An age replacement policy with minimal repair and general random repair cost

An age replacement policy is introduced which incorporates minimal repair, replacement, and general random repair costs. If an operating unit fails at age y<T, it is either replaced by a new unit with probability p(y) at a cost c₀, or it undergoes minimal repair with probability q(y) = 1−p(y). Otherwise, a unit is replaced when it fails for the first time after age T. The cost of the i-th minimal repair of an unit at age y depends on the random part C(y) and the deterministic part c_i(y). The aim of the paper is to find the optimal T which minimizes the long run expected cost per unit time of the policy. Various special cases are considered.     

Periodic replacement with minimal repair at failure and general random repair cost for a multi-unit system

A policy of periodic replacement with minimal repair at failure is considered for the multi-unit system which have the specific multivariate distribution. Under such a policy an operating system is completely replaced whenever it reaches age T (T > 0) at a cost c₀ while minimal repair is performed at any intervening component failures. The cost of the j-th minimal repair to the component which fails at age y is g(C(y),c_j(y)), where C(y) is the age-dependent random part, c_j(y) is the deterministic part which depends on the age and the number of the minimal repair to the component, and g is an positive nondecreasing continuous function. A simple expression is derived for the expected minimal repair cost in an interval in terms of the cost function and the failure rate of the component. Necessary and sufficient conditions for the existence of an optimal replacement interval are exhibited.     

Optimal control of a removable server in an M/Ek/1 queueing system with finite capacity

This paper deals with the economic behavior of a removable server in the N policy M/E_k/1 queueing system with finite capacity. Expressions for the probability mass functions of the number of customers in the system are derived and taken in closed-form. As special cases, the probability mass functions of the number of customers for the N policy M/M/1 queueing system, the ordinary M/K_k/1 queueing system, and the ordinary M/M/1 queueing system are obtained. The cost structure includes a holding cost per unit time spent in the system for each customer, costs per unit time for keeping the server on or off, a server start-up cost, a server shut-down cost, and fixed cost for every lost customer. Following the construction of the total expected cost per unit time, we determine the optimal operating policy at minimum cost.     

Approximating a set of points by a step function

Let S be a set of n points in the plane. We derive algorithms for approximating S by a step function of size k < n, i.e., by an x-monotone rectilinear polyline with k < n horizontal segments. We use the vertical distance to measure the quality of the approximation, i.e., the maximum distance from a point in S to the horizontal segment directly above or below it. We consider two types of problems: min-ε, where the goal is to minimize the error for a given number of horizontal segments k and min-#, where the goal is to minimize the number of segments for a given allowed error ε. After O (n) preprocessing time, we solve instances of the latter in O (min{k log n, n}) time per instance. We can then solve the former problem in O (min{n², nk log n}) time. Both algorithms require O (n) space. Our second contribution is an approximation algorithm for the min-ε problem that computes a solution within a factor of 3 of the optimal error for k segments, or with at most the same error as the k-optimal but using 2k − 1 segments. Furthermore, experiments on real data show even better results than what is guaranteed by the theoretical bounds. Both approximations run in O (n log n) time and O (n) space.     

One unit reliability system subject to random shocks and preventive maintenance

In this paper we consider two systems each consisting of one unit. The operating unit is subject to random shocks which occur at random times. Due to the shock the following may happen: (i) The unit is not at all affected by the shock; (ii) the failure rate of the unit increases from λ₀ to λ₁; (iii) the unit fails. The failure time of the unit is exponentially distributed. The repair, shock and preventive maintenance times follow general distributions. In System 2 there is provision of preventive maintenance, whereas in System 1 there is no provision of preventive maintenance. There is one repair man available in each system. In this paper the mean time to system failure, steady state availablities and the impact of shocks on these are studied. In System 2 the effect of the preventive maintenance on MTSF and steady-state availabilities is investigated.     

