Abstract: In recent years, maintenance optimization has attracted special attention due to the growth of industrial systems complexity. Maintenance costs are high for many systems, and preventive maintenance is effective when it increases operations' reliability and safety at a reduced cost. The novelty of this research is to consider general repair in the modeling of multi-unit series systems and solve the maintenance problem for such systems using the semi-Markov decision process (SMDP) framework. We propose an opportunistic maintenance policy for a series system composed of two main units. Unit 1, which is more expensive than unit 2, is subjected to condition monitoring, and its deterioration is modeled using a gamma process. Unit 1 hazard rate is estimated by the proportional hazards model (PHM), and two hazard rate control limits are considered as the thresholds of maintenance interventions for unit 1. Maintenance is performed on unit 2, considering an age control limit. The objective is to find the optimal control limits and minimize the long-run expected average cost per unit time. The proposed algorithm is applied to a numerical example to compare the effectiveness of the proposed policy (policy Ⅰ) with policy Ⅱ, which is similar to policy Ⅰ, but instead of general repair, replacement is performed. Results show that policy Ⅰ leads to lower average cost compared with policy Ⅱ.
Abstract: In this paper, the joint optimization of the
economic manufacturing quantity (EMQ), safety stock level,
and condition-based maintenance (CBM) is presented for a partially
observable, deteriorating system subject to random failure. The
demand is stochastic and it is described by a Poisson process.
The stochastic model is developed and the optimization problem
is formulated in the semi-Markov decision process framework. A
modification of the policy iteration algorithm is developed to find
the optimal policy. A numerical example is presented to compare
the optimal policy with the policy considering zero safety stock.
Abstract: In this paper, we propose a condition-based
maintenance policy for multi-unit systems considering the
existence of economic dependency among units. We consider a
system composed of N identical units, where each unit deteriorates
independently. Deterioration process of each unit is modeled as a
three-state continuous time homogeneous Markov chain with two
working states and a failure state. The average production rate of
units varies in different working states and demand rate of the
system is constant. Units are inspected at equidistant time epochs,
and decision regarding performing maintenance is determined by the
number of units in the failure state. If the total number of units in the
failure state exceeds a critical level, maintenance is initiated, where
units in failed state are replaced correctively and deteriorated state
units are maintained preventively. Our objective is to determine the
optimal number of failed units to initiate maintenance minimizing
the long run expected average cost per unit time. The problem is
formulated and solved in the semi-Markov decision process (SMDP)
framework. A numerical example is developed to demonstrate the
proposed policy and the comparison with the corrective maintenance
policy is presented.
Abstract: In this paper, we propose a method to model the
relationship between failure time and degradation for a simple step
stress test where underlying degradation path is linear and different
causes of failure are possible. It is assumed that the intensity function
depends only on the degradation value. No assumptions are made
about the distribution of the failure times. A simple step-stress test
is used to shorten failure time of products and a tampered failure
rate (TFR) model is proposed to describe the effect of the changing
stress on the intensities. We assume that some of the products that
fail during the test have a cause of failure that is only known to
belong to a certain subset of all possible failures. This case is known
as masking. In the presence of masking, the maximum likelihood
estimates (MLEs) of the model parameters are obtained through an
expectation-maximization (EM) algorithm by treating the causes of
failure as missing values. The effect of incomplete information on the
estimation of parameters is studied through a Monte-Carlo simulation.
Finally, a real example is analyzed to illustrate the application of the
proposed methods.
Abstract: This paper presents a maintenance policy for a system
consisting of two units. Unit 1 is gradually deteriorating and is
subject to soft failure. Unit 2 has a general lifetime distribution
and is subject to hard failure. Condition of unit 1 of the system
is monitored periodically and it is considered as failed when its
deterioration level reaches or exceeds a critical level N. At the
failure time of unit 2 system is considered as failed, and unit 2
will be correctively replaced by the next inspection epoch. Unit 1
or 2 are preventively replaced when deterioration level of unit 1
or age of unit 2 exceeds the related preventive maintenance (PM)
levels. At the time of corrective or preventive replacement of unit
2, there is an opportunity to replace unit 1 if its deterioration
level reaches the opportunistic maintenance (OM) level. If unit
2 fails in an inspection interval, system stops operating although
unit 1 has not failed. A mathematical model is derived to find
the preventive and opportunistic replacement levels for unit 1 and
preventive replacement age for unit 2, that minimize the long run
expected average cost per unit time. The problem is formulated and
solved in the semi-Markov decision process (SMDP) framework.
Numerical example is provided to illustrate the performance of the
proposed model and the comparison of the proposed model with an
optimal policy without opportunistic maintenance level for unit 1 is
carried out.
Abstract: In this paper, we present a model and an algorithm for
the calculation of the optimal control limit, average cost, sample size,
and the sampling interval for an optimal Bayesian chart to control
the proportion of defective items produced using a semi-Markov
decision process approach. Traditional p-chart has been widely
used for controlling the proportion of defectives in various kinds
of production processes for many years. It is well known that
traditional non-Bayesian charts are not optimal, but very few optimal
Bayesian control charts have been developed in the literature, mostly
considering finite horizon. The objective of this paper is to develop
a fast computational algorithm to obtain the optimal parameters of a
Bayesian p-chart. The decision problem is formulated in the partially
observable framework and the developed algorithm is illustrated by
a numerical example.
Abstract: In this paper, we present a new maintenance model
for a partially observable system subject to two failure modes,
namely a catastrophic failure and a failure due to the system
degradation. The system is subject to condition monitoring and the
degradation process is described by a hidden Markov model. A
cost-optimal Bayesian control policy is developed for maintaining
the system. The control problem is formulated in the semi-Markov
decision process framework. An effective computational algorithm is
developed, illustrated by a numerical example.
Abstract: In this paper, we investigate the residual life prediction
problem for a partially observable system subject to two failure
modes, namely a catastrophic failure and a failure due to the system
degradation. The system is subject to condition monitoring and the
degradation process is described by a hidden Markov model with
unknown parameters. The parameter estimation procedure based on
an EM algorithm is developed and the formulas for the conditional
reliability function and the mean residual life are derived, illustrated
by a numerical example.
Abstract: In this paper, we present a maintenance model of a
two-unit series system with economic dependence. Unit#1 which is
considered to be more expensive and more important, is subject to
condition monitoring (CM) at equidistant, discrete time epochs and
unit#2, which is not subject to CM has a general lifetime distribution.
The multivariate observation vectors obtained through condition
monitoring carry partial information about the hidden state of unit#1,
which can be in a healthy or a warning state while operating. Only the
failure state is assumed to be observable for both units. The objective
is to find an optimal opportunistic maintenance policy minimizing
the long-run expected average cost per unit time. The problem
is formulated and solved in the partially observable semi-Markov
decision process framework. An effective computational algorithm
for finding the optimal policy and the minimum average cost is
developed, illustrated by a numerical example.