Shey-Huei Sheu

Extended optimal replacement model with random minimal repair costs

Abstract This paper proposes a generalized replacement policy where a system has two types of failures and is replaced at the n-th type I failure (minor failure) or first type II failure (catastrophic failure) or at age T, whichever occurs first. Type I and type II failure are age-dependent. Type I failures are removed by minimal repairs. The cost of the minimal repair of the system at age z depends on the random part C(z) and the deterministic part c(z). The expected cost rate is obtained. The optimal n ∗ and optimal T ∗ which would minimize the cost rate are discussed. Various special cases are considered. Finally, a numerical example is given.

A generalized age and block replacement of a system subject to shocks

Abstract A system is subject to shocks that arrive according to a nonhomogeneous Poisson process. As shocks occur a system has two types of failures. Type I failure (minor failure) is removed by a minimal repair, whereas type 11 failure (catastrophic failure) is removed by an unplanned (or unscheduled) replacement. The choice of these two possible actions is based on some random mechanism which depends on the number of shocks suffered since the last replacement. For an age replacement maintenance policy, planned (or scheduled) replacements occur whenever an operating system reaches age T, whereas in the block replacement case, planned replacements occur every T units of time. The aim of this paper is to derive the expressions for the expected long-run cost per unit time and the total α-discounted cost for each policy. The optimal T ∗ which would minimize the cost rate or the total α-discounted cost is discussed. Various special cases are detailed. A numerical example is given to illustrate the method.

Optimal number of minimal repairs before replacement of a system subject to shocks

A system is subject to shocks that arrive according to a nonhomogeneous Poisson process. As shocks occur a system has two types of failures. Type 1 failure (minor failure) is removed by a minimal repair, whereas type 2 failure (catastrophic failure) is removed by replacement. The probability of a type 2 failure is permitted to depend on the number of shocks since the last replacement. A system is replaced at the times of type 2 failure or at the nth type 1 failure, whichever comes first. The optimal policy is to select n* to minimize the expected cost per unit time for an infinite time span. A numerical example is given to illustrate the method.

OPTIMAL ECONOMIC PRODUCTION QUANTITY POLICY FOR IMPERFECT PROCESS WITH IMPERFECT REPAIR AND MAINTENANCE

This study integrates maintenance and production programs with the economic production quantity (EPQ) model for an imperfect process involving a deteriorating production system with increasing hazard rate: imperfect repair and rework upon failure (out of control state). The imperfect repair performs some restorations and restores the system to an operating state (in-control state), but leaves its failure until perfect preventive maintenance (PM) is performed. There are two types of PM, namely imperfect PM and perfect PM. The probability that perfect PM is performed depends on the number of imperfect maintenance operations performed since the last renewal cycle. Mathematical formulas are obtained for deriving the expected total cost. For the EPQ model, the optimum run time, which minimizes the total cost, is discussed. Various special cases are considered, including the maintenance learning effect. Finally, a numerical example is presented to illustrate the effects of PM, setup, breakdown and holding costs.

The generally weighted moving average control chart for detecting small shifts in the process mean

Abstract A generalization of the exponentially weighted moving average (EWMA) control chart is proposed and analyzed. The generalized control chart we have proposed is called the generally weighted moving average (GWMA) control chart. The GWMA control chart, with time‐varying control limits to detect start‐up shifts more sensitively, performs better in detecting small shifts of the process mean. We use simulation to evaluate the average run length (ARL) properties of the EWMA control chart and GWMA control chart. An extensive comparison reveals that the GWMA control chart is more sensitive than the EWMA control chart for detecting small shifts in the mean of a process. To enhance the detection ability of the GWMA control chart, we submit the composite Shewhart‐GWMA scheme to monitor process mean. The composite Shewhart‐GWMA control chart with/without runs rules is more sensitive than the GWMA control chart in detecting small shifts of the process mean. The resulting ARLs obtained by the GWMA control chart when the assumption of normality is violated are discussed.

Optimal age-replacement policy of a system subject to shocks with random lead-time

Abstract This paper considers a generalized age-replacement policy of a system subject to shocks with random lead-time. A system is subject to shocks that arrive according to a non-homogeneous Poisson process. A model is developed for the average cost per unit time and is based on the stochastic behavior of the assumed system and reflects the cost of storing a spare as well as the cost of system downtime. The minimum-cost policy time is described and discussed. Various special cases are considered. Because the model and its analysis are general, several existing results are shown to be subsumed by this model.

Optimal burn-in time to minimize the cost for general repairable products sold under warranty

Burn-in is used to improve product quality pre-sale. Particularly for products with an initially high failure rate sold under warranty, burn-in can be used to reduce the warranty cost. Since burn-in is usually costly and adds directly to the product manufacturing cost, optimizing the length of the procedure is a major problem. This investigation considers a general repairable product sold under warranty, and examines the optimal burn-in time for achieving a trade-off between reducing the warranty cost and increasing the manufacturing cost (since burn-in can be considered part of the manufacturing process). The expected total cost per unit sold is derived for various warranty policies (failure-free policies with and without renewing, rebate policy). The conditions required for burn-in to be beneficial are derived. Finally, a numerical example is presented.

A generalized group maintenance policy

This paper proposes a two-phase maintenance policy for a group of identical repairable units. We define the time-interval (0, T] as the first phase, and the time interval (T, T + W ] as the second phase. As individual units fail individual units have two types of failures. Type I failures (minor failures) are removed by minimal repairs (in both phases), whereas Type II failures (catastrophic failures) are removed by replacements (in the first phase) or are left idle (in the second phase). A group maintenance is conducted at time T + W or upon the kth idle, whichever comes first. The optimal policy is to select T∗, W∗ and k∗ to minimize the expected cost per unit time for an infinite time span. Various special cases are considered. Numerical examples are given to illustrate the method.

A Bayesian approach to an adaptive preventive maintenance model

Abstract In this paper we consider a Bayesian theoretic approach to determine an optimal adaptive preventive maintenance policy with minimal repair. By incorporating minimal repair, maintenance and replacement, the mathematical formulas of the expected cost per unit time are obtained. When the failure density is Weibull with uncertain parameters, a Bayesian approach is established to formally express and update the uncertain parameters for determining an optimal adaptive preventive maintenance policy. Furthermore, various special cases of our model are discussed in detail.

Extended optimal replacement model for deteriorating systems

Abstract This paper proposes a generalized replacement model where a deteriorating system has two types of failures and is replaced at the Nth type I failure (minor failure) or first type II failure (catastrophic failure) or at the working age T, whichever occurs first. The probability of type I failure and type II failure is permitted to depend on the number of failures since the last replacement. These systems can be repaired upon type I failure, but are stochastically deteriorating, i.e., the lengths of the operating intervals are stochastically decreasing, whereas the durations of the repairs are stochastically increasing. The expected cost rate is obtained. The optimal N ∗ and optimal T ∗ which would minimize the cost rate are discussed. Various special cases are considered. Finally, a numerical example is given.