The Reconfigurable Manufacturing Systems

Published Date: 02 Nov 2017

Reconfigurable manufacturing systems (RMSs) have been acknowledged as a promising means of providing manufacturing companies with the required production capacities and capabilities. This is accomplished through reconfiguring the system elements over the time for a diverse set of individualised products often required in small quantities and with short delivery lead time. This necessitates the requirement of mapping the manufacturing system capabilities and other characteristics by developing a suitable index. In this paper an index has been developed to measure the reconfigurability of RMSs keeping in mind their various core characteristics such as modularity, scalability, convertibility and diagnosability. These characteristics have been mapped together using multi-attribute utility theory. One could easily use this index to find the reconfigurability of a system possessing different characteristics. An illustrative example is provided to reveal the application of the proposed methodology on a given system. Insight gained would be of much interest to the decision makers managing the complexity of a manufacturing system for diversified products.

Keywords: reconfigurable manufacturing system (RMS); modularity; convertibility; scalability; diagnosability; reconfigurability; multi-attribute utility theory

1. Introduction

With increasing global competition, traditional manufacturing systems, e.g., dedicated manufacturing systems, mass production systems, flexible manufacturing systems, have become inadequate in supporting the rapid production of customised products with low costs and high profitability. In response to the limitations of such systems and the fast changing environments, reconfigurable manufacturing systems (RMSs) have been proposed as a promising means for manufacturing companies to produce products while meeting individualised customer requirements (Koren et al. 1999). Ideal reconfigur-able manufacturing systems possess six core RMS characteristics: modularity, integrability, customised flexibility, scalability, convertibility, and diagnosability (as shown in Figure 1).

A typical RMS will have several of these characteristics, though not necessarily all. When possessing these characteristics, RMS increases the speed of responsiveness of manufacturing systems against unpredicted events, such as sudden market demand changes or unexpected machine failures. Various researches can be found out in literature

regarding RMSs, but very little steps have been taken towards capturing reconfigurability of a manufacturing system. Reconfigurability has been an issue in computing and robotics for many years. In general, reconfigurability is the ability to repeatedly change and rearrange the components of a system in a cost-effective way. In this paper we propose an index to measure the degree of reconfigurability of a reconfigurable manufacturing system on the basis of its core characteristics using multi-attribute utility theory. The same has been applied and tested on a sample data set.

The remainder of this paper is structured as follows: Section 2 describes the need for a reconfigurability index while Section 3 consists of theoretical background in this area. Section 4 deals with core characteristics of RMS and the methods to map them. In Section 5, multi-attribute utility theory based approach is discussed to link the various characteristics of RMS into a single function to evaluate reconfigurability of the system. An illustrative example has been worked out in Section 6 where reconfigurability of eight different systems is evaluated and compared. Lastly, the discussion and recommendations for future work is portrayed in Section 7.

2. Need for a reconfigurability index

A changing manufacturing environment characterised by aggressive competition on a global scale and rapid changes in process technology requires creating production systems that are themselves easily upgradeable and into which any emerging technology and new functions can be readily integrated. These conditions require a responsive new manufacturing approach that enables:

Increasing frequency introduction of new products;

Changes in the components for existing products;

International Journal of Production Research 1671Large fluctuations in product demand and product mix;

Changes in government regulations (safety and environment);

Changes in process technology.

These changes are driven by aggressive economic competition on a global scale, more educated and demanding customers, and a rapid pace of change in process technology. These drivers reflect a new balance among economy, technology and society. To survive in this dynamic manufacturing environment, companies must be able to react to changes rapidly and cost-effectively. Reconfigurability is an engineering characteristic that deals with design of production machines and manufacturing systems for customised products in the cost effective market. If the system and its machines are not designed at the outset for reconfigurability, the reconfiguration process will prove lengthy and, therefore, impractical.

