wijaya10[1]

Graphical Method for Visualization of Machine’s Downtime (Case study of Scaling Machine)

Andi R. Wijaya Mechanical & Industrial Engineering Gadjah Mada University, Indonesia Div. of Operation & Maintenance Engineering, Luleå University of

Technology, Sweden

[email protected]

Jan Lundberg Division of Operation and Maintenance Engineering

Luleå University of Technology Luleå, Sweden

+46 (920) 491748

[email protected]

Uday Kumar Division of Operation and Maintenance Engineering

Luleå University of Technology Luleå, Sweden

+46 (920) 491826

[email protected]

ABSTRACT Visualization is the foundation for human to understand as human think and create in a graphic world. By nature, maintenance activity is a multi discipline approach, where maintenance engineer should be able to convey their idea to people with various backgrounds. In this situation, visualization is a powerful mode; it can act as a bridge to eliminate the knowledge gap within the group. Knight (2001) developed Jack-knife diagram for visualizing total downtime and factors influencing the failure (failure frequency and mean downtime) in a point estimation. As failure data is a probabilistic in nature, it is important to look not only point estimation but also interval estimation, so the precision and uncertainty of estimation can be identified. This paper proposes a way of visualizing total downtime and factors influencing the failure (failure frequency and mean downtime) in interval estimation. Case study from scaling machines is used for illustration.

Keywords Graphical method, Jack-knife diagram, Interval estimation.

1. INTRODUCTION A quote from Aristotle ‘Now we have already discussed imagination in the treatise On the Soul, and we concluded there that thought is impossible without an image’. It emphasizes that visualization is the foundation for human to understand as human think and create in a graphic world. Presenting data in visual form (graphs, pictures and diagrams) can enhance data comprehension, decision-making and communication of data information (Roth and Bowen, 2003; Tory and Möller, 2004). The reason is due to stimulation of cognitive processes (visual chunking, mental imagery and parallel processing) and reduction in cognitive load (Winn, 1994; Card et al, 1999). By nature, maintenance activity is a multi discipline approach, where maintenance engineer should be able to convey their idea to people with various backgrounds. The key success in this type of situation is relying on how to communicate. Communication is only successful when both the sender and the receiver understand the same information as a result of the communication. It is widely accepted that visualization can improve the effectiveness of the communication. It can act as a bridge to eliminate the barrier of knowledge gap within the group. In a study on effective

communication within the organization, Yates (1985) found that the use of graphs as a managerial tool is one of the key success. Purpose of this study is to develop a graphical method that can be used as visual communication tool for maintenance engineering in communicating to people with various backgrounds.

2. DATA VISUALIZATION Data visualization is a process of converting raw numerical data into graphical depiction of the data. The goal is to support decision making through the use of properly designed graphical representation of information. Verbal and numeric cues are insufficient to trigger some insight into the specific nature of the problem (Larkin and Simon, 1987). Presenting data in graphics helps to break a mental block by providing a memory structure to aid the decomposition of information in the problem (Lohse, 2001). Schmid (1954) has been summarized the advantage of graphs as compared with textual and tabular forms as follow;

1. Graphs are more effective in creating interest and in appealing to the attention of the reader

2. Visual relationships, as portrayed by graphs, are more clearly grasped and more easily remembered.

3. It saves time, since the essential meaning of large masses data can be visualized at a glance

4. It can provide a comprehensive picture of a problem that makes possible a more complete and better-balanced understanding.

