• Journal of Korean Society for Quality Management
• /
• v.22 no.2
• /
• pp.33-40
• /
• 1994

Most software reliability models and other methods attempt to estimate some measures based on its fault history. There are several phases of the software life cycle including testing phase. We can propose it's stopping rule to decide when to stop the testing and pass it on to the next phase by considering the detailed structure of software and calculating the failure rate when each fault was detected. Downs (1985) proposed a method which was developed for estimating the failure rate applicable only to two-level profiles. In this paper, I extended to profiles involving more levels.

• The Korean Journal of Applied Statistics
• /
• v.33 no.2
• /
• pp.137-145
• /
• 2020

Phase I clinical trials (Dose Finding Studies) are the first step in administering new drugs developed through animal experiments or in vitro experiments to humans. An important area of interest in designing Phase I clinical trials is determining the dose that provides the greatest efficacy and acceptable safe dose to the patient. In this paper, we propose a method to determine the maximum tolerated dose considering efficacy and safety using Biased coin design and stopping rule. The proposed method is compared with existing methods through simulation.

• Journal of the Korean Data and Information Science Society
• /
• v.23 no.6
• /
• pp.1085-1091
• /
• 2012

Phase I clinical trials are designed to identify an appropriate dose; the maximum tolerated dose, which assures safety of a new drug by evaluating the toxicity at each dose-level. The adjusted maximum tolerated dose estimation is presented by stopping rule in phase I clinical trial on this research. The suggested maximum tolerated dose estimation is compared to the standard method3 and NM method using a Monte Carlo simulation study.

• Journal of the Korean Statistical Society
• /
• v.21 no.1
• /
• pp.1-13
• /
• 1992

This article deals with variable selection problem under a newly formed predictive heteroscedastic discriminant rule that accounts for mulitple homogeneous covariance matrices across the K multivariate normal populations. A general version of predictive discriminant rule, a variable selection criterion, and a criterion for stopping with further selection are suggested. In a simulation study the practical utilities of those considered are demonstrated.

• Journal of the Chungcheong Mathematical Society
• /
• v.14 no.2
• /
• pp.47-54
• /
• 2001

Let {Xn, n = 1,2,${\cdots}$} be i.i.d. random variables with the only unknown parameters mean ${\mu}$ and variance a ${\sigma}^2$. We consider a sequential confidence interval C1 for the mean with coverage probability 1-${\alpha}$ and expected length of confidence interval $E_{\theta}$(Length of CI)/${\mid}{\mu}{\mid}{\leq}k$ (k : constant) and give some asymptotic properties of the stopping time in various limiting situations.

• Communications for Statistical Applications and Methods
• /
• v.6 no.2
• /
• pp.543-564
• /
• 1999

The principal aim of a sequential phase I clinical trial in which the toxicity reponses of a group of patient(s) determine the dose level of the next patient(s) group is to estimate the maximal tolerated dose(MTD) of a new drug, In this paper we compared with a simulation study the performance of the MTD estimates that are determined by a stopping rule in a design and also those that are determined by analyzing the data after a clinical trial is terminated. To the latter belong the mean median mode and maximum likelihood estimates. For the Standard Methods the stopping rule MTD is quite inefficient but the median MTD has a best efficiency and is robust with respect to the three different toxicity curves. The problem of non-convergence of MLE MTD is severe. A more improved MTD estimate is produced by combining the advantages of the various MTD estimates and its efficiency is better than the single median MTD estimate especially for the toxicity curve of an unlucky choice of dose levels. The simulation results suggest that simple types of phase I designs can be combined with relatively standard analytic techniques to provide a more efficient MTD estimate.

• Journal of the Korean Statistical Society
• /
• v.24 no.2
• /
• pp.293-301
• /
• 1995

Sums of independent random variables $S_n = X_1 + \cdots + X_n$ are considered, where the $X_n$ are chosen according to a stationary process of distributions. For $c > 0$, let $t_c$ be the smallest positive integer n such that $$\mid$S_n$\mid$ > cn^{\frac{1}{2}}$. In this set up we are concerned with finiteness of expectation of $t_c$ and we have some results of sign-invariant process as applications.

• Journal of Korean Society of Transportation
• /
• v.22 no.4 s.75
• /
• pp.147-158
• /
• 2004

A class of SWP(Stochastic Wane Propagation) models microscopically mimics individual vehicles' stochastic behavior and traffic jam propagation with simplified car-following models based on CA(Cellular Automata) theory and macroscopically captures dynamic traffic flow relationships based on statistical physics. SWP model, a program-oriented model using both discrete time-space and integer data structure, can simulate a huge road network with high-speed computing time. However, the model has shortcomings to both the capturing of low speed within a jam microscopically and that of the density and back propagation speed of traffic congestion macroscopically because of the generation of spontaneous jam through unrealistic collision avoidance. In this paper, two additional rules are integrated into the NaSch model. The one is SMR(Stopping Maneuver Rule) to mimic vehicles' stopping process more realistically in the tail of traffic jams. the other is LAR(Low Acceleration Rule) for the explanation of low speed characteristics within traffic jams. Therefore, the CA car-following model with the two rules prevents the lockup condition within a heavily traffic density capturing both the stopping maneuver behavior in the tail of traffic jam and the low acceleration behavior within jam microscopically, and generates more various macroscopic traffic flow mechanism than NaSch model's with the explanation of propagation speed and density of traffic jam.

• Journal of Korean Society for Quality Management
• /
• v.17 no.2
• /
• pp.17-26
• /
• 1989

This paper is concerned with forecasting the existing number of errors in the computer software and optimizing the stopping time of the software test based upon the forecasted number of errors. The most commonly used models have assessed software reliability under the assumption that the software failure late is proportional to the current fault content of the software but invariant to time since software faults are independents of others and equally likely to cause a failure during testing. In practice, it has been observed that in many situations, the failure rate decrease. Hence, this paper proposes a mathematical model to describe testing situations where the failure rate of software limearly decreases proportional to testing time. The least square method is used to estimate parameters of the mathematical model. A cost model to optimize the software testing time is also proposed. In this cost mode two cost factors are considered. The first cost is to test execution cost directly proportional to test time and the second cost is the failure cost incurred after delivery of the software to user. The failure cost is assumed to be proportional to the number of errors remained in the software at the test stopping time. The optimal stopping time is determined to minimize the total cost, which is the sum of test execution cast and the failure cost. A numerical example is solved to illustrate the proposed procedure.

• The Korean Journal of Applied Statistics
• /
• v.35 no.2
• /
• pp.251-263
• /
• 2022

Phase I clinical trial is called 'Dose finding study'. It is first step of experimenting on humans with new drugs developed through animal experiments or vitro experiments. The important area of interest in designing Phase I clinical trial is determining the dose that acceptable level to the patients and provides the greatest efficacy. In this paper, we explain about methods to determine the maximum tolerated dose using various stopping rules. The SM3, NM, Rim, J3, BSM methods are compared through simulation. And we consider how the methods might be reformed. As a result of the simulation, BSM estimated the MTD closest to the target toxicity probability. J3 method required the least number of subjects. These results are due to the feature of the stopping rules of both methods. The BSM adds 2 or 1 subject at the same dose level when there is a toxic reaction. In addition, the J3 method has a smaller number of subjects than the other methods. If the methods are improved by combining these features, MTD can be estimated more efficiently. If the total number of subjects can be reduced while using the stopping rule of the BSM, accurate estimation is possible for a small number of subjects.