As the need for a reconfigurable manufacturing system increases so also does a need for an index which can enumerate the reconfigurability of a system. It becomes of foremost importance in the interest of the manufacturer to know the various characteristics of the RMS. He should also be well equipped to decide and judge the optimal reconfigurability of his manufacturing system. This index thus provides a deep insight into the reconfigur-ability of a system keeping in mind its various aspects like modularity, scalability, convertibility, etc. It is a tool which could help the manufacturer in deciding how reconfigurable his system is. As the tool takes the help of the core characteristics of reconfigurability, it also helps them in understanding the various aspects of reconfigur-ability. It enables them to directly link reconfigurability to the fundamental parameters of the manufacturing system. It is very useful in the process of decision making for deciding which parameter needs more attention for increasing the reconfigurability of the RMS.

In this paper we use the multi-attribute utility model to map the various characteristics of reconfigurability. Each attribute is given an appropriate weightage based on the needs and requirement of the manufacturer and thus the reconfigurability of the system is assessed using these weights.

3. Theoretical background

Koren et al. (1999) proposed a new type of manufacturing system, designated as a reconfigurable manufacturing system (RMS) which is quite different than the dedicated manufacturing lines and flexible manufacturing systems. For the RMS, it is described that they are designed at the outset with adjustable resources in order to provide exactly the capacity and functionality that are needed, exactly when required. Reconfigurable systems must be designed at the outset to be reconfigurable, and must be created by using hardware and software modules that can be integrated quickly and reliably; otherwise, the reconfiguration process will be both lengthy and impractical.

Achieving this design goal requires an RMS to possess several characteristics like modularity, scalability, convertibility, diagnosability, customised flexibility and integrability. There have been quite a number of research articles on capturing these different characteristics of RMS. Bi et al. (2007) generalised the strategies to meet the requirements of a manufacturing system and then used it to compare and distinguish different manufacturing technologies. They concluded that the RMS paradigm is one of the most effective paradigms to meet some of the key requirements such as changes and uncertainty.

1672 K. Gumasta et al.

Tang and Qiu (2004) presented a virtual production line-based (VPL) approach to the design and operation of a reconfigurable manufacturing system. They discussed the algorithms to maximise the productivity of RMS. Singh et al. (2007) established a decision making module to evaluate existing and new generation manufacturing systems by trading off among tangible and intangible parameters. Fuzzy logic has been used by them to capture the vagueness and uncertainty of the decision maker. Abdi and Labib (2003) used an analytical hierarchy process (AHP) for structuring the decision making process for the selection of a manufacturing system among feasible alternatives based on an RMS study.

Holtta et al. (2005) proposed a method to measure modularity. They looked at the fundamental degree of coupling of a product, independent of where the module boundaries are set and therefore developed a new index, the singular value modularity index (SMI) based on the decay pattern of the design structure matrices (DSM) singular values. Luke (1993) proposed that a cost effectiveness based definition of scalability is more reliable than any scalability definition that is blind to the subtle relationships existing between processor and workload scaling. These parameters should not be scaled as if they were linked by a constant of proportion, instead they should each be scaled in proportions that deliver the maximum effective performance gains. Without this criterion, a measurement methodology may increase workload when reasonable performance gains are achievable without workload increase.

Deif and ElMaraghy (2007) presented simulation results and analyses aiming at helping capacity scalability planners in reconfigurable manufacturing systems to investigate the best scalability policy for various demand scenarios. Modelling was based on a system dynamic approach to better reflect the dynamic nature of both modern market demand patterns as well as the capacity scalability process. Son et al. (2001) showed that an homogeneous paralleling flow line (HPFL) system method can be an alternative manufacturing system design approach under an environment where line balancing is not easy or cost-effective and production demand will increase more than the capacity of a single optimally designed transfer line (TL). With the HPFL approach, it is possible to obtain finer steps of capacity changes than conventional transfer line type mass production systems with similar cost. This characteristic of cost-effective capacity changes will meet the scalability requirements of reconfigurable manufacturing systems.

Koren et al. (2003) concluded that by measuring the convertibility of the configuration, machines, and material handling elements, the convertibility metrics defined here provide a quantitative assessment for characteristics of manufacturing systems that make certain design alternatives inherently better than others in terms of responsiveness. Clark and Paasch (1996) described a diagnostic modelling methodology for a conceptual system, a partially defined system, and an embodied system. The methodology is based on the relationship between a system’s functions and its line replaceable units (LRUs).

