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Improving productivity of automated tissue converting lines: an empirical model and a case study a
Roberto Cigolini & Tommaso Rossi
b
a
Department of Management, Economics and Industrial Engineering, Politecnico di Milano, Milano, Italy b
Institute of Technology, Università Cattaneo–LIUC, Castellanza (VA), Italy
c
Piazza Leonardo da Vinci, 32; 20133, Milano, Italy E-mail:
Available online: 21 Feb 2007
To cite this article: Roberto Cigolini & Tommaso Rossi (2004): Improving productivity of automated tissue converting lines: an empirical model and a case study, Production Planning & Control: The Management of Operations, 15:5, 550-563 To link to this article: http://dx.doi.org/10.1080/09537280412331280921
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Production Planning & Control, Vol. 15, No. 5, July 2004, 550–563
Improving productivity of automated tissue converting lines: an empirical model and a case study
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ROBERTO CIGOLINI and TOMMASO ROSSI
Keywords Productivity, simulation, automated systems This study is focused on minor stoppages as sources of variance within automated production lines in industrial environments, and it suggests the handling of the problem through a combined phenomenon–mechanism analysis and simulation approach. The resulting seven-step methodological pattern has been applied to a real-life case study of a tissue converting line: the product type and the machine speed have been identified as causal factors for minor stoppages and the wrapper machine has been chosen to exemplify the methodology. Results point out that the speed of the wrapping machine– which allows the daily throughput of line to be maximized–
changes when products change, thus highlighting a trade off between minor stoppages and wrapper speed. However, in some other cases, minor stoppages are more detrimental than the machine speed is useful.
1. Introduction In today’s machine-dominated industrial environments, plants and machineries are often completely automated, thus yielding high complexity. Due to automation, invested capital has dramatically grown for-
Authors: Roberto Cigolini, Department of Management, Economics and Industrial Engineering, Politecnico di Milano, Milano, Italy; Correspondence to: Piazza Leonardo da Vinci, 32; 20133, Milano, Italy. E-mail:
[email protected]. Tommaso Rossi, Institute of Technology, Universita` Cattaneo–LIUC, Castellanza (VA), Italy. ROBERTO CIGOLINI is Associate Professor at the Department of Management, Economics and Industrial Engineering of Politecnico di Milano and lecturer in Production & Logistics Management. He graduated cum laude in Production and Management Engineering at Politecnico di Milano in 1994. From 1999 to 2002 he was Co-Director of the MBA programme at the MIP Business School and now he is Co-Director of the Facility & Property Management Master Course. He is also a founding member (2001) of the Technical Committee on Semiconductor Factory Automation (IEEE Robotics and Automation Society) and a member of the National Maintenance Commission of UNI (the Italian branch of ISO). His main research interests are primarily related to the production planning and control techniques and supply-chain management, to the evaluation of technology-related intangible resources, to the intellectual property strategies, to the facilities, property and assets management and to the project management technique, mainly in the area of modularization. TOMMASO ROSSI graduated in Production and Management Engineering at Politecnico di Milano in 2000. From 2001 to March 2004 he attended the PhD course in Industrial Engineering at the Politecnico di Milano. Since October 2002 he has been Researcher at the Department of Industrial Engineering of Universita´ Cattaneo, LIUC di Castellanza, where he runs the courses of Operations Management and Supply-chain Design. He is a member of the National Association for Industrial Plants and the National Association for Quality. His research interests concern production planning, network design, simulation and hybrid production systems.