Limit distributions for dependent thinning of dissipative point processes

Let N_p be the thinned version of a point process N={t_j, t₀t₁…t_j…} on the real line R: a point is deleted with probability 1−p, and retained with probability p, 0<p<1. The aim of this paper is to characterize the class of all possible distributions (as p→0) for the process N_p, when the thinning mechanism involve a Markov correlation between thinned events.Such a problem arise in the theory of rare events and its applications to traffic theory, reliability and ecology problems.     

Adhesion study of tetra methyl cyclo tetra siloxanes (TMCTS) and tri methyl silane (3MS)-based low-k films

Chemical vapor deposited (CVD) low-k films using tri methyl silane (3MS) precursors and tetra methyl cyclo tetra siloxanes (TMCTS) precursors were studied. Films were deposited by means of four processes, namely, O₂, O₂ + He process and CO₂, CO₂ + O₂ process for 3MS and TMCTS precursors, respectively. Interfacial adhesion energy (G_c), of low-k/Si samples, as measured by a 4-point bending test displayed a linear relationship with film hardness and modulus. Fractography studies indicated two possible failure modes with the primary interface of delamination being either at low-k/Si or Si/epoxy interface. In the former, once delamination initiated at the low-k/Si interface, secondary delamination at the Si/epoxy and epoxy/low-k interfaces was also observed. Films with low hardness (<5 GPa) displayed a low G_c (<10 J/m²) with an adhesive separation of Si/epoxy, epoxy/low-k, and low-k/Si interfaces. Whereas, films of high hardness (>5 GPa) displayed interfacial energies in excess of 10 J/m² with separation of Si/epoxy and epoxy/low-k interfaces, thus indicating excellent adhesion between the Si and low-k films. Films with high hardness have less carbon in the system causing it to be more “silicon dioxide” like and exhibiting better adhesion with the Si substrate.     

Stochastic analysis of a multi-unit cold standby system working in orbit form

This paper considers the analysis of a single server n-similar unit system. Initially k(<n) units form an orbit which functions if one unit functions at a time and the remaining n − k units work as cold standbys. When a unit fails in the orbit it is instantaneously replaced by one of the standbys with the help of a perfect transfer switch. The system is said to fail when n − k + 1 units have failed. The distribution of time to failure and time to repair of a unit are negative exponential. Using the regenerative point technique several reliability characteristics are obtained to carry out the cost-benefit analysis.     

On a vacation queue with instantaneous customer loss

The paper studies an M/M/1 queueing system with variable batch-size arrivals and single exponential departures. The system is subject to time-homogeneous server vacations. In addition, a variable bulk customer loss of j units occurs with probability π_j (j = 0, 1, 2, 3,.. . M) where Σ π_j = 1 , at an instant when a vacation starts. The vacation times follow a general probability distribution. The probability generating functions of the number in the system have been determined and some particular cases of interest have been discussed. Finally some steady state results have been derived.     

A two-unit cold standby system with imperfect repair and excessive availability period

A two-unit cold standby redundant system supported by a single repair facility is considered. The units after repair do not behave like new ones and a unit can be repaired, at most, k(k < ∞) times. The failure time distribution of either unit is different after each repair. Further, the system performance is maintained for a random time even after breakdown. The reliability characteristics are provided for the model.     

First-principles calculation of sulfur–selenium segregation in ZnSe1−xSx: The role of lattice vibration

First-principles phase diagram calculations based on density functional theory within the generalized gradient approximation in combination with Monte Carlo (MC) techniques and cluster expansion were performed for the ZnSe_1−xS_x alloys. Formation energies were used as a basis for fitting cluster expansion Hamiltonians. All formation energies of ZnSe_1−xS_x alloys are positive, showing that ZnSe_1−xS_x alloys is a miscibility gap system and has a tendency to phase separation. For ZnSe_1−xS_x alloys the phase diagram computed with conventional cluster expansion shows a miscibility gap with consolute temperature T_c=327 K. The contributions of lattice vibration reduce T_c to 281 K (about 15%). We presented a MC study of the spatial distribution of S and Se in ZnSe_0.5S_0.5 alloys. We found that, the system becomes more homogeneous including lattice vibration at lower temperature. It is consistence with the calculation of phase diagram of ZnSe_1−xS_x alloys.     