4. Characteristics of RMS 4.1 Modularity

The compartmentalisation of production functions and requirements into operational units can be manipulated between alternate production schemes to achieve the optimal arrangement to fit a given set of needs. In a reconfigurable manufacturing system, many components are typically modular (e.g., machines, axes of motion, controls, and tooling).

International Journal of Production Research 1673When necessary, the modular components can be replaced or upgraded to better suit new applications.

N-1

SMI(XDSM) = 1 — 1 X Qi(Qi — Qi+1), (1)

N x Q1 i

=1Modularity can be evaluated by considering the fundamental degree of coupling of a product independent of where the module boundaries are set (Holtta et al. 2005). The modularity index developed is based on the decay pattern of the design structure matrices (DSM) singular values and hence called singular value modularity index (SMI). Firstly, a binary component-component DSM is formed in which a value of ‘1’ is assigned to the components of the corresponding row and column which are connected and a value of ‘0’ is assigned to the components which are not connected. Diagonal elements are assigned the value ‘0’. Singular value decomposition (SVD) is performed on the DSM. The singular values are the diagonal elements of the middle matrix of the three matrices which are obtained from singular value decomposition of DSM. The singular value modularity index (SMI) is used to quantify modularity as:

where Qi, are the singular values of the DSM arranged in a descending order, and N is the number of components (rows/columns in a DSM). The singular values describe the principal components of interconnectivity of the system. The SMI metric is able to quantify the degree of modularity without introducing arbitrary module boundaries. The modularity is inversely proportional to the number of connections between different components. Hence it can be seen that loosely coupled systems have higher modularity value than the compact systems.

4.2 Scalability

The specific definition stated for scalability in Koren et al. (1999) is ‘the ability to adjust the production capacity of a system through system reconfiguration with minimal cost, in minimal time, over a large capacity range, at given capacity increments’. According to Luke (1993) an alternate definition of scalability can be found when scalability is defined as the ability to maintain cost effectiveness as workload grows. When this approach is considered the subjective definition is replaced by an objective definition of optimal cost effectiveness. This calls for the need of a cost effectiveness function that is relevant to scalability. Luke proposed such a function which helps to evaluate scalability.

As given by Luke (1993):

Effectiveness = 2 t1 (2)

texecN,

,

where t1 represents the time required to execute the work on a single processor; and

texec = k N, (3)

where k is the minimum number of operations required to complete the task and is described as the scaling parameter. Hence, the total work = k. N refers to the number of processors. Thus it can be inferred that as the workload (k) increases, executable

N C

CM PiM • 61674 K. Gumasta et al.

time (texec) increases while on the contrary as the number of processors (N) increase, the executable time (texec) decreases.

Whenever texec is independent of the number of processors (N), the system cannot be said to be scalable as increasing the number of processors will not increase the performance of the system and thus the scalability value of the system is zero. However, when texec is dependent on the number of processors, we calculate the effectiveness value of the system and the scalability value of the system is captured. Thus scalability can be directly equated to the effectiveness of the system.

4.3 Convertibility

Convertibility is defined as the capability of a system to adjust production functionality, or changes from one product to another (Koren et al. 2003). System convertibility may have several levels. Conversion may require switching spindles on a milling machine (e.g., from low-torque high-speed spindle for aluminium to high-torque low-speed spindle for titanium), or manual adjustment of passive degrees-of-freedom changes when switching production between two members of the part family within a given time.

System convertibility includes contributions due to machines, their arrangements or configuration, and material handling devices. These factors are mapped together for an overall intrinsic assessment of system convertibility:

CS w1CC w2CM w3CH• 4

Where CC, CM and CH are convertibility metrics associated with the configuration, machine, and material handling, respectively, which are further defined in subsequent sections such that each metric has a scale of 0–10. The weights w1, w2 and w3 are adjustable in nature.

As stated in Koren et al. (2003), CC can be evaluated as:

CC ~• 5

Where:

R refers to the number of routing connections in each configuration;

X is the minimum number of replicated machines at a particular stage in

the process plan;

I is the minimum increment of conversion.

