Application of Logistic Regression in Resolving Influential Risk

Proceedings of the 2016 International Conference on Industrial Engineering and Operations Management Kuala Lumpur, Malaysia, March 8-10, 2016

Application of Logistic Regression in Resolving Influential Risk Factors Subject to Corrosion Under Insulation

Nurul Rawaida Ain Burhani, Masdi Muhammad, Ainul Akmar Mokhtar, Mokhtar Che Ismail. Department of Mechanical Engineering

Universiti Teknologi PETRONAS Perak, Malaysia

[email protected]

Abstract— Corrosion under insulation (CUI) is an increasingly important issue for piping especially for oil and gas industries due to its unexpected catastrophic disaster and automatic impact on the environmental problem. To ensure this CUI problem did not spark sudden surprise in plants, ambiguous factors that contribute to the deterioration of CUI should be recognized and taken care seriously. Thus, this research will unearth the most influential factors for the CUI deterioration using logistic regression model. Results show most influential factors are insulation type followed by availability of elbow in pipe design, other than service temperature. This finding can be a guideline for inspection planning purpose and priority in the maintenance schedule.

Keywords—corrosion under insulation; logistic regression; logistic model; influential factors.

I. INTRODUCTION

Corrosion under insulation (CUI) is localized corrosion attacking the interface of metal between the metal surface and its insulation. Insulation is frequently applied to maintain process temperatures that reduce energy loss and associated costs including precaution for safety issues. CUI is typically difficult to perceive until it becomes a serious problem, especially in chemical, oil and gas industries that have been operating for decades [1]. These failures can be catastrophic for our environment or at least have undesirable economic effect during downtime and restoration. In 2003, Exxon Mobile Chemical indicated the highest incidence of leaks in the chemical and refining industries is due to CUI. The costs for piping maintenance are between 40% and 60% for CUI detection and cure for CUI occurrence. Afterward in 2008, National Association of Corrosion Engineers (NACE) fulfills a survey, from 30 facilities, 17 experiences CUI as a major challenge they have to confront. More, NACE study about corrosion costs in 2011 specifies that corrosion costs in the US are approximating $1 trillion annually, and logically will exceed that unfortunate milestone in future [2-5].

In this study, a logistic regression model, which describes a relationship between an outcome and a set of independent variables, is used. This logistic regression analysis (LRA) has been using widely, either in the medical field, business and marketing studies or as simple as determining yes or no in the decision-making process [6-9]. More detailed in this study, the LRA is used to understand as well as resolve the contributing factors of CUI occurrence and investigate the interactions between these factors by analyzing the binary responses. Factors affecting the CUI rate as indicated by scholarly works such as insulation types, service temperatures, and other factors will be tested and analyzed as variables to determine a most influential factor for CUI occurrence [10-12]. Knowing how these CUI factors associated is important as a guideline for inspection planning purpose and priority in operational plant maintenance schedule.

II. METHODOLOGY

A. Logistic Regression Method

To determine the influential factors that contribute to CUI, logistic regression analysis (LRA) was applied based on thefollowing summary:

1) Data Collection: The literature review and petrochemical plants data in Malaysia is used. Data are narrow to 15 to 20years piping only. The visual inspection data treated as binary data (CUI found = 1; no CUI = 0).

2) Define all possible variables that contribute to the formation of CUI: A regression can simultaneously handle bothquantitative and qualitative explanatory variables. In this LRA, the response variable is CUI occurrence whereas the

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explanatory variables can be either quantitative or qualitative variables. The quantitative variables are service temperature and age of the pipe while the qualitative variables are the type of insulation and design of pipe.

