An attempt is made in this thesis to study some stochastic models of both reliability and
inventory systems with reference to the following aspects:
(i) the confidence limits with the introduction of common-cause failures.
(ii) the Erlangian repair time distributions.
(iii) the product interactions and demand interactions.
(iv) the products are perishable.
This thesis contains six chapters.
Chaper 1 is introductory in nature and gives a review of the literature and the techniques
used in the analysis of reliability systems.
Chapter 2 is a study of component common-cause failure systems. Such failures may
greatly reduce the reliability indices. Two models of such systems (series and parallel)
have been studied in this chapter. The expressions such as, reliability, availability and
expected number of repairs have been obtained. The confidence limits for the steady
state availability of these two systems have also been obtained. A numerical example
illustrates the results.
A 100 (1 - a) % confidence limit for the steady state availability of a two unit hot and
warm standby system has been studied, when the failure of an online unit is constant and
the repair time of a failed unit is Erlangian.
The general introduction of various inventory systems and the techniques used in the
analysis of such systems have been explained in chapter 4.
Chapter 5 provides two models of two component continuous review inventory systems.
Here we assume that demand occurs according to a poisson process and that a demand
can be satisfied only if both the components are available in inventory. Back-orders
are not permitted. The two components are bought from outside suppliers and are
replenished according to (s, S) policy. In model 1 we assume that the lead-time of
the components follow an exponential distribution. By identifying the inventory level
as a Markov process, a system of difference-differential equations at any time and the
steady-state for the state of inventory level are obtained. Tn model 2 we assume that the
lead-time distribution of one product is arbitrary and the other is exponential. Identifying
the underlying process as a semi-regenerative process we find the stationary distribution
of the inventory level. For both these models, we find out the performance measures such
as the mean stationary rate of the number of lost demands, the demands satisfied and the
reorders made. Numerical examples for the two models are also considered.
Chaper 6 is devoted to the study of a two perishable product inventory model in which
the products are substitutable. The perishable rates of product 1 and product 2 are two
different constants. Demand for product 1 and product 2 follow two independent Poisson
processes. For replenishment of product 1 (s, S) ordering policy is followed and the
associated lead-time is arbitrary. Replenishment of product 2 is instantaneous. A demand
for product 1 which occurs during its stock-out period can be substituted by product 2 with
some probability. Expressions are derived for the stationary distribution of the inventor}'
level by identifying the underlying stochastic process as a semi-regenerative process. An
expression for the expected profit rate is obtained. A numerical illustration is provided
and an optimal reordering level maximising the profit rate is also studied.
To sum up, this thesis is an effort to improve the state the of art of (i) complex reliability
systems and their estimation study (ii) muitiproduct inventory systems. The salient
features of the thesis are:
(i) Analysis of a two-component reliability system with common-cause failures.
(ii) Estimation study of a complex system in which the repair time for both hot standby
and warm standby systems are assumed to be Eriangian.
(iii) A multi-product continuous review inventory system with product interaction, with a
(s, S) policy.
(iv) Introduction of the concept of substitutability for products.
(v) Derivation of expressions for various statistical measures.
(vi) Effective use of the regeneration point technique in deriving various measures for both
reliability and inventory systems.
(vii) Illustration of the various results by extensive numerical work.
(vii) Consideration of relevant optimization problems. / Mathematical Sciences / PhD (Statistics)
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:unisa/oai:uir.unisa.ac.za:10500/692 |
| Date | 04 1900 |
| Creators | Hargreaves, Carol Anne |
| Contributors | Yadavalli, S. S. |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 1 online resource (ix, 137 leaves) |
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