5. It can bring out hidden facts and relationships and can stimulate analytical thinking and investigation.

This superiority of graphs over textual and tabular forms makes graphs as major components in recent science reform documents (Friel, Curcio and Bright, 2001). In maintenance engineering, however, the development of the graph for data visualization is not significantly developed. In most publication related to maintenance, a classic Pareto diagram still be utilized for presenting failure data despite of its deficiency (Lin and Titmuss, 1995; Ashraf, et al, 1998; Hennessy, 2000; Platfoot, 2000; Kortelainen, et al, 2003; Das, 2005). Knight (2001) pointed out three shortcomings of Pareto analysis in maintenance engineering application. First, where an outcome is a product of two factors, a Pareto diagram based on one factor alone cannot determine which factor is dominant in contributing to the problems. Second, by focusing on any one factor to the exclusion of others, it may miss identifying individual events having high time consumption, or those that may consume relatively little

The 1st international workshop and congress on eMaintenance 2010, 22-24 June, Luleå, Sweden

99 ISBN 978-91-7439-120-6

average time but have the ability to cause operational disturbances. Third, Pareto diagram is not useful for trending comparisons across different time periods. To overcome these shortcomings, Knight have developed Jack-knife diagram. In his method, number of failure and mean downtime is plotted in a logarithmic scatter plots. Plotting in logarithmic allow a constant downtime to be appeared as a constant straight lines with uniform negative gradient. It still reserves the basic information of Pareto diagram (to highlight the most contributed downtime) and enables identification of the dominant factors influencing the failure (failure frequency and mean downtime). In his method, downtime is presented as a single value (point estimation). In the last decade, presenting data as point estimation is considered to be insufficient (Altman et al, 2000; Curran-Everett, 2004; Council of Science Editors, 2006). Presenting estimation should also be accompanied by the precision and the uncertainty of the estimation. As failure data is a probabilistic in nature, it is essential to see also the reliability of an estimate (Gardner and Altman, 2000). Two components might have same value of downtime, but at a given confidence level their interval might differ significantly. Thus it is important in visualizing failure data to show not only point estimation but also the interval estimation, so the precision of estimation and the uncertainty of the estimation can be identified.

3. INTERVAL ESTIMATION In this study, interval estimation is determined by using the assumption that failure times have Weibull distribution and the repair times have lognormal distribution. It is well known that failure times are often modeled with Weibull distribution (Abernethy, 2000; Wiseman, 2001; Schroeder and Gibson, 2006). About 85% - 95% of all failures data are adequately described with Weibull distribution (Barringer, 2009). The reasons are that Weibull distribution has the ability to provide reasonably accurate failure analysis with small sample size and it has no specific characteristics shape and depending upon the values of the parameters it can adapt shape of many distributions (Abernethy, 2000). The shapes of the Weibull distribution for a different shape parameter are shown in figure 1.

Figure 1. Weibull Distribution

It also known that lognormal distribution is widely used to model repair times (Rausand and Høyland, 2004; Bovaird and Zagor, 2006; Schroeder and Gibson, 2006). About 85%-95% of all repair times are adequately described by log normal distribution (Barringer, 2009). The skewness of the lognormal distribution with a long tails to the right fit to represent the repairment situation. In a typical repairment situation, most of the repairs are completed in a small time interval but in some cases it can take

much longer times. The shapes of the lognormal distribution for different parameters are shown in figure 2. The probability density function of Weibull distribution is given as

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛=

− ββ

ηηηβ yyyg exp)(

1

, 0>y (1)

where β > 0 is the shape parameter and η > 0 is the scale parameter of the distribution. The expected value, in this case is Mean Time between Failure (MTBF), is given by

ηβ

μ ⎟⎟⎠

⎞⎜⎜⎝

⎛+Γ== 11)( yYE (2)

Figure 2. Lognormal Distribution

The probability density function of lognormal distribution is given as

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

−=2)ln(

21exp

21)(

σμ

πσx

xxf , 0>x (3)

where μ and σ are the mean and standard deviation of the variable’s natural logarithm. The expected value, in this case is Mean Time to Repair (MTTR), is given by

⎥⎦⎤

⎢⎣⎡ +== 2

21exp)( σμμ xXE (4)

Let the total life time of component defined as Total time = DT + UT (5) where DT is downtime and UT is uptime, and MTTR and MTBF is given by

m

DTMTTR = (6)

m

UTMTBF = (7)

where m is number of failures. For a given uptime, downtime can be formulated by using equation (6) and (7) as