Probabilistic analysis of a two-unit cold standby system with two-phase repair and preventive maintenance

This paper deals with cost-analysis of a single-server two-unit cold standby system subject to random inspection and k-failure modes. A switch is used to operate the standby unit which works successfully with known probability p(=1 −q). The service facility plays the dual role of inspection and repair of both failed unit and failed switch. Identifying the system at suitable regenerative epochs, the integral equations are set up for the probabilities of system being in the “up” or “down” state. Laplace transform technique is adopted to solve these equations and various reliability characteristics of interest to system designers and operations managers have been obtained.     

A new mathematical approach to multi-area power system reliability evaluation

In the original interconnected system reliability model the system state space consists of a set of all n-tuples X = (x₁, x₂,…, x_l, x_l+1,…, x_n) where x₁, x₂, x₃,…, x_l are generation capacities and x_l+1, …, x_n are intertie capacities. Corresponding to each load state i we have state space S_i. For each S_i there exists a map F_i:S_i → R. For each i, S_i is then decomposed into sets of acceptable states A_ks and sets of unacceptable states B_ls. Each B_l is then classified accordingly as it is a loss of load in a particular area or not. Then the appropriate reliability indices are calculated. In this approach the maximal flow function is viewed as a map F: _iS_i → R. It is shown that F is a piecewise linear function. It is also shown that there is a one-one correspondence between B sets with the same area loss of load to each of the linear functions. A useful result which aids in the reduction of computational time of frequency calculation of loss of load is then derived.     

Properties of high-Tc superconducting circular waveguides with Meissner boundary

The propagation properties of the TE-modes in a high-temperature superconducting circular waveguide using the Mei\ner boundary conditions on the wall are presented for the first time. The results show that now the normalized cutoff parameterk _c R, (whereR is the radius of the superconducting circular waveguide andk _c the cutoff wavenumber,) is dependent on the radius unlike conventional metallic circular waveguide whose normalized cutoff parameterk _c R is a constant for a given mode and the filled dielectrics. Instead of TE₁₁-mode now TE₀₁ mode becomes the dominant mode and the normal component of magnetic field for the dominant mode is not equal to zero on the wall. Other unique results of high-T _c superconducting circular waveguides are illustrated, too.     

Some characteristics on a finite queue with normal partial and total failures

In this paper we consider that units arrive at a service station in a Poisson fashion with rate λ and are served exponentially by a single server with rate μ in normal working condition, and with slower rate v (v < μ) in the case of partial failure of the service channel. The total failure of a unit is repaired with repair rate β₁ and that of partial failure with repair rate β₂. The partial and total failure rates for the service channel are a₁ and a₂, respectively. The system will function even if a partial failure occurs. The waiting room is finite and the service discipline is a first come first served basis (FCFS). The purpose of this paper is to obtain a steady-state probability generating function for the number of customers present in the system for different states. The probability of various states, along with corresponding results for the particular cases of the system, has been derived.     

Influence of thermal contact resistance on thermal impedance of microelectronic structures

The thermal impedance Z_th(jω) has been calculated numerically for a silicon chip glued on a ceramic substrate. The non perfect thermal contact is taken into account by modelling the chip-substrate interface as a thermal contact resistance r_c. If Z_th is represented as a Nyquist plot, mainly two circular arcs are observed. The high frequency arc is found to be almost independent from r_c, whereas the low frequency part is largely influenced by r_c. The thermal resistance R_th = Z_th(jω = 0) increases linearly with r_c, as known from the literature. Additionally, our simulations have shown that similar conclusions can be drawn for the real and imaginary part of Z_th at a fixed frequency ω ≠ 0.     