The minimum increment of conversion (I) is one of many factors used to select preferred manufacturing system configurations. It is an important indication of how quickly new or different products can be introduced. For example, configuration (a) in Figure 2 has a minimum increment of conversion of 1.00, or 100%, that is, in order to introduce a new product, the entire line must be shut down, changed over, and restarted. Configuration (b), however, can be partially converted to a new product after shutting down only 50% of the machines.

System convertibility is also dependant on machine convertibility, CM:

International Journal of Production Research 1675Figure 2. Different manufacturing systems.

The machine convertibility, CM for each of the N individual machines in the system is based on the premise that some machines have features and characteristics that make them inherently more convertible. These features include whether the machine is:

Equipped with an automatic tool changer or multi head spindle;

Easily reprogrammed, with flexible software;

Modular, with flexible hardware components;

Equipped with flexible fixturing capability;

Equipped with a large capacity tool magazine.

Similarly material handling convertibility can be calculated as:

PN i1 CH

CH  7

N

The CH metric for each material handling device that connects machines is found by assessing if it is:

Following a free route or not;

Multidirectional;

Reprogrammable;

Asynchronous motion;

Automatic.

4.4 Diagnosability

Diagnosability is the ability to automatically read the current state of a system for detecting and diagnosing the root-cause of output product defects, and subsequently correct operational defects quickly.

Diagnosability investigation can be divided between diagnosability of components and systems. Diagnosability of a system can be further divided into system detectability,

1676 K. Gumasta et al.

predictability, and distinguishability. Detectability is a measure of the time that passes before the fact that a failure exists and is recognised. Predictability is a measure of the time that will pass before a certain failure will occur. Distinguishability is a measure of the time required to determine which of a system’s line replaceable units (LRUs) is the cause of the loss of functionality. An LRU is a complex component that is designed for replacement, quickly at the organisational level. LRUs speed up repair, because they can be stocked and replaced quickly from inventory, restoring the larger system to service.

Distinguishability can be calculated using the following relationship:

D Pi1 lPIi1=Ci 1=CLRU}

1 1=CLRU~n 8

i1 PIi

determining the impact of the i-th value dimension on the overall evaluation (also calledWhere:

D is the distinguishability;

n is the total number of possible indications,

CLRU is the total number of LRUs

Ci is the number of candidates for each indication i;

PIi is the probability of indication i.

A distinguishability of one, or 100%, means that every possible indication would have only one candidate and diagnosis is trivial. A distinguishability of zero means that for any indication, all LRUs in the system are candidates, and each LRU must be checked individually until the faulty LRU is discovered. Thus, distinguishability can easily be mapped with the diagnosability of a system.

As all the characteristics of RMS have been assessed, it can be interpreted that these characteristics are independent of each other. Quantifying all these characteristics is just not sufficient to compare or judge how much reconfigurable a system is. Thus here arises an utmost need for a function that can map all these characteristics under a single variable name that we call the system’s reconfigurability index. This has been achieved using multi-attribute utility theory.

5. Multi-attribute utility theory

Multi-attribute utility theory (MAUT) is a label for a family of methods. These methods are the means to analyse situations and create an evaluation process. The objective of MAUT is to attain a conjoint measure of the attractiveness (utility) of each outcome of a set of alternatives. Thus, the method is recommended when prospective alternatives must be evaluated to determine which alternative performs best.

According to MAUT, the overall evaluation R(x) of an object x is defined as a weighted addition of its evaluation with respect to its relevant value dimensions (Huber 1974). The common denominator of all these dimensions is the utility for the evaluator. The overall evaluation is defined by the following overall value function:

n

XRx wivx. 9

i1

Here, R is the evaluation of the object on the i-th value dimension and w the weight

International Journal of Production Research 1677

Figure 3. Manufacturing system (g).the relative importance of a dimension), n is the number of different value dimensions, and:

Xwi  1. 10

In order to capture reconfigurability, four different characteristics namely modularity, scalability, convertibility and diagnosability have been mapped together in this paper. Therefore reconfigurability of a manufacturing system can be evaluated as:

R  wMM wSS wCC wDD. 11

Where:

reconfigurability; M: modularity;

scalability;

convertibility;

diagnosability;

wM: modularity weightage;

wS: scalability weightage;

wC: convertibility weightage;

wD: diagnosability weightage.

