See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/272413172 A Complexity Index for the Design Process Conference Paper · August 2001 CITATIONS READS 32 1,125 2 authors, including: Bimal Kumar Northumbria University 176 PUBLICATIONS 1,169 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: Development of Level 2 BIM Strategy for NHS Scotland View project BIM Strategy for NHS Scotland View project All content following this page was uploaded by Bimal Kumar on 14 June 2016. The user has requested enhancement of the downloaded file. COMPLEXITY INDEX OF A DESIGN PROCESS Abstract This paper is aimed at developing an approach for measuring the complexity index of a design process. In the absence of any unified definition about complexity of a design process it is proposed that it is the ‘total information content’ associated in the chosen complexity generating factors (CGF) within the different activities of a design process. The amount of information content acts as a measuring yardstick for establishing the complexity index (CI) of the design process. The measure of complexity would be an advantage to managers/ project planners during the planning phase of similar design processes, identifying the reasons of complexity so that the effective measures are directed to reduce it and a practical acceptance of the definition of complexity. The results presented in this paper presupposes the involvement of human resources in all the aspects of a design process and complexity of the design process is dependent on the user’s skill and the context in which it is measured. Keywords: Complexity Generating Factor (CGF), Partial Complexity Generating Factor (Pcgf), Information Parameters (IPs), Partial Complexity Index (PCI), Overall Complexity Index (OCI), Partial Information Content, (PCI). 1. Introduction 1.1 Defining Complexity Complexity is difficult to define. Johnson reports that there is still no agreed – upon definition, much less a theoretically – rigorous formalization, despite the fact that complexity is currently a “hot” research topic. Johnson quotes Dan Stein, chairman of the physics department at the University of Arizona: “ Everybody talks about it.[But] in the absence of a good definition, complexity is pretty much in the eye of the beholder.” (http://www.complexsystems.org/commentaries) Researchers have tried to define it based on the characteristics of complexity in the context of their own fields. But not a single definition seems comprehensive enough to suit all the situations where complexity exists. Complexity is a very slippery term and means different things to different people. Claud E. Shannon was among the first to propose a measure of complexity, which was based on the very reasonable assumption that the amount of information processed by the system in question reflects its complexity (www.thesoulatwork.com/book/matter.html). But this idea was limited to the problems related in the field of information theory. Weaver (1948) has discussed on the ranges of complexity and is quantifiable by analytic mathematics concentrating on specific elements. The approach suggests a limitation on account of the nature of complexity, which was typical of 17th, 18th and 19th century sciences Klir (1985). Perrow (1965), Mohr (1971), Waxman (1996) have all defined the complexity in terms of the degree of difficulty of the search process in performing the task, the amount of thinking time required to solve work-related problems and the body of knowledge that may provide guidelines for performing the task which all appear to be a subjective issue. Balding et.al (1971) have been able to establish a linear relationship between product complexity and savings on account of manufacturing complex components on a NC machine rather than on conventional machines but this relationship does not address the complexity of the involved design process (manufacturing). Any conclusion regarding the complexity of the design process involved on the above basis would be erroneous as shown in Fig.1 Ashby (1973) has highlighted the idea that complexity is directly related to a person’s interest and has varied meanings depending on the context of study. But this definition does not include the list of interests a person would be interested in and how far these interests would have an important impact on the outcome of the result. Thompson (1981) considers complexity as a measure of difficulty in co-ordinating a production process comprising of activities that lack uniformity of work. Kusiak et. al (1993) have suggested the decomposition approach for detecting parallelism among activities that reduces the product development time. At the same time the measure of difficulty needs to be identified without which it would not be a trivial task to arrive to any result regarding the nature of complexity. Wallace (1987) has identified design task, design team, design techniques, and design output as the one’s to be influenced by the complexity of the design process. This indicates an