Enhanced Welding Operator Quality Performance Measurement: Work Experience-Integrated Bayesian Prior Determination
Computing in Civil Engineering XXXXXXXXXX
© ASCE
Enhanced Welding Operator Quality Performance Measurement: Work Experience-
Integrated Bayesian Prior Determination
Yitong Li, S.M.ASCE1; Wenying Ji, A.M.ASCE2; and Simaan M. AbouRizk, M.ASCE3
1Ph.D. Student, Dept. of Civil, Environmental, and Infrastructure Engineering, George Mason
Univ., Fairfax, VA XXXXXXXXXXE-mail: XXXXXXXXXX
2Assistant Professor, Dept. of Civil, Environmental, and Infrastructure Engineering, George
Mason Univ., Fairfax, VA XXXXXXXXXXE-mail: XXXXXXXXXX
3Professor, Dept. of Civil and Environmental Engineering, Univ. of Alberta, Edmonton, AB T6G
2W2, Canada. E-mail: XXXXXXXXXX
ABSTRACT
Measurement of operator quality performance has been challenging in the construction
fa
ication industry. Among various causes, the learning effect is a significant factor, which
needs to be incorporated in achieving a reliable operator quality performance analysis. This
esearch aims to enhance a previously developed operator quality performance measurement
approach by incorporating the learning effect (i.e., work experience). To achieve this goal, the
plateau learning model is selected to quantitatively represent the relationship between quality
performance and work experience through a beta-binomial regression approach. Based on this
elationship, an informative prior determination approach, which incorporates operator work
experience information, is developed to enhance the previous Bayesian-based operator quality
performance measurement. Academically, this research provides a systematic approach to derive
Bayesian informative priors through integrating multi-source information. Practically, the
proposed approach reliably measures operator quality performance in fa
ication quality control
processes.
INTRODUCTION
Pipe spool fa
ication is essential to the successful delivery of an industrial construction
project (Wang et al XXXXXXXXXXDuring the process of pipe fa
ication, welding is an important step
and its quality must be examined to ensure the specified requirements are satisfied. Although
welding is undertaken by skilled operators, variations commonly exist in welding operator
quality performance due to the lack of essential knowledge and skills (Ji et al XXXXXXXXXXTherefore,
eing able to reliably measure welding operator quality performance is crucial since the reliable
performance measurement leads to considerable advancement in project quality performance,
which would further decrease rework cost and overcome schedule delays. To achieve this goal, Ji
and AbouRizk XXXXXXXXXXhave developed a Bayesian statistics-based method to estimate operator
quality performance by assuming operator quality performance is stationary over time. However,
one of the most significant factors—the learning effect (i.e., the continuously improved quality
performance as operator work experience increases)—was neglected, which leads to a biased
estimation of operator quality performance.
This research aims to enhance the previously developed approach to reliably measure
welding operator quality performance by incorporating the effect of work experience.
Specifically, the objective is achieved by (1) selecting a learning curve model to describe the
elationship between quality performance and work experience; (2) applying the beta-binomial
egression to derive the equation of the selected model; (3) determining a informative prior to
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epresent quality performance for a given operator; (4) demonstrating the advantages of the
enhanced Bayesian-based approach using a case study. The remainder of this paper is a
anged
as follows. In the next section, previous work on Bayesian-based operator quality performance
measurement is discussed. After that, the newly proposed methodology is introduced step by
step. In the following section, a practical case study is conducted to demonstrate the advantages
of the newly proposed approach. Finally, contributions, limitations, and future work are
concluded.
PREVIOUS WORK
Previously, Ji and AbouRizk XXXXXXXXXXhave advocated the advantages of using a Bayesian-
ased operator quality performance measurement to incorporate inspection sampling uncertainty.
