Cost benefit analysis of series systems with warm standby components

This paper deals with the cost benefit analysis of series systems with warm standby components. The time-to-repair and the time-to-failure for each of the primary and warm standby components is assumed to have the negative exponential distribution. We develop the explicit expressions for the mean time-to-failure, MTTF, and the steady-state availability, A _T () for three configurations and perform a comparative analysis. Under the cost/benefit (C/B) criterion, comparisons are made based on assumed numerical values given to the distribution parameters, and to the cost of the components. The configurations are ranked based on: MTTF, A _T (), and C/B where B is either MTTF or A _T ().     

Optimal production run time for two-stage production system with imperfect processes and allowable shortages

This paper considers a two-stage production system with imperfect processes. Shortages are allowed, and the unsatisfied demand is completely backlogged. In addition, the capital investment in process quality improvement is adopted. Under these assumptions, we first formulate the proposed problem as a cost minimization model where the production run time and process quality are decision variables. Then we develop the criterion for judging whether the optimal solution not only exists but also is unique. If the criterion is not satisfied, the production system should not be opened. An algorithm for the computations of the optimal solutions is also provided. Finally, a numerical example and sensitivity analysis are carried out to illustrate the model.     

Tool replacement policy for one-sided processes with low fraction defective

In most manufacturing industries, tool replacement policy is essential for minimizing the fraction defective and the manufacturing cost. Tool wear is caused by the action of sliding chips in the shear zone, and the friction generated between the tool flank and workpiece. This wear, apparently, is a dominant and irremovable component of variability in many machining processes, which is a systematic assignable cause. As the tool wear occurs in the machining processes, the fraction of defectives would gradually become significant. When the fraction defective reaches a certain level, the tool must be replaced. Therefore, detecting suitable time for tool replacement operation becomes essential. In this paper, we present an analytical approach for unilateral processes based on the one-sided process capability index C _PU (or C _PL ) to find the appropriate time for tool replacement. Accurate process capability must be calculated, particularly, when the data contains assignable cause variation. By calculating the index C _PU (or C _PL ) in a dynamical environment, we propose estimators of C _PU (or C _PL ) and obtain exact form of the sampling distribution in the presence of systematic assignable cause. The proposed procedure is then applied to a real manufacturing process involving tool wear problem, to demonstrate the applicability of the proposed approach.     

Steady-state probability of the randomized server control system with second optional service, server breakdowns and startup

This paper deals with the 〈N,p〉-policy M/G/1 queue with server breakdowns and general startup times, where customers arrive to demand the first essential service and some of them further demand a second optional service. Service times of the first essential service channel are assumed to follow a general distribution and that of the second optional service channel are another general distribution. The server breaks down according to a Poisson process and his repair times obey a general distribution in the first essential service channel and second optional service channel, respectively. The server operation starts only when N (N≥1) customers have accumulated, he requires a startup time before each busy period. When the system becomes empty, turn the server off with probability p (p∈[0,1]) and leave it on with probability (1?p). The method of maximum entropy principle is used to develop the approximate steady-state probability distribution of the queue length in the M/G(G, G)/1 queueing system. A study of the derived approximate results, compared to the established exact results for three different 〈N,p〉-policy queues, suggests that the maximum entropy principle provides a useful method for solving complex queueing systems.     

The randomized vacation policy for a batch arrival queue

This paper examines an M^[x]/G/1${\text{M}}^{[\text{x}]}/\text{G}/1$ queueing system with a randomized vacation policy and at most J vacations. Whenever the system is empty, the server immediately takes a vacation. If there is at least one customer found waiting in the queue upon returning from a vacation, the server will be immediately activated for service. Otherwise, if no customers are waiting for service at the end of a vacation, the server either remains idle with probability p   or leaves for another vacation with probability 1-p$1-p$. This pattern continues until the number of vacations taken reaches J. If the system is empty by the end of the J  th vacation, the server is dormant idly in the system. If there is one or more customers arrive at server idle state, the server immediately starts his services for the arrivals. For such a system, we derive the distributions of important characteristics, such as system size distribution at a random epoch and at a departure epoch, system size distribution at busy period initiation epoch, idle period and busy period, etc. Finally, a cost model is developed to determine the joint suitable parameters (p^∗,J^∗)$(p^{\ast }\text{,}{J}^{\ast })$ at a minimum cost, and some numerical examples are presented for illustrative purpose.     