influence of the complexity on the overall design rather than the definition or causes of complexity. In the area of measuring software complexity Chaitin (1987) and others hold the view that simple tasks can be done by short computer programs and vice versa , measured in terms of ‘algorithmic complexity’. The basic idea is that the length of its most compact description measures complexity of a task. But the length of even the shortest computer program depends upon the design of the software as well as coding. The problem with this definition, as Chaitin concedes, is that random sequences are invariably more complex because in each case the recipe is as long as the whole thing is specified; it cannot be “compressed”. Zurn (1991) has quantified a number of factors and incorporated them in a model that can be used for assessing new product introduction. The quantified factors include product innovation, product complexity, and design maturity, schedule pressure and others. Ahn and Crawford (1994) have adapted a number of software metrics for analysing the complexity of computational design processes in terms of control structure, data dependencies between design tasks. There approach is based on the hypothesis that complexity of engineering design processes (with respect to computational aspects) can be analysed and evaluated by adapting criteria identified from “software complexity” in Computer science. They have drawn similarities between computer programs and computational design processes. This method would work with only the parts of the design process, which have computational contents and would not address the qualitative aspect of the design process. Pugh (1996) has quantified the complexity of a product and defined it as being proportional to number of parts; number of different types of parts, number of interconnections and interfaces and the number of functions that the product is expected to perform. He has also stressed the need of combining the quantified complexity with an approach called ‘load lines’ to reach the goal of simplicity. This approach suggests a measure for a product complexity without addressing the complexity of the associated design process. Biren(1998 ) is of the view that it is the combination of new and old practices, such as old-fashioned habits, new life cycle environment, changes, and mounting regulations, which imparts complexity to many of the product development efforts. These causes of complexity in the absence of any of its measurability are more towards the subjectivity of the definition. 1.2 The Growing Complexity in Companies Complexity is a term normally used in everyday situations to describe a characteristic, which is not yet possible to quantify precisely. On account of this the lead-time for design and operations planning accounts for 60% of the delivery time [Wiendahl] for customerspecific products. Research has often shown that both the development times for the products or variants and the production lead times in the direct areas are about 50% too high, taking international competition as a basis. Frizelle & Woodcock (1995), Frizelle (1995), Frizelle (1998), Braha et. al (1999) have classified 'complexity' as having structural and operational aspects. The only difference in the works of Frizelle and Braha is that the former has assumed the structural component of the complexity to arise from the impact the product structure has on the resources that will produce it whereas the latter states that it is a function of its representation. Similarly for the functional part the former takes into account the uncertainty involved in manufacturing and the latter believes that design complexity is a function of its probability of successfully achieving the required specifications. Complexity in production arises on account of the production structures known as ‘structural complexity’ and as ‘dynamic complexity’ because of the production procedures involved. The former type of complexity (structural complexity), which exists on account of the production structures, is due to the superposition of the product range on the resources required for its manufacture. A product that is simple for one facility to manufacture may be complex for another. Moreover an increase in either the product range or the number of processes involved will result in the overall structure becoming more complex. The number of processes and products involved thus measures structural complexity. Whereas the latter type of complexity (dynamic complexity), which is more related to, the operational part deals with the uncertainty involved in manufacturing which appear once the plant starts to manufacture. Typical examples are plant breakdowns, absenteeism, shortages and unbalanced flow. Their effect is to generate queues. The resulting complexity is called operational complexity. 