UTMTBFMTTRDT = , (8)

Since the failure time distribution is Weibull and the repair time distribution is lognormal, equation can be rewritten as


100 ISBN 978-91-7439-120-6

UTDTy

x

μμ

= , (9)

and interval estimation for downtime can be determined by finding a confidence interval for YX μμ . The confidence interval can be determined by an approximate method and an exact method. In the approximate method, the confidence interval is determined by establishing confidence intervals for xμ and

yμ

to obtain an “at least” type confidence interval. In exact method, the confidence interval for YX μμ is established simultaneously. The exact confidence interval is more accurate than approximate the confidence interval. Another advantage is that since the confidence interval is solved simultaneously, the result can be treated as a single dimension rather than two dimensions. By adopting procedure developed by Masters et al (1992), the exact confidence interval for YX μμ is given by

py

Xb

y

XaP

m

ii

G

y

x

m

ii

G

=

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛+Γ

⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅<<

⎟⎟⎠

⎞⎜⎜⎝

⎛+Γ

⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅

∑∑=

−

=

−

1

1

2

1

1

2

211

2exp

211

2exp

βββ

βββ

ηβ

σ

μμ

ηβ

σ (10)

which implies a 100p% confidence interval for DT is

UTy

XbDTUT

y

Xa

m

ii

G

m

ii

G

⋅

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛+Γ

⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅<<⋅

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛+Γ

⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅

∑∑=

−

=

−

1

1

2

1

1

2

211

2exp

211

2exp

βββ

βββ

ηβ

σ

ηβ

σ (11)

where

GX = geometric mean of lognormal distribution

η = scale parameter of Weibull distribution y = time between failure σ = standard deviation of time to repair’s natural logarithm β = shape parameter of Weibull distribution a = constant for lower limit b = constant for upper limit

To establish a 100p% confidence interval for DT, the value for a and b has to be determined so that

[ ] pdwwgbwaPb

a

==<< ∫ )( (12)

The cumulative distribution function (cdf) of W for a given value of b (the probability of the even that W is less than or equal to b) can be computed as follow

( )∫ ∫ −∞

⎥⎦

⎤⎢⎣

⎡−−

Γ=

bn

mdwdzwzwzzn

m

n

bG0

1

0

22

2

21ln

2exp

22)()(

βπβ (13)

where m = number of failures n = number of repairs.

Tables of G(b) for selected values is presented in table 1.

Table 1. Factors for Computing Confidence Interval of Down Time

(Gray and Lewis, 1967)


101 ISBN 978-91-7439-120-6

4. CONFIDENCE JACK-KNIFE DIAGRAM In this study, a new way of presenting failure data is developed allowing a visualization of the downtime estimation that are accompanied by the precision and the uncertainty of the estimation at a given confidence level. As the proposed diagram is developed based on the jack-knife diagram, hence it shall be referred as a confidence jack-knife diagram. A confidence Jack-knife diagram is presenting as log-log graph (both the vertical and horizontal axis of a plot is scaled logarithmically). The horizontal axis represent time to repair and the vertical axis represent number of failures. Downtime is determined by the multiplication of time to repair and number of failures. As the diagram is presenting in log-log graph, a curve of a constant downtime can be presented as a straight lines with uniform negative gradient, see figure 3.