3) Input all variables data into logistic regression function: To insert variables, details of them are specified. The quantitative variable further classified as a continuous and categorized variable. Age or year of service is considered under continuous variable (i.e. 6, 10 and 15 years of services) while service temperature considered as a categorical variable. The qualitative variable such as types of insulation is also regarded as categorical covariates. Here, dummy variable needs to be used to overcome the weakness of the categorical variable as it cannot be meaningfully interpreted in the regression model. Dummy variables are artificial explanatory variables in a regression model whereby the dummy codes are a series of numbers assigned to indicate the group. In dummy variable, it will be dichotomous variable as each variable is assumed one of two values, 0 or 1, denoting whether an observation falls in a particular group. For dummy variable to be used, if there are K groups, one needs to have K - 1 dummy variables to represent K groups. Let say, if there are six service temperature groups, one needs to have five dummy variables to represent the group that one of the groups will not be represented as a dummy variable. It will be considered as a reference to which each of the group should be compared. In this study, categorical variables are service temperature, insulation type, and pipe design. Service temperature clustered to five group based on API 581.

4) Estimate parameter using maximum likelihood estimation (MLE) to determine goodness of fit: From the logistic function, the logistic regression model is attained through the parameter z that can be composed as the linear sum of the explanatory variables as follows:

Z = β0 + β1 x1 + β2 x2 + ... + βn xn (1)

Where x1, x2,... xn are termed as the independent variables of interest and β0, β1, β2,… βn are the coefficient representing unknown parameters. Estimates of the parameters β0, β1, β2,… βn are obtained using a mathematical technique called maximum likelihood. This likelihood means the probability has been evaluated as a function of the parameters with fix data [13]. Likelihood allows the estimation of unknown parameters based on known outcomes. For this concept, theoretically, it will choose initial estimates of the regression coefficients, such as β0 = 0. At each iteration t, it will update the coefficient, and this iteration will stop when the percentages of error decrease to the smallest value that approximately becomes zero.

5) Test the significance of each parameter and eliminate insignificance variables: Once a full logistic regression model is developed, the backward stepwise elimination procedure will be used to remove the explanatory variable with an insignificant coefficient. The backward stepwise elimination procedure begins with a full model. Then, the variables that are found to be insignificant are eliminated from the model in an iterative process.

6) Determine the most influential factor subject to CUI: After the elimination of each variable, the fit of the model is tested to ensure that the model still adequately fits the data. The analysis has been completed when no more variables can be eliminated from the model,

III. RESULTS & DISCUSSIONS

A. Model Validation Model validation is done by comparing results generated via JavaScript and statistical analysis software (SAS). Data taken

from Evans Country case study was used [14]. In the case study, the data was fitted to the logistic regression model using JavaScript as developed in [15]. The results showed that the logistic regression model developed in SAS produced the same coefficients as the results using JavaScript by Kevin Sullivan. Thus, it is proved that the logistic regression model developed using SAS is acceptable.

B. Result Analysis Data from an actual plant in East Coast Malaysia are analyzed. Five steps of backward stepwise elimination procedure are

done base on the R2 value. This stepwise backward elimination continues until all p-value is significant for all factors as shown in Table I. But, it is a must to ensure the R2 value is not too low, and the gap between the first elimination is lower than 10% to avoid misinterpretation of results and model. Steps 1 to 5 of stepwise backward elimination are as publicized in Table I. Earlier; it is observed that most of the variables are insignificant based on the high p-value, which should be lower than α = 0.05. Those insignificant factors are removed from the model using the backward stepwise elimination procedure. The insignificant variables in steps 1 to 4 are pipe category (big bore and small bore), a design of pipe (vertical, horizontal and straight pipe). Later in step 5, the most significant factors of CUI occurrence are left. They are the type of insulation, elbow design of pipe and service temperature, with R2 value of 0.6041.



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TABLE I. THE ESTIMATED PARAMETERS AND THEIR SIGNIFICANCE FOR A LOGISTIC REGRESSION MODEL

Steps Appearance

R2 value Factors p-value

1 0.6091

Insulation Material Pipe design (elbow) Pipe design (straight) Pipe design (horizontal) Pipe design (vertical) Service temperature Pipe category

0.0002 0.0026 0.3798 0.0800 0.3214 0.0031 0.4755

2 0.6089

Insulation Material Pipe design (elbow) Pipe design (straight) Pipe design (horizontal) Pipe design (vertical) Service temperature