Since modularity, scalability, convertibility and diagnosability values are on a scale of 0–1, the value of reconfigurability also lies on a 0–1 scale. Weights of individual attributes can be calculated in many ways. Statistical analysis of the data collected from manufacturers is used to evaluate individual weights in this article.

6. An illustrative example

In this section, we illustrate our methodology on the example shown in Koren et al. (2003). Although the data used in the example is not actual, it is representative. Here we show the calculations for the system type (g) (Figure 3). In Figure 2 different coloured (shaded) boxes denote different machines or operations. A step by step procedure to a reconfigurability index is discussed in this section. After calculating reconfigurability for different systems given in Figure 2, a comparison is made to identify the most reconfigurable system among them.

Step 1: Modularity of a system is measured on the basis that a module can be connected to many other modules. Thus there can be various kinds of modularity like modularity of a machine which considers machine modules and modularity of a system which considers

1678 K. Gumasta et al.

Table 1. Modularity values for systems (a) to (h).

System

o1

o2

o3

o4

o5

o6

Modularity

1.8019

1.8019

1.2470

1.2470

0.4450

0.4450

0.8150

1.4142

1.4142

1.4142

1.4142

0.0000

0.0000

0.7643

2.8284

2.8284

0.0000

0.0000

0.0000

0.0000

0.5286

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

3.0000

3.0000

0.0000

0.0000

0.0000

0.0000

0.5000

1.4142

1.4142

1.4142

1.4142

0.0000

0.0000

0.7643

2.8284

2.8284

0.0000

0.0000

0.0000

0.0000

0.5286

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

1.0000

modules of a whole system which themselves are machines. For measuring the modularity of the system we first need to draw the design system matrix (DSM).

A1

A2

B1

B2

B3

B4

A1

0

0

1

1

1

1

A2

0

0

1

1

1

1

DSM = B1

1

1

0

0

0

0 :

B2

1

1

0

0

0

0

B3

1

1

0

0

0

0

B4

1

1

0

0

0

0

Here A1, A2, B1, B2, B3 and B4 are the machines shown in Figure 3.

Performing the singular value decomposition on the DSM using the svd command in MATLAB, we obtain three different matrices. Out of which the middle matrix, also known as singular matrix is:

2:8284

0

0

0

0

0

0

2:8284

0

0

0

0

0

0

0:0000

0

0

0

S =

:

0

0

0

0:0000

0

0

0

0

0

0

0:0000

0

0

0

0

0

0

0:0000

Using Equation (1), we obtain the modularity as 0.5286. Modularity values for the rest of the systems are shown in Table 1.

Step 2: Next we calculate the convertibility of the system. For this we need to first evaluate configuration convertibility (CC), machine convertibility (CM) and material handling convertibility (CH).

For calculating CC we first find the values of R, X and I for the system. From Figure 3 it can easily be noticed that R = 14 and the number of replicated system X = 2. The minimum increment of conversion (I) of the considered system is 0.33, i.e., in order to introduce a new machine two of the six machines have to be shut down (say A1 and B1). Therefore using Equation (5), we obtain CC = 84.

International Journal of Production Research 1679Figure 4. Machine convertibilityC0M.

Normalizing CC using the equation given by Koren et al. (2003):

CC,normalised = 1 +

(12)

log(CC,k-parallel) X 1 CC,k-serial 9

( )

log CC

CC,serial

Normalised value of CC, i.e., CC,normalised = 6.43.

We also calculate the machine convertibility CM = 5 (assuming standard CNCs, as shown in Figure 4) and CH = 3.5 as given in Koren et al. (2003).

Assigning equal weights to CC, CH and CM we evaluate the system convertibility as 0.5 (while calculating system convertibility C, we use the normalised value of CC, i.e., CC,normalised, 0.643, CH as 0.35 and CM as 0.5 to obtain the value of C within the range (0,1)).

Assuming all the CNCs to be standard CNCs, convertibility values for the rest of the systems are shown in Table 2.

Step 3: As defined in Section 3, diagnosability is the measure of the ease of finding the cause(s) of an occurrence of abnormal situation (it is also termed as indication). From Equation (8), we see that diagnosability of the system depends on the total number of machines in the system and the number of candidates responsible for each indication. For example if there is some problem in the finishing of the job, the machines responsible are milling, drilling and grinding machines.