Figure 3. Confidence Jack-knife Diagram To establish confidence jack-knife diagram, three estimation points should be determined. These three points are mean, upper limit and lower limit of downtime. The mean downtime for a given uptime is determined from equation (8), and the upper limit and lower limit of downtime are determined from equation (11). Prior calculation, level of confidence should be decided. The choice for the level of confidence is somewhat arbitrary, in practice values of 90%, 95% and 99% are often used (Snedecor and Cochran, 1989). After the three estimation points are determined, the next step is to determine their coordinates in the diagram. The coordinates for the mean downtime, abscissa (time to repair) is MTTR and ordinate (number of failures) is determined as

MTBF

UTmmean = (14)

For lower limit and upper limit of downtime, abscissa is provided by equation below

[ ]MTTRDTDT

LmeanLTTR logloglog10 +−= (15)

where TTRL = time to repair of limit (upper or lower) DTL = downtime of limit (upper or lower) DTmean = mean downtime

and ordinate is determined as

L

LL TTR

DTm = (16)

The interval estimation is then established by connecting these three points with a straight line, see figure 3.

5. APPLICATIONS AND EXAMPLES To give an illustration on how to construct a confidence jack-knife diagram and how it can be applied, two examples are given bellow. Example 1 In this example, confident Jack-knife diagram is used for visualization of downtime that can be used as an aid for prioritization of significant components. Data of unplanned downtime for scaling machine is presented in table 2. Failures data and repairs time data are sorted in ascending order. Confident Jack-knife diagram is constructed for a given uptime of 8000 unit time and a confidence interval of 90%. Step by step for plotting component A on jack-knife diagram is providing as follow; 1. First step is determining the downtimes (mean, upper and

lower limit). Mean downtime (DTmean) is calculated by equation (8) and for uptime (UT) = 8000, MTBF = 942.09 and MTTR = 4.88, it gives 41.52. Upper and lower limit of downtime is calculated by equation (11). Prior the calculation of upper limit of downtime (DTUL), value for b should be determined first. Since number of repairs (n) = 10, and σ = 0.91, then n/σ2 = 12.12 and number of failures (m) = 9. From table 1, if n/σ2 = 10, G(b) = 0.95, and m = 9, then b = 39.427. If n/σ2 = 15, G(b) = 0.95, and m = 9, then b = 36.897. By using linear interpolation, b is approximately 38.61. DTUL is calculated for b = 38.61, σ = 0.91,

GX = eμ = e1.17 = 3.23, β = 0.83, and η = 850.89 that gives 104.2. Similar procedure applied for calculation of lower limit of downtime (DTLL). From table 1, if n/σ2 = 10, G(b) = 0.05, and m = 9, then b = 8.9081. If n/σ2 = 15, G(b) = 0.95, and m = 9, then b = 9.4707. By using linear interpolation, b is approximately 9.09. DTUL is calculated for b = 9.09, σ = 0.91,

GX = eμ = e1.17 = 3.23, β = 0.83, and η = 850.89 that gives 24.54.

2. Second step is determining the coordinates of the three downtimes. For DTmean abscissa is MTTR (4.88) and ordinate is calculated by equation (14), for UT = 8000 and MTBF = 942.09, then mmean = 8.49. Abscissa of DTUL and DTLL can be determined by equation (15). For DTLL = 24.54, DTUL = 104.2, DTmean = 41.52 and MTTR = 4.88, then TTRUL = 7.4 and TTRUL = 3.5. Ordinates of DTUL and DTLL is determined by equation (16) that gives mLL = 6.1 and mUL = 12.8.

3. Third step is establishing interval estimation by connecting the three estimation points by a straight line.

Following similar procedure, the rest of component can be plotted in the diagram. A diagram for components of scaling machine is shown in figure 4.


102 ISBN 978-91-7439-120-6

Figure 4. Confidence Jack-knife diagram for components of scaling machine

From figure 4, it can be observed that presenting in interval estimation provides better insight into the hidden fact of the data than presenting in point estimation. For example in the prioritization of significant components based on downtime, it visualize that two different orders of the rank can be constructed. The order of significant components based on the mean estimation (likelihood) and lower limit estimation (best scenario) is B, E, F, C, H, A, G, D, while based on the upper limit estimation (worst scenario) is B, H, E, C, F, A, G, D. This kind of

information is needed especially for certain activities where the decision should be based on three scenarios (optimistic, most likely and pessimistic), eg. planning and budgeting of maintenance activities.