In their research, operator quality performance is reflected by fraction nonconforming (i.e.,
percentage repair rate) as indicated below:
X
p
n
(1)
Where p denotes fraction nonconforming, X denotes the number of welds which fails
inspections, and n denotes the total number of welds. To cover the sampling uncertainty, a beta
distribution , Beta a b was chosen to model the prior distribution for the Bayesian-based
fraction nonconforming estimation. The prior distribution represents operator quality
performance when no inspection results are collected. The posterior distribution describes the
latest measurement of operator quality performance by continuously adding more inspection
esults. An analytical solution for the posterior distribution follows:
, Beta X a n X b (2)
In Bayesian statistics, two types of priors are commonly used, namely, informative priors—
probability distributions derived from historical data or subjective knowledge; and
noninformative priors—vague, flat, and diffuse probability distributions that have the lowest bias
to prior estimation when information is insufficient (Ji and AbouRizk 2017).
In estimating the welding operator quality performance, Ji and AbouRizk XXXXXXXXXXused a
noninformative prior distribution 1/ 2,1 / 2Beta without incorporating the learning effect of
operators. The reliability of a Bayesian statistic-based method is heavily dependent on the prior
determination (Winkler XXXXXXXXXXIncapable of determining reliable priors leads to unreliable
posterior inferences, which further misleads practical decision support. Therefore, in aims of
improving the existing approach, an informative prior determination method, which is able to
incorporate work experience, is developed in this study.
METHODOLOGY
The research methodology of this study is demonstrated as Figure 1. First, the Plateau
learning curve model is selected to illustrate the relationship between operator quality
performance and work experience. Then, a beta-binomial regression approach is utilized to
derive the unknown parameters for the selected learning curve model. After that, informative
priors are determined through the derived learning curve equation. Lastly, posterior distributions
are computed by incorporating newly collected inspection data.
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Plateau Learning Curve
Modeling
Beta-Binomial
Regression
Informative Prior
Modeling
Posterior Distribution
Determination
Figure 1. Research methodology flow chart.
Plateau Learning Curve Modeling: The Plateau model (Baloff 1971) describes a linear-log
model with a constant term which indicates the operator’s steady-state performance. The Plateau
model is selected to represent the relation between welding operator quality performance and
work experience. It is applicable in this research because operator quality performance reaches a
steady-state as operators gain enough practices. The Plateau model in this research is represented
in Equation (3):
A B( ) CFN n (3)
Where FN denotes fraction nonconforming and n denotes the total number of welds. A, B,
and C are unknown parameters that can be derived using the regression approach described in
the next section.
Beta-Binomial Regression: Regression is a statistical technique to determine the
elationship between dependent variable and independent variables. For this research, the beta-
inomial regression model is selected to derive parameters in the Plateau model.
R's gamlss package (Stasinopoulos and Rigby 2018) is a regression package which allows all
the parameters of the distribution of the dependent variable to be modeled as non-linear functions
of the independent variables (Rigby and Stasinopoulos XXXXXXXXXXIn this study, gamlss function is
used to model the mean and the variation of fraction nonconforming (i.e., dependent variable) as
a non-linear function of the total number of welds (i.e., independent variable). Here, variations of
fraction nonconforming are assumed to be the same for all values of total welds and are
epresented as FN . The relationship between the mean value of fraction nonconforming and
total number of welds follows Equation (3) can be represented as:
A B( ) CFN n
(4)
This equation allows defining an exclusive mean value of fraction nonconforming for every
operator based on their total number of welds (i.e., work experience).
Informative Prior Modeling: In the Bayesian-based operator quality performance
measurement approach, the prior distribution of fraction nonconforming is represented with a
eta distribution as shown in Equation (5), which can be reparametrized using and , where
(shown as Equation (6)) is the mean value of a beta distribution, and (shown as Equation
(7)) represents the spread of the distribution. The reparametrized equation is shown as Equation
(8).
,Beta a b (5)
a
a
(6)
1
a
(7)
, ,1
,
FN i FN i
FN FN
Beta
(8)
In Equation (8), ,FN i is computed from Equation (4) which represents the mean value of
fraction nonconforming for operator i with the total number of welds in . The reparametrized
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eta distribution is used as the informative prior distribution for the Bayesian-based approach