1.3 Need for measuring complexity It has been established that measurement is vital for controlling any process because it is difficult to manage what cannot be measured (DeMarco,T. 1982). In addition to many researchers noted physicist Lord Kelvin, software engineers Tom Demarco, researcher Chryssolouris, 1994, have stressed importance of measuring complexity. Presently design process complexity is highly subjective and is the cause of many engineering and management related problems. The complexity of design process is the cause of many management problems in industrial companies (Frizelle et.al 2000). Practitioners in the area of project management frequently describe their projects as simple or complex (Baccarini, 1996) when they are discussing management issues. This indicates a practical acceptance that complexity makes a difference to the management of projects. Therefore an understanding of project complexity and how it might be managed is of significant importance. Complexity of products and its associated design processes have always been of some concern to mankind. The present way of attributing complexity to a product and its design process appears to be a simple mental task at which the design evaluators are highly proficient. This mental task is frequently undertaken every time they make interaction with the product or/ and its design process. Researchers ( Waxman 1996) have defined complexity as a subjective matter and to a greater extent are dependent on the user solving a problem. Design evaluators have often maintained records regarding the complexity of products or its related design processes as mental models. However looking closely it is found to be a very subjective issue of attributing complexity to anything in a qualitative sense. Usually the design evaluators are able to assign complexity to products or/and its related design processes but often are not able to say how they arrive at that conclusion. Researchers (Chryssolouris, 1994) call for increased efforts to make this complexity quantifiable. It is only after this measurability is achieved can fresh approaches be developed for reducing complexity in production systems and so produce a systematic reduction in complexity. A transition from the qualitative understanding of complexity to a quantitative understanding would be a highly desirable and necessary step towards the understanding of overruns of design projects (Calinescu, A. et. al. 2000). Design projects are typically plagued with schedule and cost overruns ranging between 41% - 258% and 97% - 151% respectively (Norris, K.P. 1971, Murmann, P.A. 1994). A factor in these overruns can be attributed to projects being more complex than originally anticipated at the I nitial planning stages. Although research has been carried out in this area there is currently no method for measuring the complexity of the design process. In order to schedule projects and estimate costs more accurately it is essential that complexity of the design process can be measured. 1.4 Complexity Measurement One of the earliest researcher to establish the fact that complexity could be measured had been Von Neumann (Gidado, 1997) according to which complexity can be measured provided if it was to be related to such things as the dimension of a state space, the length of a programme or the magnitude of a ‘cost’ in money or time. Rosen (1987) also shares the idea of a threshold value of complexity as expressed by Von Neumann. Griffin (1997) has developed number of metrics including product complexity, management complexity, and amount of change to measure product development cycle time. One of the most respected attempts for developing an objective measure of complexity was made by John Tyler Bonner, of Princeton University. He suggested to count the number of different cell types in the organism can perform, and that is the clue to complexity. Bonner was able to show higher complexity in larger species by this measure, but he did not try to determine whether it increased through evolutionary time. (http://www.thesoulatwork.com/book/matter.html) Salingaros (1997) has established the idea of architectural temperature and harmony in order to quantify the qualitative attributes of the building structures to establish the complexity index of the world famous building structures. His model uses ideas of Christopher Alexander to estimate certain intrinsic qualities of a building and predicts a building’s emotional impact. His model on measuring the complexity of architectural buildings is quite subjective and lacks objectivity in the absence of a scale. Pressing Jeffery defines complexity as the minimal cost of computing an approximate solution to the problem. So instead of basing complexity on number of structural levels or capacity for adaptation, here complexity is based on a minimum set of resources (cost) (http://www.cs.indiana.edu/Noetica/OpenForumIssue8/Pressing.html page 3) Bashir et. al(1999) have found out the product complexity on the assumption that it depends on the number of functions a product is designed to deliver and the depth of its functional tree. The use of this approach is limited because of the depth of functional