Production Planning & Control ISSN 0953–7287 print/ISSN 1366–5871 online # 2004 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI: 10.1080/09537280412331280921
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Improving productivity of automated tissue converting lines cing many firms to undertake extended financial commitments. As a consequence, once plants have been designed for a given expected production rate, even minor stoppages due to failures, defects etc. are to be avoided, since the connected losses of production have a relevant impact on the overall manufacturing cost, and ultimately on final customers since the time the machines spend in non-productive activities reduces the time available for value generation. According to the total productive maintenance (TPM) approach, production losses can be categorised into six main areas (see e.g. Nakajima 1988, Rich 1999), i.e. (i) breakdown losses, which result from equipment defects, failures and the related repair activities, which in turn costs a great deal in terms of labour, materials etc.; (ii) set-up and equipment adjustments, which causes time losses due to the production process forced to cease; (iii) speed and slow running losses, which occur to prevent defective parts production; (iv) defective quality and re-work; (v) yield losses, which result from wasted inputs or any unused input to the production process; (vi) minor stoppages, caused by a huge number of random events. Minor stoppages are the least noticeable losses and they are often neglected due to the reduced time of each stoppage. However, they can represent a large amount of production time if considered as a whole, since they are repeated many times per day or even per shift: e.g. Kuhmonen (1997) observed, for a 17-machine job shop, more than 27,000 minor stoppages per year, which corresponded to 9,500 production hours lost, while Noe` and Rossi (2003) counted, for a 12-machine department, more than 220 minor stoppages per day corresponding to, on average, 12.5% of daily production capacity being lost. Minor stoppages are serious problem in flow-shop environments, where few operators attend paced and automated production lines (Kuhmonen and Lakso 1996, Katila 2000). The availability of the whole line is badly affected even by a very small stoppage, until an operator removes the problem: e.g. when production lines run during night shifts without operators, if a jam occurs (i.e. a product is not well positioned in the feed unit) the whole line can be stopped for the entire remaining part of the shift. However, even if production managers believe that minor stoppages must be eliminated, many companies accept these disturbances as part of normal life, mainly due to these losses being hard to detect, quantify and analyse. Thus, the aim of this paper lies in suggesting, within the general framework of the TPM approach, a methodological pattern to increase automated lines productivity by minimizing minor stoppages. In particular, after an overview about the research framework (see section 2), the model is introduced in
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section 3: it first identifies the main causes of minor stoppages; then it estimates the inter-arrival probability function referred to the minor stoppage considered as a stochastic variable; finally, the model’s effectiveness is assessed through simulation. In section 4 the proposed method is applied to a real-life case study of an automated tissue converting line, while section 5 reports some concluding remarks and suggests future research paths.
2. Background The field addressed in this study involves two main areas, i.e. TPM and simulation. TPM is a production management approach, basically oriented to maximize the overall machine productivity, to define and implement a preventive maintenance plan for the life cycle of each machine and to involve all the company functions (Rich 1999). Simulation is a decision support tool for several application fields, i.e. hardware and software design, business processes re-engineering, service organizations analysis, etc. (Kelton et al. 2002). Even though TPM is provided with almost as many interpretations as companies which adopt it (e.g. Cigolini and Turco 1997), the first two objectives of TPM recalled above consist basically in eliminating all the types of production losses. To this end, popular TPM applications are focused on operational disturbances, i.e. losses due to breakdowns (see e.g. Nakajima et al. 1988, Nakajima 1989). Most of the techniques suggested in this area are based on achieving better operators expertise (Toikka and Kuivanen 1993) and so these techniques are oriented to shorten machine’s mean downtime by reducing the number of breakdowns rather than through a quicker response in failures correction (Takashi and Osada 1990). Furthermore, TPM procedures–almost all of the ones developed by the Japan Institute of Plant Maintenance– deal with breakdowns, set-up (Culley et al. 1997), speed losses, defective quality, yield losses and minor stoppages: they apply the so-called phenomenon–mechanism (P–M) analysis (Shirose 1997), where the phenomenon represents the abnormal event to be controlled, and the mechanism represents a group of equipment elements with a common function. The basic principle of P–M analysis lies in first understanding what happens and how it happens (e.g. when a stoppage occurs or a machine produces defective parts); then causal factors can be identified and addressed, and losses can be eliminated (Shirose et al. 1995). In more detail, P–M analysis is composed of eight steps (see figure 1): first the observation and comprehension of the phenomenon has to be clarified, for which
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R. Cigolini and T. Rossi 1. Clarify the phenomenon
2. Conduct a physical analysis
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3. Define the phenomenon’s constituent conditions
Carefully define and categorize the abnormal occurrence
Describe the phenomenon in physical terms, e.g. how the parts or process conditions change in relation to each other to produce the defect or failure Identify all the conditions that will consistently produce the phenomenon
4. Study production input correlations (4Ms)
Look for potential cause and effect relations between the constituent conditions and equipment (machine, jigs and tools) materials, work methods and human factors
5. Set optimal conditions (standard values)
Review the equipment’s current precision levels to determine where new or revised standards are deficient
6. Survey causal factors for abnormalities
Using appropriate measuring methods, confirm which factors identified in steps 3 and 4 exhibit deviating conditions
7. Determine abnormalities to be addressed
Review survey results and list all abnormalities (including slight defects) to be addressed
8. Propose and make improvements
Implement a corrective measure or improvement for each abnormality, then institute operating standards and preventive maintenance procedures to maintain optimal conditions
Figure 1. Steps in P–M analysis (from Shirose et al. 1995).