A recursive algorithm evaluating the exact reliability of a circular consecutive k-within-m-out-of-n:F system

A circular consecutive k-within-m-out-of-n:F system consists of n cyclically ordered components ε₁…ε_n, ie. ε_i+1 succeedes e_i, iε {1,…,n-1}, e₁ succeedes e_n. The system fails if any m consecutive components include k or more failed ones. A recursive algorithm is presented evaluating the reliability of a system with independent components whose failure probabilities may be unequal. This algorithm is computer implementable for “not too large m” (e.g. m 8 for PC machines).     

New challenges to the modelling and electrical characterisation of ohmic contacts for ULSI devices

Continuing developments in semiconductor process and materials technology have enabled significant reductions to be achieved in the contact resistance R_c of devices. This reduction is commonly assessed in terms of the specific contact resistance (SCR) parameter ρ_c (Ω cm²) of the metal–semiconductor interface. Such a reduction in SCR is essential, for as device dimensions decrease, then so also must ρ_c and the corresponding contact resistance in order not to compromise the down-scaled ULSI device performance. Thus the ability to accurately model contacts and measure ρ_c is essential to ohmic contact development. The cross kelvin resistor (CKR) test structure is commonly used to experimentally measure the Kelvin resistance of an ohmic contact and obtain the specific contact resistance ρ_c. The error correction curves generated from computer modelling of the CKR test structure are used to compensate for the semiconductor parasitic resistance, thus giving the SCR value. In this paper the increased difficulty in measuring lower ρ_c values, due to trends in technology, is discussed. The challenges presented by the presence of two interfaces in silicided contacts (metal-silicide–silicon) is also discussed. Experimental values of the SCR of an aluminium–titanium silicide interface is determined using multiple CKR test structures.     

The magnetic properties in transition metal-doped chalcopyrite semiconductors

We calculated the chemical trends of transition metal-doped chalcopyrite diluted magnetic semiconductors by use of the Korringa–Kohn–Rostoker Green's function method and the coherent potential approximation combined with the local density approximation. The ferromagnetism was stable in V- and Cr-doped chalcopyrite diluted magnetic semiconductors (DMSs). In the cases of Fe and Co doping, however, the spinglass-like state was realized. On the other hand, in the cases of Mn-doped I–III–VI₂ and II–IV–V₂-type DMSs, the ground state was ferromagnetic and spinglass-like states, respectively. We explained these chemical trends by considering the electron configurations and the crystal field effect. Moreover, we evaluated Curie temperatures (T_cs) of Cr-doped chalcopyrite semiconductors and expected that T_cs of Cu(Al,Cr)S₂ and Ag(Ga,Cr)S₂ were much higher than room temperature.     

Microstructure-critical current relationships in hard superconductors

The pinning of the flux line lattice (FLL) by crystal lattice defects gives rise to a critical current density J_c for hard superconductors. The volume pinning force density F_p = ‖BXJ_c‖ however, depends both on the elementary interaction force f_p between a single defect and the FLL and on the nature of the summation of these many f_p’s. The latter will depend on the spatial arrangement of defects and on the elastic and plastic deformation properties of the FLL. For localized defects the f_p is a strong function of defect “size”, reaching a maximum when the size is approximately the coherence length, and is approximately proportional to H_c ²(T) (1−h) where H_c is the thermodynamic critical field and h is the reduced magnetic field H/H_c2. The summation model must give a F_p which obeys the following empirical rules: 1) F_p has a maximum at a reduced field h_p which decreases with increasing defect density ρ and f . 2) F_p at h > h_p is structure insensitive while F_p at h < h_p is structure sensitive. 3) A scaling law is obeyed if T is changed, i.e., F_p = H_c2(T)_m .f(h), where m is ∿2.5 andf(h) is only a function of reduced field and microstructure. Experimental evidence for these generalizations is presented and a model which predicts these results is outlined and quantitatively tested. Work supported by the U. S. Energy Research and Development Administration.