tree, which in turn would depend on the function of the product and the end user of that product. According to this method a product could have more than one complexity index, as it would be governed by the function of the product. At the same time it does not address the underlying design process in the manufacture of that product According to Seth Llyod (Suh 1999) there are some three- dozen different ways scientists use the word ’complexity’. Frizelle & Woodcock (1995), Frizelle (1995), Frizelle (1998), Braha et. al (1999) have classified 'complexity' as having structural and operational aspects. The only difference in the works of Frizelle and Braha is that the former has assumed the structural component of the complexity to arise from the impact the product structure has on the resources that will produce it whereas the latter states that it is a function of its representation. Similarly for the functional part the former takes into account the uncertainty involved in manufacturing and the latter believes that design complexity is a function of its probability of successfully achieving the required specifications. Suh (1990), Haik et.al(1999), Calinescu et.al(1998), Davidson et.al have indicated the importance of information content while dealing with the complexity in their respective areas of interest. These researchers have drawn analogy from the pioneering work of Shannon (1948) on mathematical theory of communication where the amount of information (for example, in a message transmitted between individuals) increases as the number of possible messages increases and decreases as the number of possible messages decreases. A greater set of possible messages corresponds to a greater uncertainty on the part of the recipient as to the message content and higher information content in the message. Researchers like Suh (1990), Haik et.al(1999), Calinescu et.al(1998), Davidson et.al have been able to measure the information content in their areas of interest but the scale of information measurement is not considered at any stage. Bennet (Suh 1990) coined a different measure of complexity called ’logical depth’. It is to gauge how long it would plausibly take for a computer to go from a simple blueprint to the final product. Though useful, it seems to be limited to processes in which there is a logical structure of some sort. Tang et.al 2001 do not consider complexity and complicatedness of a system as synonyms. They consider complexity as an inherent property of systems and complicatedness as a derived property that characterizes an execution unit’s ability to mange a complex system. 2. Generators of Complexity and Context 2.1 Complexity Generating Factors (CGFs) These are the proposed factors, which have been assumed to impart complexity to a design process. The choice of Complexity Generating Factors is dependent on the user and is used as a first step for measuring the complexity of the design process in a particular part of the context. There is a comprehensive list of CGFs for every part of the context. Annexure: A 2.2 Partial Complexity Generating Factors (Pcgfs) All the Complexity Generating Factors are subdivided into partial complexity generating factors (Pcgfs). This division of Cgfs into Pcgfs is necessary to facilitate measurement of complexity on account of their CGFs. All the Pcgfs would contribute some partial complexity (PC) in their own way towards its CGF and the sum total of these PCs would give an index known as partial complexity index (PCI) of the design activity on account of the chosen CGF. Annexure: B 3. Proposed Understanding about the complexity of the design process 3.1 Proposed Definition of Complexity The complexity of a design process with reference to an user is defined in terms of the information content associated with the chosen Complexity Generating Factors of design activities in a given part of context of a design process. 3.2 Equation Development Information content has been used as a measuring tool for complexity because of a number of reasons ----- people involved in the design process deals with information in various form like reading drawings, selecting processes, teams, materials and likewise many more. Wiendahl et.al 1994 have also established through surveys that nowadays 75% of the employees in industrial companies do not work with materials but with information. The concept of ‘ entropy’, which is used in thermodynamics to quantify the ‘disorder’ that arises in a system due to ‘variety’ and ‘uncertainty’, has been used in measuring the complexity of a design process. In information theory too the concept of entropy has been defined as the ‘expected amount of information’ to describe a system covering all the various possible states of the system as given by Shannon’s equation for measuring information content I= - pi log 2 pi ------------------------------------------(1) Where p i = Probability of the system to be in a particular state Similarly an equation has been proposed for measuring the Information