precise guidelines are given. The second lies in the physical analysis, whose object is to explain how the phenomena occur in terms of physical principles and quantities.1 The third phase is the identification of the conditions either necessary or sufficient for the occurrence of the abnormal event; these conditions must be searched for in four production inputs, i.e. men, machines, materials and methods. The fourth step deals with the cause–effect relationships between conditions and production inputs, which leads to a review of the
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equipment, people, materials and methods. Step 5 is concerned with the optimal conditions for each potential source of variance, according to a road map developed by the Japan Institute of Plant Maintenance. The sixth phase leads to determine, for each causal factor, the most effective method to value the gap between actual and optimal condition, to determine the way to point out the factor at the machine location and, finally, to compare the causal factor actual value to the benchmark determined in step 5. Finally, in the seventh phase, the
In turn, it consists of four sub-steps: (i) identifying operating principles; (ii) identifying operating standards; (iii) identifying interacting elements; (iv) quantifying physical changes involved.
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Improving productivity of automated tissue converting lines factors that actually generate variance can be highlighted and (step 8) corrections and improvements can be made. Referring now to simulation, the main purpose of this technique lies in the study of complex systems: e.g. supply chains, production plants, warehouses, etc. The success of simulation as a research and management instrument is testified by numerous surveys (e.g. Lane et al. 1993, Gupta 1997) and it is due to several factors (Robinson 1994, Pidd 1998, Law and Kelton 2000): first of all, the cost, since building a model is likely to be much cheaper than experimenting with the real system. Then the time factor, since the majority of models are much faster than real time: this allows results to be evaluated as soon as the simulation run is finished, while obtaining the same from the real world would take days, weeks or even months. Then the repeatability, since experiments on a model can be repeated just by running again the model under the same conditions, while repeating an experiment in the real-life environment will not give the same outcome due to some random conditions. Then the safety, since e.g. impacts of a new factory layout should be fruitfully explored by using a model rather than by trial and error in the real world. Then the complexity, since when the real system is too complex or it does not submit to physical laws, analytic models are hard to create, and the simulation is the best choice. Finally, whenever the real system does not exist, experimenting with the real world is not an option. Even if simulation appears the most suitable tool to verify and to improve the design of operational policies (Ulgen and Upendram 2000, Williams 2000), no significant applications have been already found in TPMoriented projects and, in particular, referring to steps 5 to 8 of P–M analysis. For this reason, the innovative contribution of the methodology presented here lies in using simulation as a test-bed to try out new decision patterns for reducing minor stoppages without running the risk of experimenting on the real system.
3. Proposed model To improve productivity by minimizing minor stoppages, P–M analysis allows all the potential causes for minor stoppages to be identified. These causes often have also positive effects on other types of losses: e.g. suppose that in a flow shop minor stoppages increase with machine speed: high speed has also a positive effect on speed losses. So simulation helps to highlight the trade
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off between the losses reduced by the causal factors and the occurrence over time of minor stoppages. Recalling the example of the flow shop introduced above, the easiest way to take a decision (whether minor stoppages are more harmful than the machine speed is useful) should lie in running the considered machine at different speeds and in analysing its productivity. This may prove feasible when stand alone machines are considered and so the cost of making such tests is not relevant by comparison to the year’s production cost. However, when dealing with automated production lines, real-life experience suggests that experiments done directly on the line are infeasible, since they would take too much time and so they are too expensive: production lines are composed of many machines, each of them running at specific speed, so the number of experiments increases beyond any reasonable limit. Moreover, the effect of minor stoppages on the line’s productivity is not the sum of the losses on each machine (Cigolini and Grando 2004). Thus, due to the interactions among machines, for each combination of the machines’ speeds, a different experiment has to be done, which means that e.g. a three-machine line, each running at two speed levels (high or low), yields n23 experiments, where n represents the number of replications required to obtain an adequate data likelihood. Furthermore, such an experimental campaign should be performed for each product, which means that the number of experiments becomes untreatable in the majority real-life industrial environments and simulation appears as the only option. The methodology proposed here involves seven steps, summarized in the following. The first four phases correspond to the first four steps of P–M analysis2 (see also section 2). Step 5 consists in setting-up a statistical model capable of identifying the minor stoppages inter-arrival probability function for each value of the various causal factors. Step 6 consists in building the line model to simulate the interaction among machines. Finally, within step 7, the simulation model is run and the experimental campaign is performed according to all the configurations of the causal factors. Whereas steps 5 to 8 of P–M analysis usually lead to physical improvement of standards and to failures suppression, the proposed methodology treats variance by selecting the optimal configuration of causal factors. This management-oriented interpretation of TPM, by comparison to the traditional P–M analysis, allows to minimize minor stoppages by merely finding an appropriate combination of process parameters and
That is: (i) observation and comprehension of the phenomenon; (ii) physical analysis; (iii) identification of the conditions for the abnormal event; (iv) cause-and-effect relationships between conditions and production inputs.