In some cases, the maximum downtime is limited to certain value and in this regards it is important to know how likely that the downtime of components exceed that limit. Suppose that due to the consequences of the failure, it is decided that limit for the maximum downtime is 300 unit time and it is demanding that the maximum probability of error is 5%. Then it can be seen from figure 4 that component B, E and H at the confidence level of 95% will exceed the limit.

Since in the confidence Jack-knife diagram, the downtime is presenting as a function of time to repair and number of failures it also visualizes the reliability and maintainability issues. It shows which components that need to be improved their reliability or/and maintainability. In figure 4, it shows that the high downtimes of component B, F, E and C are mainly due to the reliability problem (high value for the number of failures), while the high downtime of component H is mainly due to maintainability problem (high value for the time to repairs).

Suppose the smoothness (uninterrupted) of the operation is taken into consideration in the prioritization of significant components. For the similar value of downtime, a high frequent of interruption with a short duration is less favor than a low frequent of interruption with a long duration. Then it can be seen in the figure 4 that in comparing the components of F, E and H, which have approximately equal mean downtime, a higher priority should be given to components F and E than component H.

Example 2.

In this example, confidence Jack-knife diagram is used to visualize the effectiveness of design alternatives in reducing

Table 2.Failure data of scaling machine


103 ISBN 978-91-7439-120-6

downtime. In practice, strategy of redesign for reducing downtime can be classified into three strategies, they are;

a. Design out Maintenance (DOM), in this strategy, aim is to improve reliability of the product so the number of failures are reduced but the time to repairs are remain constant,

b. Design for Maintenance (DFM), in this strategy, aim is to improve maintainability (how ease to maintain) of the product so the time to repairs are reduced but the number of failures are remain constant,

c. Combination of DOM and DFM, in this strategy, aim is to improve both maintainability and reliability of the product.

To give an illustration, a set of artificial data is generated portraying a typical design improvement scenario. Distribution fitting of failures data of mechanical component shows that time to fail fit to Weibull distribution with β = 2.0, η = 565.5 and MTBF = 501.1 and time to repair fit to lognormal distribution with μ = 3.05, σ = 0.47 and MTTR = 23.57. For an uptime of 11000 unit time, it gives a mean downtime of 517.4 unit times. To reduce downtime, five alternative designs have been developed. The first two designs (design A and B) adopted DOM strategy, thus attempt is to increase MTBF by keeping a constant MTTR. The second two designs (design D and E) adopted DFM strategy, thus attempt is to reduce MTTR by keeping a constant MTBF. The third design (design C) adopted a combination of DOM and DFM strategy. Trial test have been conducted to evaluate the effectiveness of the alternative designs in reducing downtime. Results of the trial test (given in ascending order) are shown in table 3.

Table 3. Results of trial test of design alternatives

From the table 3, it can be calculated that all five alternatives designs have an equal ratio of MTTR/MTBF, approximately 0.035. It indicates that all design alternatives have an equal mean downtime. For an uptime of 11000 unit times, it gives a mean downtime of approximately 386.5 unit times which is lower than the current design (517.4 unit times). A question arise is which design alternative should be employed. Confidence Jack-knife diagram is used to visualize the effectiveness of the five design alternatives. Following similar procedure as example 1, the diagram is constructed, as shown in figure 5.

Figure 5. Confidence Jack-knife diagram of design alternatives

From figure 5, it shows that though the five design alternatives have an equal mean downtime but their 95% confidence interval are varied significantly. In case of lower limit (best scenario), a discrepancy of approximately 40 unit times is observed, while in case of upper limit (worst scenario), a discrepancy of approximately 200 unit time is observed.