Content in a design activity/ process as given below presupposing the involvement of different resources (e.g. people, machine and material) in different departments. For a design activity the total information content ‘Id’ could be written as --G P S Id = - pi log 2 pi ---------------------------------------(2) r 1 i 1 j 1 And for design process total information content ‘Ip’ could be written as --N Ip = - n 1 G P S p log r 1 i 1 j 1 i 2 pi ----------------------------------------(3) Where N= Design activities G= Complexity Generating Factors (CGFs) P= Information Parameters (IPs) S= States of Information Parameters (IPs) pi = probability of an Information Parameter (IP) ‘i’ to be in state ‘j’ 4. Description of the Model The terminology used in this model can be found in appendix as Annexure:Terminology and the schematic diagram of the model is attached as Annexure D. The model has three main modules---- contextual, partial complexity generating factors and information processing. User input is needed for making a selection for the type of a design activity and then the part of the context in which the complexity has to be measured. Each of the part of context has a set of predefined complexity generating factors, which are the first step for measuring the complexity of the design activity. These CGFs have their further subdivisions into partial complexity generating factors (Pcgfs), which are instrumental in ‘activating’ the information parameters (IPs) without which the progress of the design activity is not possible. After the appropriate selection of the information parameters and the ‘states’ the information-processing module calculates the information content using the equation mentioned. The Complexity Index Generator (CIG) within the information-processing module shown in Annexure D is responsible for generating the partial or/and overall complexity index (PCI/OCI) of a design process. It consists of the following: Matrix showing the different ‘CAUSES’ for complexity while managing the Information Parameters (IPs)/States/Solution steps on account of a selected complexity generating factor. Development of Assessment Scales for measuring the identified ‘CAUSES’ in the matrix explained at serial number 1 above. Analysis of the identified ‘ CAUSES’ on user defined degrees within the assessment scales. Compiling and interpreting the information for complexity as a result of steps mentioned at serial numbers 2 and 3 respectively. 5. Working of Model through an example Description of the example: An operator has to accomplice a design process (say manufacturing a gear) in which one of the design activities is say machining. The objective is to measure the complexity of the design activity. The very first step is to fix the part of the context in which this activity has to be measured for complexity (Say Work). Next comes the selection of the complexity generating factors, which is user dependent (Say Usage of Resources). After this the selection is made regarding the partial complexity generating factor (Say Operator) as this would help in activating the Information Parameters in the Partial CGFs module. Annexure D After fixing the above information the following steps are followed: STEP: 1 This method presupposes that the PIC of a design activity has been worked out using equation (2) within a specified set of conditions. Annexure E. STEP: 2 Either accept the matrix of ‘CAUSES’ as such or alter the position of causes as per the operator’s idea. This step is important as the X-axis of the matrix denotes the distribution of Partial Information Content (PIC) in an increasing order, which as per definition is a measure of complexity. For some operators some causes may be more relevant than the causes from the point of view of complexity so in that case those causes would be kept far from the origin and vice versa. Annexure F STEP: 3 Distribute the Partial Information Content (PIC) found in step: 1 along the X-axis in an increasing order as the value of complexity increases along the axis. This distribution of PIC has been made on the fact that PIC obtained in step: 1 is a result of the use of the IPs/States/Solution Steps of the design activity, which form a part of this matrix too. But one has to be careful while distributing the partial information content as it should be distributed in a logical way and should not cross its maximum value. By logic the operator should not assign a higher contribution of the PIC to a cause like ‘Manageable IPs’ which is at (I, A) than to a cause, which says ‘Broad range of IPs which are vague or ambiguous’ at (III, A) which is placed in a higher level and vice versa so here the user has to use his experience and commonsense. Viz. in this case PIC of 50 has been distributed as 10, 20, 40 and 50 within the different levels; it could have been 10, 20, 30, 50 or 10, 30, 40, 50 depending upon the user. Annexure F STEP: 4 Identify the probable causes(s) from the ‘Matrix showing the different ‘CAUSES’ for complexity while managing