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without directly modifying the line or the product. Moreover, also the use of simulation is a strength of the proposed methodology in that it allows the best causal factors settings to be figured out without performing expensive and time-consuming experiments on the real system. Before applying the method described above to a real-life case study, some methodological remarks about step 5 to 7 are required. With reference to step 5, either exponential or Weibull distribution is very useful to represent the time to failure (Mood et al. 1991, Montgomery 1999, Greene 2000): Weibull probability function is suggested since it is able to consider a variable hazard, whilst probability density of the exponential distribution is constant. To avoid biased estimators for the parameters, the maximization of the log-likelihood function3 is recommended (see also Appendix 1). Concerning steps 6 and 7, the scheme should be applied for a sound simulation study proposed by Law and Kelton (2000) and ArenaTM should be used to build the simulation model of the system (see also Law and McComas 1990, Montgomery 1991, Banks et al. 1996, Law 1999). In particular, ArenaTM combines the use friendliness of high-level simulators with the flexibility of simulation languages and with the programming features offered by the generalpurpose tools, e.g. Visual Basic, Cþþ etc. (Kelton et al. 2002).4
4. Case study The methodology outlined in section 3 has been applied to a real-life manufacturing plant belonging to the tissue converting branch of industry. The context at hand has been chosen since it is quite general: it presents problems similar to production systems belonging to several other process-oriented industries, e.g. fibre-glass, cigarettes etc. The considered case study focuses on an Italian company whose plant is composed of four automated tissue converting lines: two lines (S1 and S2) are assigned to the kitchen towel rolls production, while the others (S3 and S4) are assigned to the toilet paper rolls production. Subsection 4.1 describes the tissue converting process, while subsection 4.2 presents an in-depth analysis of the above outlined method applied to a real-life industrial case.
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4.1. Tissue converting process The so-called tissue converting process converts paper reels manufactured by a continuous paper machine into commercial-sized paper rolls (either toilet paper rolls or kitchen rolls) by using the same technology. A converting line is composed of two groups of machines: the converting machines, which convert reel into rolls, and the packaging machines, which pack rolls into commercial packs (primary packaging), then packs into bundles and put bundles onto pallets. In more detail, the machines of a standard converting line are seven, briefly described in the following. The first machine is the re-winder, which is composed of six parts: (i) the unwinder, where the parent reels coming from the upstream warehouse are positioned for unwinding; (ii) the core winder, which manufactures a cardboard tube (core) on which the tissue web will be wound; (iii) the compressing unit, where the web is compressed between two cylinders: pressure transfers the pattern of the steel cylinder on the web sheet; (iv) the printing unit, where words, logos, even pictures etc. can be lined, since the web passes through rolls which bear the cliche´ to be printed; (v) the re-winder, i.e. the heart of the converting line: it unwinds the parent reel and rewinds it into smaller logs with the same width as the parent reel and the diameter of the finished product; the re-winder also perforates the tissue web at predetermined intervals, it checks the sheets contained in each log and the log diameter; (vi) the tail sealer, which seals the final log tail coming from the re-winder with a line of glue, easily visible at the start of a new tissue roll. The second machine is the accumulator which collects the sealed logs in appropriate channels connected by a chain. If either upstream or downstream machines are stopped, the accumulator instructs the production process to stop. The third machine, i.e. the lag saw, cuts the logs to the desired length by means of a circular rotating blade. Then the logs are sent through a conveyor to the downstream packaging machine. The fourth machine is the (optional) diverter, which allows roll flow to be balanced whenever more than one packaging line is placed downstream of the re-winder. The fifth machine, i.e. the wrapper, wraps the rolls in the pack they will be sold in. An (optional) handler can be placed downstream, to apply a handle to the pack; the finished packs are sent by a conveyor to the downstream bundler,
The maximization of the likelihood function can be conducted by means of specific econometric software tools (e.g. RatsTM), or through the ExcelTM solver tool, which has been employed to obtain the results presented in section 4. 4 ArenaTM contains also a statistic toolbox which allows several probability functions (including the Weibull one) to be very easily modelled.