0.0001 0.0018 0.2190 0.0600 0.3114 0.0058

3

0.6077

Insulation Material Pipe design (elbow) Pipe design (straight) Pipe design (horizontal) Service temperature

0.0000 0.0003 0.1962 0.0600 0.0041

4 0.6068

Insulation Material Pipe design (elbow) Pipe design (horizontal) Service temperature

0.0000 0.0001 0.0581 0.0033

5 0.6041 Insulation Material Pipe design (elbow) Service temperature

0.0000 0.0000 0.0029

The coefficient of each significant factors is determined after the results comprise only significant factors, which determined by the p-value in stepwise backward elimination. Other than that, it must be noted that R2 value, from the first to the last elimination should not have a high variance that will make the equation model is not valid. For this study, R2 values from the first to the last elimination accumulate of only 8.2% reduction. It is still in acceptable range value and valid for the logistic regression model. Based on the result, most significant factors for CUI occurrence are insulation material, elbow design of pipe and service temperature. To enhance this logistic regression model, the insulation material and service temperature are convened into their group. Insulation materials of piping are classified by the cellular glass, perlite, and calcium silicate material. Supplementary, for service temperature, they cluster based on API 581. The cluster service temperature groups are indicated in Table II. Then, the final coefficient for each parameter is determine using SAS and tabulated in Table II.

TABLE II. FINAL COEFFICIENT FOR PARAMETERS IN LOGISTIC REGRESSION MODEL

Factor Appearances

Coefficient Wald Test Intercept -2.8780 -6.1230 Insulation Material: Cellular Glass 1.9685 5.7865 Perlite 1.1496 5.3422 Calcium Silicate 1.5090 5.7694 Design of pipe (Elbow) 0.7139 4.8765 Service temperature: Group 1 (49°C to 93°C) 0.8954 4.2515 Group 2 (-12°C to 16°C) 0.6749 3.8030 Group 3 (16°C to 49°C) 0.4695 3.4038 Group 4 (93°C to 121°C) 0.6457 3.6793 Group 5 (less than -12°C & more than 121°C) 0.2761 2.8785


Proceedings of the 2016 International ConfKuala Lumpur, Malaysia, March 8-10, 2016

978-1

From Table II, a general equation of a lsystems can be written as (2).

y(x) = -2.8780 + 1

+ 0.6749 x6 +

Where x1, x2, and x3 are dummy variableare dummy variable for service temperatureFigure 1 and Figure 2.

Fig. 1 Probability of CUI occurre

The probability of CUI occurrence with with no elbow. For pipe with the elbow, the pipe design, the probability falls between 30in plants.

Besides, service temperature groups shbetween different materials. The higher the occurrence. Based on the graph plotted, seoccurrence followed by service temperature with coefficients of 0.8954, 0.6749, 0.6457,design also follows this trending sequence. Tcoefficient of 0.2761 gives the lowest probcomplies with the NACE SP 0198-2010 that

Focusing on the insulation types, highesfollowed by calcium silicate and perlite fofollows the trending of poor to excellent typ2010 [17]. In purpose of enriching this studyis utilizing binary data only. Manipulatinginsulation rate. Thus, this will enhance in res

Corrosion under insulation (CUI) is an chemical plants due to its astonishing catastrCUI problem did not spark sudden surprise i

1) Factors that contribute to the deteriomodel includes the definition of all possible

ference on Industrial Engineering and Operations Manag6

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linear function of independent variables for the corrosion

1.9685x1 + 1.1496 x2 + 1.5090 x3 + 0.7139 x4+ 0.8954 x5

0.4695 x7 + 0.6457 x8 + 0.2761 x9 (2)

e for insulation material; x4 is the availability of elbow in pe groups. Simple graphical display for this logistic regre

ence for 20 years operation for pipe design with elbow (left) and no elbo

an elbow in pipe design has overall higher percentage compossibility of CUI circumstance are in the range 50% to70

0% to 50% scale. Thus, it is important to reduce if possible

how quite a steady trend while insulation material clearcoefficient obtained, the higher impact and probability o

ervice temperature in Group 1 (49°C to 93°C) shows higin Group 2(-12°C to 16°C), Group 4 (93°C to 121°C), and

, and 0.4695 respectively. The probability of CUI occurreThe service temperature of Group 5 (less than -12°C and bability of CUI occurrence for both pipe design with elbt critical temperature is between 49oC to 93oC [16].

st probabilities of CUI occurrence after long service are thor both pipe design with elbow and no elbow. This sequpes of insulation material use based on an experiment doney in future, other available models can be used since this g piping thickness can determine individual remainingsolving the most influential factors subject to CUI.

