C. E. Love

A simple recursive Markov chain model to determine the optimal replacement policies under general repairs

Abstract A repairable system (machine) is subject to failure. At each failure epoch, a general repair is performed. Such repairs return the system to a working condition somewhere between ‘good-as-new’ (a perfect repair) and ‘bad-as-old’ (a minimal repair). An important question for such systems is at what time should a major overhaul be conducted to return the unit to a ‘good-as-new’ state. Two policies are investigated in this research: (1) overhaul at fixed intervals and (2) overall at variable intervals by conducting each overhaul on the first failure following a predetermined time. We show in this research that both of these policies can be analyzed using a simple recursive Markov model thereby permitting the best of these policies to be identified in any particular situation. The Markov model is quite general, permitting a wide variety of structures to be investigated. Scope and purpose Considerable research has been conducted on the issue of periodic replacement times for failing systems. Typically in such analysis, each random failure is assumed to be repaired minimally and the replacement (or major overhaul) is assumed to refresh the failure intensity of the system. More recently, there has been recognition that repairs often serve to improve the system by partially resetting its failure intensity. Such a repair effect is known as a general (or an imperfect) repair. Previous research has extended well-known renewal functions into generalized renewal functions in order to estimate the impact of these general repair processes. In this paper we propose an alternative approach based on Markov chains which yields a simpler, more flexible model.

Acceptable quality level versus zero-defects: some empirical evidence

Abstract Within the literature on quality control there is a debate between two competing views of the cost of quality control. The first of these is the concept of an acceptable quality level as put forth by Juran and later, by Taguchi using the well known Taguchi Loss Function. This view proposes that an optimal level of quality exists for a firm wherein it balances the cost of conformance to quality standards against the cost of non-conformance. The second view is that of zero-defects as expounded by Schneiderman, Crosby and others. Here it is argued that optimal quality exists only at the zero-defect level and total cost of quality continue to fall as the zero-defect level is approached. In this research we demonstrate under fairly mild conditions that these two apparently contradictory views of quality can be complementary to each other. The research develops a model of total quality costs wherein the short-run quality control problem is consistent with the acceptable quality level view while the long-run quality control problem is consistent with the zero-defect view. The consolidation of these two views is similar in form to the traditional model utilized in economics wherein a firm at a point in time operates on a short-run average cost curve while simultaneously following a long-run average cost curve over time.

Classifying and controlling errors in forecasting using multiple criteria goal programming

Abstract This paper is concerned with the use of multiple criteria goal programming as a method of combining forecasts. The forecasts to be combined can come from a variety of forecasting techniques as well as from a variety of forecasting lead times. The model provided in this paper provides a generalization of previous work in the use of mathematical programming in combining forecasts. The generalizations are of two types; an error classification scheme such that the decision-maker can prioritize error types, and an error tolerance zone such that errors that fall within the prescribed tolerance zone may have no impact on the final forecasting model. The resultant structure affords considerably more flexibility in developing a model that matches the priorities deemed important to the decision maker given the forecasting information available.

An optimal maintenance policy for skipping imminent preventive maintenance for systems experiencing random failures

In this study we investigate systems that experience random failures and establish decision rules for performing renewal maintenance; that is, a preventive replacement (PR) policy. We seek a policy that is both simple to execute from the point of view of the maintenance planner but also a policy that is an improvement on existing schemes. We show that our policy is a hybrid of traditional time-based and age-based schemes and one that yields considerable cost savings. Our hybrid policy involves two decision variables. One decision variable is the time between PRs. Hence, for the maintenance planner, the times at which PRs are performed are chronologically fixed. Random failures can occur, however, and the machine receives an emergency renewal (ER) at these times. Hence, within these chronological times, a second decision time is identified. Should an ER occur between the start of a cycle and this second decision time, then the planned PR would still be performed at the end of the cycle. However, if the first ER occurs after this second decision time, then the PR at the end of the cycle is skipped over and the next planned PR would take place at the end of the subsequent cycle. With this simple mechanism, PRs that follow on too closely after an ER are avoided, thus saving the unnecessary expense. Numerical examples are given to examine the validity of the model, using four different failure density functions, namely Weibull, normal, uniform, and negative exponential.

Source/sink inventory control for vehicle rental systems

Abstract The problem of operating a vehicle rental system in a two-location environment is investigated. Two interdependent processes are identified as operating simultaneously. Units are rented out, ultimately to be returned to their original location. Secondly, units are rented out from one location but returned to a second location. As a result, the number of units of equipment at each location is constantly changing. In general, these “one-way” flows setup equipment imbalances which require periodic rebalancing of the system. Formulation takes the form of a multi-period dynamic program. Both transient and steady-state cases are investigated. Solution specifies the optimal number of units each location should hold on reserve in each period for “one-way” rentals. Finally, a restocking decision is embedded into the problem, in order to determine the optimal quantity of equipment lo be periodically rebalanced between locations due to “one-way” flows. Limitation of the procedure is explained. The size of the resulting dynamic program makes solution of the general multi-location problem computationally unfeasible. Approximation procedures are suggested to circumvent this limitation.