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Improving productivity of automated tissue converting lines i.e. the sixth machine, which puts the packs in appropriate bundles. Finally, the pallet-maker (i.e. the seventh machine) builds pallets with the bundles coming from an upstream conveyor. The process studied through the proposed methodology and modelled via simulation refers to line S4, which is not provided with any accumulator and is equipped by two packaging units: the former one is employed to produce big-sized packs, while the latter one to produce small-sized packs. When a packaging line works, the other one experiences the so-called standby status. Therefore, the diverter is used just to switch the production flow from a packaging line to the other one. Moreover, since the machines are very near each other, all the conveyors can be considered as mere decoupling buffers, according to the ASME diagram reported in figure 2. Finally,
Paper reels warehouse
Rewinder
Lag saw
Diverter
BPW input conveyor
SPW input conveyor
Big packs wrapper (BPW)
Small packs wrapper (SPW)
BPW output conveyor
SPW output conveyor
Bundler 1
Bundler 2
Palletizer input conveyor
Palletizer
Pallets warehouse
Figure 2. ASME diagram of the tissue converting line S4.
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four operators look after line S4: two of them attend to the rewinding unit, while the others operate on the packaging units.
4.2. Proposed model application To allow an easier understanding of the methodological pattern followed, without lacking generality, only the small-sized packs wrapper machine of the tissue converting line S4 is supposed to be plagued by minor stoppages. First of all (step 1 of the P–M analysis), the phenomenon, i.e. the minor stoppages occurrence on the wrapper, has to be clarified. According to Shirose et al. (1995), in industrial environments such as line S4, minor stoppages are shorter than 15 minutes, and they take place during some specific machine operations, e.g. elevation, wrapping and unloading, but not always under the same circumstances, i.e. during the morning start-up, in neighbourhood of a changeover or after long runs. Moreover, the time interval between two consecutive stoppages is uneven and no significant differences can be pointed out, in minor stoppages frequency, between regulartime and overtime or between shifts covered by different teams of operators. Step 2, i.e. explaining the phenomenon in terms of physical principles, has been carried out for the wrapper operations during which minor stoppages occur, i.e. elevation, wrapping and unloading, and is summarized in tables 1, 2 and 3. Step 3 consists in identifying the conditions for the phenomenon occurrence. In the wrapper case, these conditions refer to the rolls-on-the-bearing-plate-in-wrong-position machine status and to the standby-position-occupied (i.e. output conveyor full) machine status. Step 4, which allows the causal factors to be identified, is synthesized in figure 3, where the wrapping machine speed is measured in strokes per minute, since each stroke corresponds to an elevation and, as a result, to one roll pack wrapped. At first sight, the relationship between the machine speed (i.e. the causal factor) and output-conveyor-full status (i.e. the constituent condition) is intuitively clear: if the machine wraps a number of roll packs greater than the capacity of the output conveyor, the latter one will be full. The same is not true for the relationship between the product type and the machine speed (i.e. the causal factors) and the rolls-in-wrong-position status (i.e. the constituent condition). However, during the elevation, the rolls are never constrained but only supported by the moving parts, which inherently generates instability condition, due to the behaviour of the tissue rolls during the deceleration of the bearing plate during the pack elevation from the store to the wrapping area. The higher the plate deceleration, the higher the probability that
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R. Cigolini and T. Rossi Table 1. Operating principles and standards in the wrapping process.
Operation
Elevation Stroke end plate
Operating principle
Operating standard
The elevator, through a bearing plate, transports the tissue rolls from the store to the wrapping area. In the latter a stroke end plate is present to stop the pack.
(1) Cause of high productivity required the elevation must be completed in a very short time. Thus several elevations are executed per minute. (2) The bearing plate must reach the wrapping area. (3) The detachment of the rolls from the plane must be avoided or at least limited.
In the wrapping area the rolls on the bearing plate are wrapped with the packaging film, which is cut and then electrically soldered to give the final package.
(1) Bearing plate in the wrapping area. (2) Rolls on the bearing plate must be in the right position. (3) Availability of the packaging film. (4) Equipment for the electric solder must work.
Rolls
Bearing plate
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Elevator
Wrapping Wrapping area Packaging film Rolls Bearing plate
Unloading Rolls pack
After the wrapping operation the wrapper unloads the rolls pack in the standby position (the first part of the output conveyor).
(1) The unloading equipment must work. (2) The standby position must be free (the standby position is occupied only when the whole output conveyor is full).