By just considering the downtime, design B might be the best alternative, as it has the lower value of the downtime at the worst scenario. However the stability of the strategies (DOM or/and DFM) should also be taken into consideration. It can be observed from figure 3 that in comparison of DOM and DFM strategies, the downtime in case of DFM is more sensitive to distribution parameters than in case of DOM. Changing the lognormal distribution parameters from μ = 2.5, σ = 0.86 (design A) to μ = 2.8, σ = 0.36 (design B), will alter the downtime up to approximately 200 unit times. While changing the Weibull distribution parameters from β = 2.0, η = 757.6 (design E) to β = 6.7, η = 719.4 (design D) will alter the downtime by approximately 40 unit time. Thus in this particular case, strategy of DOM gives better stability than strategy of DFM. These kind of information are needed in the decision making process and the confident jack-knife diagram can be used as an aid in visualizing alternative designs improvement.

6. Conclusions A new way of presenting failure data is developed, allowing a visualization of the downtime estimation and the precision and the uncertainty of the estimation at a given confidence level and factors influencing the failure. Presenting failure data in this new diagram provides better insight into the hidden fact of the data. It can be used as a visual communication tool for maintenance engineering in communicating failure data to people with various backgrounds.


104 ISBN 978-91-7439-120-6

7. References [1] Abernethy, R.B. (2000). The New Weibull Handbook, Gulf

Publisher Co., Houston

[2] Altman, D.G., Machin, D., Bryant, T.N. and Gardner, M.J. (2000). Statistics with Confidence, BMJ Books, Bristol, UK

[3] Ashraf W.L, Richard, F.O. and Glyn, B.W. (1998). “An Effective Maintenance System Using the Analytic Hierarchy Process”, Integrated Manufacturing Systems, Vol. 9 No. 2, pp. 87 – 98

[4] Barringer, H.P. (2009). “Which Reliability Tool Should I Use?”, available at: http://www.reliabilityweb.com/art07/reliability_tools.htm (accessed 20 January 2010).

[5] Bovaird, R.L. and Zagor, H.L. (2006). “Lognormal Distribution and Maintainability in Support Systems Research”, Naval Research Logistics Quarterly, Vol. 8 No. 4, pp. 343 – 356

[6] Card, S.K., Mackinlay, J.D. and Schneiderman, B. (1999). Reading in Information Visualization: Using Vision to Think, Morgan Kaufmann Publishers Inc., San Francisco

[7] Council of Science Editors, Style Manual Subcommittee, (2006). Scientific Style and Format: the CSE Manual for Authors, Editors, and Publishers, 7th ed., Rockefeller Univ. Press, Reston, Virginia, USA

[8] Curran-Everett D. and Benos, D.J. (2004). “Guidelines for Reporting Statistics in Journals Published by the American Physiological Society”, American Journal of Physiology – Endocrinology and Metabolism, Vol. 287, pp. E189 – E191

[9] Das, P. (2005). “Improving the Maintenance System of Tippers – A Case Study”, Economic Quality Control, Vol. 20 No. 1, pp. 51 – 67

[10] Friel, S.N., Curcio, F.R. and Bright, G.W. (2001). “Making Sense of Graphs: Critical Factors Influencing Comprehension and Instructional Implications”, Journal for Research in Mathematics Education, Vol. 32, pp. 124 – 158

[11] Gardner, M.J. and Altman, D.G. (2000). “Estimating with Confidence”, in Altman, D.G., Machin, D., Bryant, T.N. and Gardner, M.J. (eds.), Statistics with Confidence, BMJ Books, London

[12] Gray, H.L. and Lewis, T.O. (1967). “A Confidence Interval for the Availability Ratio”, Technometrics, Vol. 9 No. 3, pp. 465 – 471.

