• Journal of Korean Society for Quality Management
• /
• v.25 no.3
• /
• pp.74-85
• /
• 1997

In this paper we calculate the subgroup size necessary for detecting the change of percent defective with several detection probabilities for orginal population fraction nonconforming p, changed population fraction nonconforming $p^*$, and the ratio k=$p^*$/p in the usage of p control charts. From our calculation we can know the error level of normal a, pp.oximation in detection probability calculation and recommend the subgroup size with lower error levels of normal a, pp.oximation, and then we show the reasonable subgroup size necessary for p, $p^*$, k, and the detection probability of the change of fraction nonconforming in a process. The information that we here show in tables will be useful when p control chart users decide the subgroup size in the p control chart users decide the subgroup size in the p control chart.

• Communications for Statistical Applications and Methods
• /
• v.24 no.5
• /
• pp.481-492
• /
• 2017

This paper investigates a convergence rate of a test statistics given by two scale sampling method based on $A\ddot{i}t$-Sahalia and Jacod (Annals of Statistics, 37, 184-222, 2009). This statistics tests for longitudinal data having the existence of long memory dependence driven by fractional Brownian motion with Hurst parameter $H{\in}(1/2,\;1)$. We obtain an upper bound in the Kolmogorov distance for normal approximation of this test statistic. As a main tool for our works, the recent results in Nourdin and Peccati (Probability Theory and Related Fields, 145, 75-118, 2009; Annals of Probability, 37, 2231-2261, 2009) will be used. These results are obtained by employing techniques based on the combination between Malliavin calculus and Stein's method for normal approximation.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.32 no.9
• /
• pp.707-712
• /
• 2008

The fatigue characteristics of a material or a structure are generally derived from fatigue tests of standard specimens. However, test results of standard specimens are different from those of real structures or components. Therefore, to calculate more accurate fatigue life, the geometrical effect and surface condition must be considered by comparing test results of standard specimens with those of real structures or components. Thus the object of this paper is to evaluate the fatigue characteristics of a real waterwork pipe. Also, to evaluate fatigue characteristic based on life distribution, the statistical fatigue characteristics were analyzed by the normal distribution and related data of P-S-N curve.

• Journal of the Korean Statistical Society
• /
• v.24 no.2
• /
• pp.563-568
• /
• 1995

It is well-known that the sample mean and the sample variance are jointly sufficient under normality assumption. In this paper a proof of the joint sufficiency is given without using the factorization criterion. It is related to a finite Sanov-type conditional theorem, i.e., the conditional probability density of $Y_1$ given sample mean $\mu$ and sample variance $\sigma^2$, where $Y_1, Y_2, \cdots, Y_n$ are independently and identically distributed (i.i.d.) normal random variables with mean m and variance $\delta^2$, equals that of $Y_1$ given sample mean $\mu$ and sample variance $\sigma^2$, where $Y_1, Y_2, \cdots, Y_n$ are i.i.d. normal random variables with mean $\mu$ and variance $\sigma^2$.

• The KIPS Transactions:PartD
• /
• v.10D no.5
• /
• pp.829-836
• /
• 2003

Software Reliability Growth Model that have been studied variously. But measurement of correct parameter of this model is not easy. Specially, estimation of correct model about failure data must be establish and estimation of parameter can consist exactly. To get correct testing, we calculate the normal score and describe the normal probability plot. Use the normal probability plot, we estimate the distribution for failure data. In this paper, we estimate the software reliability growth model for through the normal probability plot. In this research, we applies software reliability growth model through distribution characteristics of failure data. If we see plot, we determine the software reliability growth model, we can make sure superior in model's performance estimation.

• Journal of Power System Engineering
• /
• v.17 no.4
• /
• pp.86-93
• /
• 2013

This paper deals with the effects of driving force and material properties on statistical distribution of fatigue crack growth rate (FCGR) for the friction stir welded joints of Al 7075-T651 aluminum plate. In this work, the statistical probability distribution of fatigue crack growth rate was analyzed by using our previous constant stress intensity factor range controlled fatigue crack growth test data. As far as this study are concerned, the statistical probability distribution of fatigue crack growth rate for the friction stir welded (FSWed) joints was found to evaluate the variability of fatigue crack growth rate for base metal (BM), heat affected zone (HAZ) and weld metal (WM) specimens. The probability distribution of fatigue crack growth rate for FSWed joints was found to follow well log-normal distribution. The shape parameter of BM and HAZ was decreased with increasing the driving force, however, the shape parameter of WM was decreased and increased with increasing the driving force. The scale parameter of BM, HAZ and WM was increased with the driving force.

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.2
• /
• pp.325-334
• /
• 2011

In this paper we consider the discrete time delayed renewal risk model. We investigate what will happen when the distribution function of the discounted proper deficit is asymptotic in the initial surplus. In doing this we establish several lemmas regarding some related ruin quantities in the discrete time delayed renewal risk model, which are of significance on their own right.

• Journal of the Korean Mathematical Society
• /
• v.46 no.2
• /
• pp.347-361
• /
• 2009

In this paper, by estimating small ball probabilities of $l^{\infty}$-valued Gaussian processes, we investigate Chung-type law of the iterated logarithm of $l^{\infty}$-valued Gaussian processes. As an application, the Chung-type law of the iterated logarithm of $l^{\infty}$-valued fractional Brownian motion is established.

• Communications for Statistical Applications and Methods
• /
• v.9 no.1
• /
• pp.101-113
• /
• 2002

In this paper we introduce a new score generating (unction for the rank regression in the linear regression model. The score function compares the $\gamma$'th and s\`th power of the tail probabilities of the underlying probability distribution. We show that the rank estimate asymptotically converges to a multivariate normal. further we derive the asymptotic Pitman relative efficiencies and the most efficient values of $\gamma$ and s under the symmetric distribution such as uniform, normal, cauchy and double exponential distributions and the asymmetric distribution such as exponential and lognormal distributions respectively.

• Journal of Institute of Control, Robotics and Systems
• /
• v.20 no.8
• /
• pp.854-867
• /
• 2014

This paper deals with the performance comparison of a PSO algorithm inspired in the process of simulating the behavior pattern of the organisms. The PSO algorithm finds the optimal solution (fitness value) of the objective function based on a stochastic process. Generally, the stochastic process, a random function, is used with the expression related to the velocity included in the PSO algorithm. In this case, the random function of the normal distribution (Gaussian) or uniform distribution are mainly used as the random function in a PSO algorithm. However, in this paper, because the probability distribution which is various with 2 shape parameters can be expressed, the performance comparison of a PSO algorithm using the beta probability distribution function, that is a random function which has a high degree of freedom, is introduced. For performance comparison, 3 functions (Rastrigin, Rosenbrock, Schwefel) were selected among the benchmark Set. And the convergence property was compared and analyzed using PSO-FIW to find the optimal solution.