In this paper we assume that a single kind of machine is associated with a particular indication. Again considering the example (Figure 3), there are two kinds of machines (A and B) and each kind of machine is responsible for a certain abnormal situation (indication). Thus, there will be two kinds of indications, one due to machines of type A and the other due to machines of type B. The probability of occurrence of each indication is assumed to be equal.

Here: C = 6;

C1= 2 for the indication from ‘A’ machines; C2 = 4 for the indication from ‘B’ machines.

Using Equation (8), we obtain the diagnosability of system (g) to be 0.25. Diagnosability values for the rest of the systems are shown in Table 3.

1680 K. Gumasta et al.

Table 2. Convertibility values for systems (a) to (h).

I

R

X

CC

CH

CM

w1

w2

w3

C

(a)

1.00

7

1

1.00

3.50

5.00

0.33

0.33

0.33

3.17

(b)

0.50

8

2

4.32

3.50

5.00

0.33

0.33

0.33

4.27

(c)

0.50

12

2

5.20

3.75

5.00

0.33

0.33

0.33

4.65

(d)

0.33

9

3

6.35

5.50

5.00

0.33

0.33

0.33

5.62

(e)

0.33

15

3

7.46

3.70

5.00

0.33

0.33

0.33

5.39

(f)

0.33

10

2

5.69

3.50

5.00

0.33

0.33

0.33

4.73

(g)

0.33

14

2

6.43

3.75

5.00

0.33

0.33

0.33

5.06

(h)

0.17

12

6

10.00

5.50

5.00

0.33

0.33

0.33

6.83

Table 3. Diagnosability values for systems (a) to (h).

Types of machines Types of indications

Probability distribution

of each indication

6 6

1/6

3 3

1/3

3 3

1/3

2 2

1/2

2 2

1/2

2 2

1/2

2 2

1/2

1 1

1

Step 4:

Scalability is a measure of effectiveness of a system. In addition, it is possible to

employ a stricter definition of scalability as any application that can maintain maximal cost effectiveness as workload increases. For the system (g) there are two types of machines hence there are two types of processes. We assume the workload of each process to be equal to k. Thus, the total workload is 6k (=2k+4k). Using Equation (3), executable time for first kind of process texec = (2k/2) + (4k/4) = 2k. The total number of machines (N) is 6. Thus, effectiveness =1/4k.

Effectiveness is found to be maximum for the system (h) (Figure 2) when all the machines are in parallel and is equal to 1/k. Thus, to bring each of the effectiveness values on the scale from 0–1, we divide them by the maximum value, i.e., 1/k. As the scalability is directly related to the effectiveness value (Luke 1993). The term scalability can be directly used instead of effectiveness.

Thus scalability, S=(1/4k)/(1/k)=0.25. Values of scalabilities for the rest of the systems are shown in Table 4.

Step 5: After determining all the four attributes of reconfigurability, we finally map them into a single function to capture reconfigurability using multi-attribute utility theory (Equation (11)).

For calculating each attribute’s weight statistical analysis is used. Data is collected from manufacturers asking them their preference or percentage importance to the respective attribute in the reconfigurability function. Preference values are decided keeping in mind the kind of changes that are expected in the product’s demand in the near future

International Journal of Production Research 1681Table 4. Scalability values for systems (a) to (h).

Types of processes Total execution time texec Total no. of machines (N) Scalability (S)

6 6k 6 0.0278

3 3k 6 0.1111

3 3k 6 0.1111

2 2k 6 0.2500

2 2k 6 0.2500

3 3k 6 0.1111

2 2k 6 0.2500

1 k 6 1.0000

Table 5. Sample weights collected for different features of RMS.