[13] Hennessy, C., Freerks, F., Campbell, J.E. and Thompson, B.M. (2000). “Automated analysis of failure event data”, Proceeding of the Modeling and Analysis of Semiconductor Manufacturing Conference, Tempe, Arizona, March 27, 2000, available at: http://www.osti.gov/bridge/purl.cover.jsp?purl=/752663-aq6kj7/webviewable/ (accessed 20 January 2010)

[14] Knights, P. (2001). “Rethinking Pareto Analysis: Maintenance Applications of Logarithmic Scatterplots”, Journal of Quality in Maintenance Engineering, Vol. 7 No. 4, pp. 252 – 263

[15] Kortelainen, H., Kupila, K., Silenius, S. and Päivike, A. (2003). “Data for Better Maintenance Plans and Investments

Policy”, TAPPI Journal, Vol.2 No. 8, pp. 8 – 12, available at: http://www.softmagic.fi/Contents/referenssit/82993803AUG08.pdf (accessed 20 January 2010)

[16] Larkin, J.H. and Simon, H.A. (1987). “Why a Diagram is (Sometimes) Worth Ten Thousand Words”, Cognitive Science, Vol. 11, pp. 65 – 99

[17] Lin, T. and Titmuss, D. (1995). “Critical Component Reliability and Preventive Maintenance Improvement to Reduce Machine Downtime”, Computers & Industrial Engineering, Vol. 29 Issues 1-4, pp. 21 – 23

[18] Lohse, G.L. (2001). “Models of Graphical Perception”, in Karwowski, W. (Ed), International Encyclopedia of Ergonomics and Human Factors, Taylor and Francis, London.

[19] Masters, B.N., Lewis, T.O. and Kolarik, W.J. (1992). “A Confidence Interval for the Availability Ratio for System with Weibull Operating Time and Lognormal Repair Time”, Microelectron Reliability, Vol. 32 No. 1, pp. 89 – 99. Platfoot, R.A. (2000). “Improving Return from Maintenance”, Proceedings of the IIR Maintenance Management 2000, April 2000, Aukland, New Zealand, available at: http://www.covaris.com.au/papers/Improving%20Return%20from%20Maintenance.pdf (accessed 20 January 2010)

[20] Rausand, M. and Høyland, A. (2004). System Reliability Theory: Models, Statistical Methods, and Applications, John Wiley and Sons Inc., New Jersey

[21] Roth, W.M. and Bowen, G.M. (2003). “When are Graphs Worth Ten Thousand Words? An Expert-expert Study”, Cognition and Instruction, Vol. 21, pp. 429 – 473

[22] Schmid, C.F. (1954). Handbook of Graphic Presentation, Ronald Press Co., New York

[23] Schroeder, B. and Gibson, G. (2005). “A Large-scale Study of Failures in High-performance-computing Systems”, Supercedes Carnegie Mellon University Parallel Data Lab Technical Report, CMU-PDL-05-112, Carnegie Mellon University, available at: http://www.pdl.cmu.edu/PDL-FTP/stray/CMU-PDL-05-112.pdf (accessed 20 January 2010)

[24] Snedecor, G.W. and Cochran, W.G. (1989). Statistical Methods, 8th Edition, Iowa State University Press., Iowa

[25] Tory, M. and Möller, T. (2004). “Human Factors in Visualization Research”, IEEE Transactions on Visualization and Computer Graphics, Vol. 10, pp. 72 – 84

[26] Winn, W.D. (1994). “Contributions of Perceptual and Cognitive Processes to the Comprehension of Graphics”, in Schnotz, W. and Kulhavy, R. (Eds.), Comprehension of Graphics, Elsevier, Amsterdam

[27] Wiseman, M. (2001). “Reliability Management and Maintenance Optimization: Basic Statistics and Economics”, in Campbell, J.D and Jardine, A.K.S. (Eds), Maintenance Excellence: Optimizing Equipment Life-Cycle Decisions, Marcel Dekker Inc., New York

[28] Yates, J. (1985). “Graphs as a Managerial Tool: A Case Study of Du Pont's Use of Graphs in the Early Twentieth


105 ISBN 978-91-7439-120-6

Century”, Journal of Business Communication, Vol. 22 No. 1, pp. 5 – 33


106 ISBN 978-91-7439-120-6

wijaya10[1]

Documents