IV. CONCLUSION increasingly important issue for piping in industries esperophic disaster and mindless impact on the environmental in plants, this study concludes:

oration of CUI successfully recognized by using logistice variables which contribute to the formation of CUI, inp

gement

n under insulation piping

pipe design; while x5 to x9 ession model is shown in

ow (right).

mpared to the pipe design 0% while for no elbow in

e, elbow in designing pipe

rly displays the impurity of specific factors to CUI ghest probability of CUI d Group 3 (16°C to 49°C) ence for no elbow in pipe more than 121°C) with a bow and no elbow. This

he usage of cellular glass, uence of CUI probability e by Williams and Evans, logistic regression model life or corrosion under

ecially petrochemical and problem. In ensuring this

c regression model. This put all variables data into



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logistic regression function, estimation of parameter using maximum likelihood estimation to determine goodness of fit, testing the significance of each parameter and eliminate insignificance variables by using backward stepwise elimination, and finally determination of the most influential factor subject to CUI.

2) The most influential factors for CUI in this study are insulation type followed by availability of elbow in pipe design,other than service temperature. It is hope that the resolved influential factors of CUI will be beneficial in plant management and can be a guideline for inspection planning purpose and priority in the maintenance schedule.

ACKNOWLEDGMENT This work was financially supported by the Ministry of Higher Education of Malaysia and Yayasan Universiti Teknologi

PETRONAS.

REFERENCES [1] Michael Lettich, “Is There a Cure for Corrosion under Insulation?”, Insulation Outlook Magazine, Nov 2005 Issue.[2] Michael Twomey, “Inspection Techniques for Detecting Corrosion under Insulation,” American Society for Nondestructive Testing, Inc. 2007. [3] Y. Paul Virmani, “Corrosion Costs and Preventive Strategies in the United States”, National Technical Information Service, Pub. No. FHWA-RD-01-

156, 2002. [4] Online Article, ITW Insulation System. Metal Corrosion under Thermal Insulation, 2010. Available: www.itwinsulation.com[5] O. Mike, D. Vijay, M. Adrian, A. Sean, G. Matthew, Nicole., G.S. Linda, L. Damien and J. Bill, “When Undercover Agents Stand the Heat: Coatings

in Action (CIA) and the Netherworlds of Corrosion Under Insulation”, Top Thinker Article, JPCL, February 2012 Issue[6] K.J. Ottenbacher, P.M. Smith, S.B. Illig, R.T. Linn, R.C. Fiedler, and C.V. Granger, “Comparison of logistic regression and neural networks to predict

rehospitalization in patients with stroke”. Journal of Clinical Epidemiology, 54, pp. 1159–1165, 2001 [7] H.A. Camdeviren, A.C. Yazici, Z. Akkus, R. Bugdayci, and M.A. Sungur, “Comparison of logistic regression model and classification tree: An

application to postpartum depression data”. Expert Systems with Applications, 32, 987–994, 2007. [8] N.Cerpa, M.Bardeen, B. Kitchenham, and J.Verner, “Evaluating logistic regression models to estimate software Project Outcomes”, Information and

Software Technology, 52, 934–944, 2010. [9] P.C. Austin, J.V. Tu, and D.S. Lee, “Logistic regression had superior performance compared with regression trees for predicting in-hospital mortality

in patients hospitalized with heart failure”, Journal of Clinical Epidemiology, doi: 10.1016/j.jclinepi.2009.12.004, 2010. [10] W. I. Pollock and J. M. Barnhart, “Corrosion of Metal under Thermal Insulation”, STP 880, 1985 [11] R. Javaherdashti, “Corrosion under Insulation (CUI): A review of essential knowledge and practice,” J. Mater. Sci. Surf. Eng., vol. 1, no. 2, pp. 36–43,