the Information Parameters (IPs)/States/Solution steps using the “Problem Solving” skill. For each of the identified cause(s) in a particular level follow the steps given belowSTEP: 5 Go to the table of ‘Assessment on Technicality Scale’ and fill in the details in the sub table of ‘Value of st for chosen CAUSE (S)’for all the causes identified in step: 4. Repeat the same exercise for the tables of ‘ Assessment on Analysability and Difficulty Scales’. Annexure: TN, Annexure: AN, Annexure: DN STEP: 6 Go to the table of ‘Summary of Assessment of Causes on different scales’ to fill in the details regarding causes and individual assessment values for technicality, analysability and difficulty (st , sa, sd). Annexure: SN STEP: 7 Go to the table of ‘Summary of the Actual Partial Information Content’ and fill in the details to find the number of causes and PIC (s)in each level of the matrix so the range of values for PIC is ascertained. Annexure: SN STEP: 8 Fill in the details of Scales for each level in the table of ‘Summary of Actual PIC for each level’. STEP: 9 Draw conclusion about the category of complexity of the design activity on the basis of the grand total of the partial information content (GTPIC). WORKING OF THE PROPOSED METHODOLOGY 1. With reference to step: 4 the ‘Causes’ are identified as: (III, A) (IV, B) (III, C) 2. As per step: 5 go to the tables of various assessment scales and fill in the details of the causes and your ideas about the various factors of the three scales. For example for the “Assessment on Technicality Scale” for the causes mentioned in 3. 4. 5. 6. 7. (1) the column number III and IV would be filled in by the operator for factors of the technicality scale, say for cause (III, A) is st 2 which is 16 and denotes that ‘worker is able to make a partial use of his skills’ similarly for cause (IV, B) operator has assigned as st4 which is 40 denoting that the ‘worker is unable to use his skills’ in spite of possessing them. Similarly for the cause (III, C) operator has assigned as st4, which is 32 denoting that the worker is unable to use the skills. So the total value of st for level III is 48 and that for IV is 40 Similarly these causes are assessed for sa and sd and the total values for sa for level III is 40 and that for IV is 30 and for sd the total values for level III is 40 and that for IV is again 30 Go to the table of ‘Summary of Assessment of Causes on different scales’ as per step: 6 and fill in the details to find the contribution of the partial information content associated with each cause identified in Step: 1. Annexure: SN As per step: 7 go the table ‘Summary of the Actual Partial Information Content’. As in this example level III has the actual PIC of 128 on account of two causes so the range of PIC for this should be <=240 and that for level IV having the actual PIC as 100 the range of PIC should be <= 150. As per step: 8 go to the table of ‘Summary of Actual Partial Information Content (PIC) for each level’ and fill in the details to find the Grand Total of the PIC (GTPIC), which in the present case is 228. Annexure: SN As per step: 9 draws conclusion on the category of the GTPIC obtained in (6) SUMMARY OF ACTUAL PARTIAL INFORMATION CONTENT (PIC) FOR EACH LEVEL Total of PIC at each level LEVELS I Actual II III IV 128 100 PIC Grand Total of PIC (GTPIC) = 228 (Highly Complex) INTERPRETING CATEGORIES OF COMPLEXITY Complexity of the design activity has been divided into different categories A, B, C and D respectively from extreme complex to simple depending on the value of its grand total of PIC (GTPIC). (A) Extremely Complex 360 < GTPIC < = 450 (B) (C) (D) Highly Complex Medium Complex Simple 180 < GTPIC < = 360 90 < GTPIC < = 180 30 < GTPIC < = 90 DISCUSSION OF THE RESULT 1. The above table summarising the final partial information content for each level denotes that the PIC in level III is more than the PIC in level IV. This helps the user to make efforts to reduce the effect on account of the ‘CAUSES’ at level III than at level IV. 2. In spite of the fact that the user has arranged the ‘CAUSES’ in an increasing order of its information content the results shows that it is not true rather the information content is dependent on the degree of assessment of the factors considered within the different scales. 3. The individual causes identified in it or different levels help to draw comparison amongst them on the basis its actual information content as shown in the table of summary of the actual partial information content (PIC). LIMITATIONS 1. Methodology can be applied to any design activity, which makes use of the skills of the operators. 2. Methodology could be applied as long as the IPs/States/Solution Steps can be formulated. 3. User dependent so the complexity Index is dynamic. 4. Methodology is not taking into account the ergonomics of the surrounding environment. 5. Accuracy of the results is dependent on the observer and the data used in finding the states. 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