Stand-by position
the tissue rolls will have stability problems; the higher the number of strokes per minute (i.e. the elevation speed), the higher the deceleration value (Gasperini and Zagnoni 2000). Furthermore, not all the products react in the same way to the same deceleration values, so another causal factor for the rolls-in-wrong-position status is the product type. Step 5 of the proposed methodology consists in estimating the Weibull distribution that represents (for each combination of causal factor values) the stochastic inter-arrival process of minor stoppages on the wrapping machine due to the rolls-in-wrong-position status (taken as the constituent condition).5 The estimate of the
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Weibull parameters (i.e. and ) has been conducted by maximizing the log-likelihood function with reference to two products (hereinafter called A and B) and to the machine speed values appropriate to them, i.e. 55, 60 and 65 strokes per minute and 130, 135 and 140 strokes per minute, respectively. The required historical times to failure series have been supplied by the wrapper PLC. For each couple of product type and machine speed, the correct estimators of the parameters are reported in table 4. Broadly speaking, the activities described above would have to be conducted for each machine of the tissue converting line S4 interested in minor stoppages
The effects of the output-conveyor-full status (i.e. the additional constituent condition) have been taken into account directly in the structure of the simulation model; see Appendix 2 for further details.
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Improving productivity of automated tissue converting lines Table 2. Interacting elements related to abnormal phenomena on the wrapper. Abnormal phenomenon
Diagram
Interacting elements Rolls, bearing plate
Bearing plate
Rolls
Rolls pack, standby position
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Minor stoppages (stops with a duration 15 min)
Output conveyor
Rolls pack Standby position
Table 3. Wrapper abnormal phenomena and quantifiable change. Abnormal phenomenon (diagram)
Interacting elements
Quantitative physical changes
Rolls, bearing plate
. Distance (a) . Distance (b)
Rolls pack, standby position
. Surface (S)
b a
S
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Physical analysis
Constituent conditions
Causal factors
Product type
Rolls in wrong position
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Physical analysis (see tables 1, 2 and 3)
Machine speed
Output conveyor full
Machine speed
Figure 3. The cause-and-effect chain concerning the wrapper.
phenomenon, even though different equipment will correspond to different constituent conditions and so to different causal factors and different distributions. Now step 6 of the proposed methodology can take place. It deals with building the simulation model of the S4 tissue converting line: only the wrapper has been considered and the model (built by using the ArenaTM meta-language) allows the evaluation of the tradeoff between the performance influenced by causal factors (i.e. the production rate) and the minor stoppages that plague the wrapping machine. A deeper description of the simulation model is presented in Appendix 2. These tradeoffs affect the throughput rate of the tissue converting line, since the throughput rate is the system performance considered to evaluate the minor stoppages effect within step 7 of the proposed methodology, i.e. the experimental design and the analysis of results. In this phase, for each value of the wrapper speed, 10 replications of the simulation model have been conducted. Each run represents a working day (i.e. eight hours) in the considered industrial environment. No Welch procedure has been executed and, as a consequence, no warmup period has been defined. The length of the simulation run has been obtained by considering both the terminating nature of the context at hand and the selected output variable (i.e. the daily throughput). The results of each replication (i.e. the 10 daily throughputs of line S4 expressed in number of pallets) have been used to determine the 95% confidence interval for the daily throughput of line S4 intended as a random variable. Table 5 summarizes the overall results for each product.
Table 4. Results of the Weibull parameters estimate referred to the wrapper Product A B
Speed (strokes/min)
b
g
55 60 65 130 135 140
0.99 0.69 1.50 0.96 1.10 1.11
10.61 8.58 2.97 6.68 5.94 4.58
Table 5. Results of the simulation campaign. Product A B
Speed (strokes/min) 55 60 65 130 135 140
0.95 interval (no. pallets/day) (114.89, (122.32, (54.79, (197.36, (190.13, (166.95,
128.71) 146.27) 62.01) 219.44) 210.67) 189.65)
Referring to table 5, notice that the optimal speed of the wrapping machine–i.e. the speed which allows the daily throughput of the tissue converting line S4 to be maximized–corresponds to 60 strokes per minute for product A and to 130 strokes per minute for product B. This means that simulation pinpointed a machine status for product A which represents a compromise between the minor stoppages occurrence and the wrapper speed. On the contrary, simulation highlighted that for product
Improving productivity of automated tissue converting lines B minor stoppages are more harmful than the machine speed is useful.
