Page 62 - Contributed Paper Session (CPS) - Volume 2

CPS1428 Enobong F. U.
where and are the shape parameters, Γ(. ) is the gamma function. The

=
mean, variance and skewness are given as = + ( − ) + ′ 2

( − ) 2 respectively.
2
(+) (++1)
However, the mean and variance were estimated as = ( + 4 + )⁄6
2
2
and = ( − ) ⁄36 , where , and are optimistic, most likely and
pessimistic times respectively. Then the central limit theorem was applied to
approximate the cumulative distribution of the project completion time to
normal. It is known that Malcom’s PERT underestimate project completion
time and some of the sources of this bias as documented in literature (see
MacCrimmon & Ryavec (1964), Elmaghraby (1977), McCombs, et. al. (2009))
include: (i) Inability to accurately estimate the pessimistic, optimistic and most
likely times. (ii) The seemingly intuitive choice of the Beta distribution. (iii)
Method of estimation of the parameters of the activity time. (iv) The critical
path method of computing project completion time which ignores near critical
paths. (v) The possibility of wrong approximation of the project duration by
normal distribution. Previous works (Premachandra (2001), Herrerias-Velasco
(2011)) revealed that Malcom’s PERT formulae of the mean and variance
restrict us to only three members of the beta family, namely, (i) = = 4
(ii) = 3 − √2 ; = 3 + √2 (iii) = 3 + √2 ; = 3 − √2. . In which case, the
1
1
skewness captured by the model is 0, and − respectively. In other words,
2 2
the estimates are unreliable when activity times are heavily tailed.
Consequently, researchers have suggested other probability distributions as
proxies for the beta distribution as well as adopting other estimation
techniques to circumvent items (ii) and (iii) above.
Some of the distributions suggested include: the normal by Cottrell (1999);
the lognormal by Mohan et al (2007), Trietsch, et. al.(2012); the weibull by
McCombs et. al. (2009); the exponential by Magott and Skudlarski (1993),
Kwon, et. al. (2010); the truncated exponential by Abd-el-Kader (2006); the
compound Poisson by Parks & Ramsing (1969); the triangular by
Elmaghraby(1977), Johnson (1997); the gamma by Lootsma (1966),
Abdelkader (2004b); the beta-rectangular by Hahn (2008); the tiltedbeta by
Hahn and Martín (2015); the uniform by MacCrimmon & Rayvec(1964) and
Abdelkader and Al-Ohali(2013); the Erlang by Bendell, et. al. (1995) and
Abdelkader (2003).
The aim of this paper is to introduce Burr XII distribution as activity time
distribution in PERT. We will present a method for the estimation of the
parameters of activity time with Burr XII distribution, and thereafter Monte
Carlo the project network to obtain PCT using MATLAB Codes. It is believed
that our method will significantly address issues in items (i), (ii) and (iii) as listed
above.

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