2014.[12] J. Bhandari, F. Khan, R. Abbassi, V. Garaniya, and R. Ojeda, “Modelling of pitting corrosion in marine and offshore steel structures – A technical

review,” J. Loss Prev. Process Ind., vol. 37, pp. 39–62, Sep. 2015 [13] S. Dowdy, S. Wearden, and D. Chilko, “Statistics for research:3rd edition”. Hoboken, New Jersey: John Wiley & Sons, Inc, 2004 [14] Kleinbaum, D.G., Kupper, L.L. and Morgenstern, H. Epidemiologic Research: Principles and Quantitative Methods. New York: Van Nostrand

Reinhold, 1982. [15] K. Sullivan, and J.C. Pezzullo, “Logistic Regression” version 05.07.02. Retrieved April 12, 2010, from http://statpages.org/logistic.html, 2007

[16] NACE SP 0198-2010, “Standard Practice Control of corrosion under thermal insulation and fireproofing materials- A system’s Approach”, NACE International, Texas, 2010.

[17] J. Williams and O. Evans, “the Influence of Insulation Materials on Corrosion Under Insulation,” NACE Int. Newc, 2010.

BIOGRAPHY Nurul Rawaida Ain Burhani is currently a Ph.D. candidate in Mechanical Engineering specialized in Reliability and Corrosion with research on “Probabilistic Life Prediction Model for Corrosion under Insulation”. Her MSc in Asset Management and Maintenance under Mechanical Engineering Department was obtained from UTP by coursework and with research on “Life Cycle Cost of Gas District Cooling Plant”. She obtained her first degrees, BSc in Mechanical Engineering from Universiti Teknologi PETRONAS. Actively involve as speaker and writer for charity work in developing youth and society.

Masdi Muhammad is a Senior Lecturer in Mechanical Engineering Department and research cluster leader for Facility and Plant Engineering, UTP. He is CEng (UK), CMRP, ASQ-Certified Reliability Engineer. He obtained his first and Master degrees, BSc in Mechanical Engineering and MSc in Manufacturing System Engineering, from Lehigh University, USA. His Ph.D. in Mechanical Engineering was obtained from UTP with research on “Reliability Model for Repairable Systems with Multi-State Degradation”. He is actively involved in research collaboration and consultancy with PETRONAS OPUs and currently supervising PhDs and MSc students in the area of Reliability and Maintenance. He has twelve years of experience working in various positions in one of the leading



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semiconductor companies, involving process and equipment engineering, product development, and material quality before joining UTP. He is a chartered engineer and member of BEM, IEM, American Society of Quality and Co-Chair of ASME-Malaysia Section.

Ainul Akmar Mokhtar is a Senior Lecturer in Mechanical Engineering Department and Head of Master Asset Management and Maintenance under Mechanical Engineering Department, UTP. She obtained her Ph.D. in Mechanical Engineering from Universiti Teknologi Petronas, Masters of Science in Manufacturing Systems, from University of Nottingham and Bachelor of Science in Industrial Engineering, from Purdue University. She has published journal and conference papers and actively involve in plant reliability consultation and training.

Mokhtar Che Ismail is an associate professor, currently a senior lecturer and Head of Centre for Corrosion Research, UTP. He obtained his Ph.D. from the University of Manchester, Masters Science (Materials Science and Engineering) from National University of Singapore and Bachelor of Mechanical Engineering from University of Newcastle. His expertise is in Corrosion Engineering, Plant Maintenance and Inspection. Active in research area including CO2 corrosion, Risk-Based Inspection, Corrosion under insulation, and Plant corrosion. As a high qualified engineer, he is also dynamic in consultation of Failure Analysis, Corrosion training in Corrosion Management, Quality Control, Corrosion Monitoring, Materials Selection and NDT.


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Application of Logistic Regression in Resolving Influential Risk