, Inc., Homewood, Illinois. (1964) pp. 465467. Dell'Isolu, A. J., "Optimizing Your Constriction Investment through Value Engineering, 1972 Transactions A.A.C.E., Grossinger N.Y.(June 24, 1972). Norden, Peter V., Manpower Utilization Patterns in Research and Development Projects, IBM Corporation, Doctorial thesis, Columbia University, New York (September 1964). Hahn, G., and Shapiro, S., Statistical Models in Engineering, Chapter 3, John Wiley & Sons (1967). Conway, R. W. and Shultz, A. Jr., "The Manufacturing Progress Function," Journal o f Industrial Endneerinx (JanuaryFebruary 1959). Cochran, E. B., "Learning: New Dimensions in Labor Standards," Journal of Industrial Engineering (January 1969). Norden. P. V.. "On the Anatomv of Develo~mentProiects" Time Fig. 7. Aggregation of subprojects. Conclusion A life cycle curve potentially describes many situations of concern to industrial engineers. of special interest is the planning of project oriented manpower. Approaches are discussed which extend ideas first suggested by Norden. One June 1973, AIIE TRANSACTIONS Mr. Peter S. Eisenhut is employed by IBM East Fishkill where heis responsible for developing advanced techniques for cost planning and cost engineering. He holds a BME degree from Cornell University and an MBA deg~eefrom the University of Rochester. Previously he was employed by Gleason Works, Rochester, New York, as a vstems analyst. MI. Eisenhut is a past Director of the MidHudson chapter of AIIE. 155