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5. Concluding remarks The study presented here is focused on automated production lines and it proposes a throughput rate optimization methodology based on simulation and on the idea of minimizing the impact of minor stoppages. The proposed methodology is composed of seven steps: the first four steps correspond to the first four steps of the classical phenomenon–mechanism (P–M) analysis, which are actually oriented to point out the causal factors of minor stoppages. Steps 5 to 7 deal with: a statistical model capable of describing the behaviour of the line; a simulation model of the line to understand how machines interact; and an experimental campaign based on the causal factor configurations to find out the best one. Machine modelling and line simulation have been introduced due to the complex interaction among machines of automated lines (i.e. every time a machine stops, also downstream or upstream machines may stop sooner or later, depending on the size of the decoupling buffers and on the machines’ speed). The proposed methodology has been applied to a reallife case study of a tissue converting line, taken under observation for one month. This allowed the product type and the machine speed to be identified as causal factors for the minor stoppages occurrence on the wrapper machine, i.e. the machine chosen to exemplify the methodology. Then, the occurrence of minor stoppages due to the output-conveyor-full status has been implicitly considered in the structure of the simulation model, while for each combination of the causal factors, the historical data referred to the rolls-in-wrong-position status6 have been used to estimate the Weibull distribution which models the minor stoppages occurrence on the wrapping machine. Finally, the simulation model of the considered line has been developed and validated, and the simulation experiments are carried out: they have been used to identify the optimal causal factor values, i.e. the wrapper speed which maximizes the line daily throughput. As a consequence, this study highlighted the importance of minor stoppages as sources of variance within many real-life manufacturing environments. On the other hand, it suggested to handle the problem through a combined P–M analysis and simulation methodological pattern. For this reason, the proposed methodology will be applied to investigate the minor stoppages
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phenomenon in a fibre-glass production system to improve its productivity. Here the use of non-standard statistical distributions will also be evaluated. For this reason, autoregressive conditional duration models are under preliminary study to represent the minor stoppages occurrence.
Appendix 1 The log-likelihood function for a Weibull distribution is given by 1: " # Fe X Ti 1 ðTi =Þ logðLÞ ¼ ¼ Ni log e i¼1 I X S FI X Ti I Ni þ NiII i¼1 i¼1 h i II II log eðTLi =Þ eðTRi =Þ ð1Þ where: Fe ¼ number of groups of times to failure available data; Ni ¼ number of times to failure in the ith time to failure data group; ¼ Weibull shape parameter (unknown a priori, the former one to be found); ¼ Weibull scale parameter (unknown a priori, the latter one to be found); Ti ¼ time of the ith group of time to failure data; S ¼ number of groups of suspension data; NiI ¼ number of suspensions in ith group of suspension data; TiI ¼ time of the ith suspension data group; FI ¼ number of interval failure data groups; NiII ¼ number of intervals in the ith group of data intervals; TiII ¼ beginning of the ith interval; II TRi ¼ ending of the ith interval. In the case of non-grouped data with no suspensions or intervals, i.e. completed data, (1) becomes (2): " # N X Ti 1 Ti logðLÞ ¼ ¼ log e ð2Þ i¼1 where N is the number of times to failure and Ti is the time of the ith time to failure. The equations for the
A sensor detects a roll turned over on the wrapper-bearing plate and it stops production.
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R. Cigolini and T. Rossi the condition which allows the waiting-for-processing status to be left and the processing status to be reached lies in the items-to-process event. The events that allow the wrapper to pass from the processing status to the waiting-for-minor-stoppage-ending status and vice versa are roll-in-wrong-position (or output-conveyor-full) and minor-stoppage-duration-ended (or output-conveyornot-full) respectively. The physical simulation model has been built by means of the ArenaTM meta-language, by considering rolls as temporary entities and by de-composing the whole structure in four main sub-models. The first submodel allows both the re-winder and the saw to be represented; the second one simulates the wrapping machine and its output conveyor; the third one models the bundler; finally, the fourth sub-model simulates the palletizing machine. Since the line gateway (i.e. the re-winder) is not plagued by any kind of stoppage, it is simply modelled by a ‘create’ block which introduces in the system 624 rolls per minute. The other machines are represented by means of the classical sequence of ArenaTM blocks, i.e. ‘seize, delay & release’ blocks, which allow the resource to be loaded, the operation to be executed and the machine to be released respectively. Within the ‘delay’ blocks, different machines are provided with different operating times, given by the inverse of the machine speed expressed in strokes per minute.
