Optimal Number Of Times Research Articles

Efficient truncated repetitive lot inspection using Poisson defect counts and prior information

Optimal truncated repetitive sampling plans for inspecting lots of manufactured material using Poisson defect count data and prior information are obtained by minimizing the expected sampling effort. The proposed plans outperform the repetitive and single inspection schemes and they are shown to be better in reducing the number of sample units drawn from the lot. In truncated repetitive plans, the lots can be reinspected, at most, an optimal number of times when their acceptance or rejection cannot be concluded from the original inspection. Assuming a gamma prior model to describe the uncertainty about the unknown defect rate, a computational procedure is proposed to determine the truncated repetitive sampling plans with minimum expected sampling effort by solving integer nonlinear programming problems. The inclusion of lot reinspections, as well as previous information into the decision criteria, also provides the practitioners with a more precise evaluation of the expected producer’s and consumer’s risks. The results obtained illustrate that truncated repetitive plans with expected risks produce important savings in inspection time and cost with respect to conventional sampling schemes based on the classical requirements of quality levels and risks. An application concerning the manufacturing of glass is provided for illustrative purposes.

Caught at the finishing line

Quantum systems habitually leak information, limiting their usefulness for practical applications. By optimally reversing the leak, this information loss has been reduced to a trickle in the solid state. If electron spins in solid materials are to be exploited in quantum computers, there is a need to minimize the quantum 'noise' that inevitably accompanies the interaction of the spins with their environment. Experiments in single crystals of malonic acid undergoing pulsed electron paramagnetic resonance now show how this can be achieved. The use of external pulses to induce the electron spins to 'flip' an optimal number of times causes their noisy interaction with the environment to be averaged towards zero, and the timescale over which spin coherence is maintained is markedly increased — from 0.04 to 30 microseconds in the system studied.

Determination of an optimal retry time in multiple-module computing systems

The 'optimal' (in some sense) amount of time used for (or the optimal number of times) retrying an instruction upon detection of an error in a computing system is usually determined under the assumption that the system is composed of a single module, within which all fault activities are confined until some module-replacement action is taken. However, a computing system is usually composed of at least three modules, namely, CPU, memory, and I/O, and the execution of an instruction often requires the cooperation of two or more modules. It is thus more realistic to consider the fault activities in multiple-module systems. In this paper, we first relax the single-module assumption and model the fault activities in a multiple-module system as a Markov process. We apply the randomization method to decompose the continuous-time Markov chain into a discrete-time Markov chain subordinated to a Poisson process. Using this decomposition, we can derive several interesting measures, such as (1) the conditional probability of successful retry given a retry period and the fact that a non-permanent fault has occurred, (2) the mean time-to-system recovery, and (3) the distribution of the time until which all modules in the system enter a fault-free state. All the measures derived are used to determine, along with the parameters characterizing fault activities and costs of recovery techniques, (a) whether or not retry should be used as a first-step recovery means upon detection of an error, and (b) the best retry period or number of retries that satisfies a given criterion, e.g., a specific probability of successful retry.

Optimal Reuse of Cuprammonium Rayon Hollow-Fibre Dialyzers

The optimal number of times a hollow-fibre cuprammonium rayon (Terumo TAF) dialyzer could be used was determined in twelve patients. Each dialyzer was reused six times. There was a highly significant decrease in neutrophil count (46.9 +/- 6.9%, mean +/- s.e.m.), platelet count (9.6 +/- 3.8%, mean +/- s.e.m.) and serum C3 concentration (10.25 +/- 2.4%, mean +/- s.e.m.) 30 minutes after the commencement of dialysis The intensity of these changes decreased with the re-use of the dialyzers up to the fourth time. There was a small, but significant increase in serum beta 2-microglobulin concentrations after a 6-hour dialysis. The difference between pre- and post-dialysis serum beta 2-microglobulin concentrations appeared to be greater during the 5th and the 6th use (18.8% and 20.5% vs 5.0% during the first use). The clearance rates of urea and creatinine showed a trend to decrease from the fourth use onwards and the ultrafiltration coefficient was significantly reduced from the third use (8.5 +/- 4.0 mean +/- s.e.m.) onwards so that at the sixth use it was only 75.8 +/- 4.8%, (mean +/- s.e.m.) of the value at the first use. It is concluded that the optimal number of uses a cuprammonium rayon hollow-fibre dialyzer can be put to is four.