A variables sampling plan based on Cpmk for product acceptance determination

Process capability indices are useful management tools, particularly in the manufacturing industry, which provide common quantitative measures on manufacturing capability and production quality. Most supplier certification manuals include a discussion of process capability analysis and describe the recommended procedure for computing a process capability index. Acceptance sampling plans have been one of the most practical tools used in classical quality control applications. It provides both vendors and buyers to reserve their own rights by compromising on a rule to judge a batch of products. Both sides may set their own safeguard line to protect their benefits. Two kinds of risks are balanced using a well-designed sampling plan. In this paper, we introduce a new variables sampling plan based on process capability index C_pmk to deal with product sentencing (acceptance determination). The proposed new sampling plan is developed based on the exact sampling distribution hence the decisions made are more accurate and reliable. For practical purpose, tables for the required sample sizes and the corresponding critical acceptance values for various producer’s risk, the consumer’s risk and the capability requirements acceptance quality level (AQL), and the lot tolerance percent defective (LTPD) are provided. A case study is also presented to illustrate how the proposed procedure can be constructed and applied to the real applications.     

Optimal control of the N policy M/G/1 queueing system with server breakdowns and general startup times

This paper deals with an N policy M/G/1 queueing system with a single removable and unreliable server whose arrivals form a Poisson process. Service times, repair times, and startup times are assumed to be generally distributed. When the queue length reaches N(N ? 1), the server is immediately turned on but is temporarily unavailable to serve the waiting customers. The server needs a startup time before providing service until there are no customers in the system. We analyze various system performance measures and investigate some designated known expected cost function per unit time to determine the optimal threshold N at a minimum cost. Sensitivity analysis is also studied.     

Fast and effective algorithms for the liquid crystal display module (LCM) scheduling problem with sequence-dependent setup time

The liquid crystal display module scheduling problem (LCMSP) is a variation of the classical parallel machines scheduling problem, which has many real-world applications, particular, in the thin film transistor liquid crystal display (TFT-LCD) manufacturing industry. In this paper, we present a case study on the LCMSP, which is taken from a final liquid crystal display module (LCM) shop floor in a TFT-LCD industry. For the case we investigated, the jobs are clustered by their product types and the machine setup time is sequentially dependent on the product types of the jobs processed on the machine. In LCMSP, the objective is to maximize the total profit subject to fulfilling contracted quantities without violating the due date and machine capacity restrictions. The LCMSP can be modelled as a multi-level optimization problem. The sub-problem of LCMSP can be transformed into the vehicle routing problem with time window (VRPTW). One can therefore solve the LCMSP efficiently using existing VRPTW algorithms. We present two new algorithms based on the savings algorithms with some modifications to accommodate the LCMSP. Based on the characteristics of the LCM process, a set of test problems is generated covering most of the real-world applications for test purposes. Computational results and performance comparisons show that the proposed algorithms solved the LCMSP efficiently and near-optimally.     

The wafer probing scheduling problem (WPSP)

The wafer probing scheduling problem (WPSP) is a variation of the parallel-machine scheduling problem, which has many real-world applications, particularly, in the integrated circuit (IC) manufacturing industry. In the wafer probing factories, the jobs are clustered by their product types, which must be processed on groups of identical parallel machines and be completed before the due dates. Further, the job processing time depends on the product type, and the machine setup time is sequence dependent on the orders of jobs processed. Since the wafer probing scheduling problem involves constraints on job clusters, job-cluster dependent processing time, due dates, machine capacity, and sequence dependent setup time, it is more difficult to solve than the classical parallel-machine scheduling problem. In this paper, we formulate the WPSP as an integer programming problem. We also transform the WPSP into the vehicle routing problem with time windows (VRPTW), a well-known network routing problem which has been investigated extensively. An illustrative example is given to demonstrate the proposed transformation. Based on the provided transformation, we present three efficient algorithms to solve the WPSP near-optimally.     

Algorithms for the wafer probing scheduling problem with sequence-dependent set-up time and due date restrictions

In this paper, we consider the wafer probing scheduling problem (WPSP) to sequence families of jobs on identical parallel machines with due date restrictions. The machine set-up time is sequentially dependent on the product types of the jobs processed on the machine. The objective is to minimize the total machine workload without violating the machine capacity and job due date restrictions. The WPSP is a variation of the classical parallel-machine scheduling problem, that can be transformed into the vehicle-routing problem with time windows (VRPTW). One can therefore solve the WPSP efficiently using existing VRPTW algorithms. We apply four existing savings algorithms presented in the literature including sequential, parallel, generalized, and matching based savings, and develop three modifications called the modified sequential, the compound matching based, and the modified compound matching-based savings algorithms, to solve the WPSP. Based on the characteristics of the wafer probing process, a set of test problems is generated for testing purposes. Computational results show that the three proposed modified algorithms perform remarkably well.