M S C D M S C D

0.1576

0.1270

0.3517

0.3637

0.2390

0.2373

0.2599

0.2638

0.3816

0.2551

0.2543

0.1090

0.2904

0.3909

0.1734

0.1453

0.2769

0.2435

0.4387

0.0409

0.1700

0.2130

0.2407

0.3763

0.1622

0.3111

0.2963

0.2304

0.1679

0.3439

0.3363

0.1519

0.3897

0.2625

0.2417

0.1061

0.4711

0.1711

0.2196

0.1382

0.2417

0.2186

0.8190

0.3507

0.0913

0.2929

0.2196

0.3962

0.2619

0.3507

0.2554

0.1320

0.2179

0.3687

0.1493

0.2641

0.2428

0.3687

0.1486

0.2399

0.3251

0.1909

0.3225

0.1615

0.3384

0.1361

0.2967

0.2287

0.1108

0.1761

0.2417

0.4714

0.1112

0.2924

0.2277

0.3687

0.2362

0.2089

0.1759

0.3790

(here the data is randomly generated using MATLAB). Since each individual has its own choice, we are estimating the value which can satisfy 95% of choice for each attribute by taking a sample of 20 readings (Table 5).

XM = 0.2442, XS = 0.2580, XC = 0.2520, XD = 0.2459 o2M = 0.0103, o2S = 0.0064, o2C = 0.0053, o2D = 0.0148.

Where X and o2 are mean and variance of the respective feature.

From the above data set, 95% confidence value of each attribute’s weight is calculated using the normal distribution statistical analysis. Value of weights is finally normalised so that they add up to give unity. We obtain the weights as:

wM = 0.2475, wS = 0.2522, wC = 0.2445, wD = 0.2557.

Step 6: Finally substituting all these weights and the modularity, scalability, convertibility, and diagnosability values into Equation (11), we obtain the degree of reconfigurability (R).

7. Discussion and recommendations for future work

From the reconfigurability values we see that reconfigurability depends on the characteristics of manufacturing system and the preference that the respective features have for the corresponding manufacturing system. Weight to a characteristic can be

1682 K. Gumasta et al.

Table 6. Reconfigurability values for systems (a) to (h).

Modularity (M) Scalability (S) Convertibility* (C) Diagnosability (D) Reconfigurability (R)

0.8150

0.0278

0.3170

1.0000

0.5419

0.7643

0.1111

0.4270

0.4000

0.4238

0.5286

0.1111

0.4650

0.4000

0.3784

1.0000

0.2500

0.5620

0.2000

0.4990

0.5000

0.2500

0.5390

0.2000

0.3697

0.7643

0.1111

0.4730

0.2500

0.3967

0.5286

0.2500

0.5060

0.2500

0.3815

1.0000

1.0000

0.6830

0.0000

0.6557

Note: *the convertibility values used here have been divided by 10 to obtain the value between 0–1 so that the final reconfigurability value obtained also remains in the region 0–1.

decided by the manufacturer on the basis of type of product being produced by the system. For example if demand for a product varies frequently then weight for scalability should be more than that of others while if at another instance quality is the top most priority then diagnosability should be assigned with higher weight. Thus, the reconfigurability value also depends on the relative importance of different characteristics.

Each characteristic of an RMS, modularity, scalability, convertibility and diagnosa-bility, is first found out and then combined together using multi-attribute utility theory. The modularity values depend on the connections between different machines in a manufacturing system. Effectiveness of the system gives us the scalability values. Convertibility includes the contributions due to machines, their arrangements or configuration, and material handling devices. Convertibility values are determined considering all these factors. Diagnosability is the ability to automatically read the current state of a system for detecting and diagnosing the root-cause of output product defects, and subsequently correct operational defects quickly.

All the attributes are finally combined to give a reconfigurability index (shown in Table 6) It can be inferred that systems (a) and (h) have the maximum reconfigurability values. In system (a), all machines are different and are placed in series and thus its modularity and diagnosability values are the highest. While in system (h), there is just a single type of machine arranged in parallel, thus its convertibility and scalability values are the highest among all systems.

This research gives a precursor for future research on quantifying reconfigurability of manufacturing systems. There are several ways to extend this work in the future. Effects of material handling devices, tools, fixtures, etc. can also be integrated in the process of judging the reconfigurability of the system. Furthermore, work can be done on sensitivity of the reconfigurability. By adding some more parameters in the reconfigurability function, a more accurate value of reconfigurability can be captured. The problem can be extended to account for more complex architectures of the reconfigurability function.