partial derivatives of the log-likelihood function are (3) and (4): X N N @ N X Ti Ti T ¼ þ log log i ¼ 0 ð3Þ @ i¼1 i¼1 N @ X Ti ¼ :N þ : ¼0 @ i¼1
ð4Þ
The simulation model of the tissue converting line S4 is based on the logical scheme represented in figures 4 and 5. The IDEF0 diagram highlights all the simulated items, i.e. not only all the machines of the line but also the wrapper output conveyor, which actually operates as decoupling buffer (see subsection 4.1). Thus, the outputconveyor-full status is a constituent condition of the minor stoppages abnormal phenomenon. Moreover, the activities cycle diagrams of the machines of line S4 makes clear that the minor stoppages occurrence has been considered only with reference to the wrapper (see subsection 4.2). The condition which allows both a generic machine and the wrapper to pass from the processing status to the waiting-for-processing status lies in the no-items-to-process event. On the contrary, SPW output conveyor full? Pallets
Rewinder Saw Small packs wrapper Bundler 2 Palletizer SPW output conveyor
Saw
Rewinding
Rewinder
Logs
Rewinder
Cutting
Saw
Rolls
Wrapping phase
Packs
Small packs wrapper Output conveyor SPW output conveyor full? Wrapping
Small packs wrapper
Bundling
SPW output conveyor
Pallets
Palletizer
Bundler 2
Waiting
Palletizing
Bundling
Bundler 2
Figure 4. IDEF0 diagram of the tissue converting line S4.
Palletizing
Palletizer
Pallets
Cutting
Bundles
Logs
Packs
Rewinding
Rolls
Paper reel
SPW output conveyor full? Bundles
Tissue converting process
Packs
Paper reel
Paper reel
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Appendix 2
Improving productivity of automated tissue converting lines (a)
(b)
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Waiting for minor stoppage ending
Processing
Processing
Waiting for processing
Waiting for processing
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Figure 5. Activities cycle diagram of a generic machine in the line S4 (a) and activities cycle diagram of the wrapper (b).
The wrapper output has been modelled by means of a ‘queue’ block and, to simulate in an appropriate manner its finite capacity and–as a consequence–the occurrence of minor stoppages due to the output-conveyor-full status, the ‘release’ block is preceded by a ‘branch’ block (to verify whether the conveyor capacity is exceeded) and by a ‘wait’ block which allows the entity not to leave the wrapper (that remains busy and not available for the next entity to be processed) if the buffer capacity is exceeded. The minor stoppages occurrence due to the rollsin-wrong-position status have been considered in the definition of the wrapper resource, due to the ArenaTM feature that allows the time to failure and (mean) time to repair of each resource to be defined. In this case the time to failure has been represented by Weibull distributions (one for each wrapping machine speed), while the mean time to repair has been expressed by a uniform distribution between 5 and 15 minutes. In the following, each block which the simulation model is composed of is presented in detail. (1) Create: it represents the re-winder since the latter is not affected by the minor stoppages phenomenon. Every 0.0016 minutes this block allows an entity ‘roll’ to be introduced in the system. The interval value has been calculated from the re-winder production rate: in 0.167 minutes the machine at hand is able to process four logs obtaining, for each of them, 26 rolls. (2) Group: it allows 26 rolls to be grouped (each group represents a log). (3) Group: it allows four temporary groups coming from (2) to be grouped. Practically, blocks (2) and (3) allow 104 rolls to be contemporary available every 0.167 minutes.
(4) Split: it splits the temporary groups coming from (3) in four groups. (5) Split: it splits the temporary groups coming from (4) in 26 entities ‘roll’. (6) Seize: it allows the resource ‘saw’ to be occupied by a single entity ‘roll’. (7) Delay: this block simulates the time each roll must spend on the saw machine (i.e. 0.01 minutes). (8) Branch: it verifies if the wrapper input-conveyor is full or not. In the former case (nq(wrapper_ conveyor_in)>¼520), the roll cannot be put on the conveyor at hand but remains on the saw machine occupying it (as a consequence, the entity ‘roll’ is sent to the ‘wait’ block 9). In the latter case (nq(wrapper_conveyor_in)¼10), the pack cannot be put on the conveyor at hand but remains on the wrapper machine occupying it (as a consequence, the temporary grouped entity is sent to the ‘wait’ block 19). In the latter case (nq(wrapper_conveyor_ out)¼5), the bundle cannot be put on the conveyor at hand but remains on the bundler machine occupying it (as a consequence, the temporary grouped entity is sent to the ‘wait’ block 29). In the latter case (nq(bundler_ conveyor_out)
