Earticle

We consider the mean value function for NHPP software reliability model and time series regression model in software failure data. We estimate parameters for the proposed models from two data sets. The values of SSE and MSE is presented from two data sets. We compare the predicted number of faults with the actual two data sets using the mean value function and regression curve.

Let p be an odd prime and c be a fixed integer with (c, p) = 1. For each integer a with $1{\leq}a{\leq}p-1$, it is clear that there exists one and only one b with $0{\leq}b{\leq}p-1$ such that $ab{\equiv}c$ mod p. Let N(c, p) denote the number of all solutions of the congruence equation $ab{\equiv}c$ mod p for $1{\leq}a$, $b{{\leq}}p-1$ in which a and $\bar{b}$ are of opposite parity, where $\bar{b}$ is defined by the congruence equation $b{\bar{b}}{\equiv}1$ mod p. The main purpose of this paper is using the mean value theorem of Dirichlet L-functions and the properties of Gauss sums to study the computational problem of one kind mean value function related to $E(c,p)=N(c,p)-{\frac{1}{2}}{\phi}(p)$, and give its an exact computational formula.

Recently, the quality of software has become a major issue. The statistical models used in making predictions about the quality of software are termed software reliability growth models (SRGM). However, the existing SRGMs have not been satisfactory in predicting software reliability behavior (Keiller and Miller(1991), Keiller and Littlewood(1984), Musa(1987)). In this paper, we present a fuzzy-based interval estimation of software errors (failures).

Software reliability in the software development process is an important issue. Software process improvement helps in finishing with reliable software product. Infinite failure NHPP software reliability models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this paper, proposes the reliability model with log type mean value function (Musa-Okumoto and log power model), which made out efficiency application for software reliability. Algorithm to estimate the parameters used to maximum likelihood estimator and bisection method, model selection based on mean square error (MSE) and coefficient of determination($R^2$), for the sake of efficient model, was employed. Analysis of failure using real data set for the sake of proposing log type mean value function was employed. This analysis of failure data compared with log type mean value function. In order to insurance for the reliability of data, Laplace trend test was employed. In this study, the log type model is also efficient in terms of reliability because it (the coefficient of determination is 70% or more) in the field of the conventional model can be used as an alternative could be confirmed. From this paper, software developers have to consider the growth model by prior knowledge of the software to identify failure modes which can be able to help.

Individual items are produced continuously from an industrial process. Each item is checked to determine whether it satisfies a lower screening limit for the quality characteristic which is the weight of an expensive ingredient. If it does, it is sold at a regular price; if it does not, it is reprocessed or sold at a reduced price. The process mean may be adjusted to a higher value in order to reduce the proportion of the nonconforming items. Using a higher process mean, however, may result in a higher production cost. In this paper, the optimal process mean and lower screening limit are determined in situations where the probability that an item functions well is given by a logistic function of the quality characteristic. Profit models are constructed which involve four price/cost components; selling prices, cost from an accepted nonconforming item, and reprocessing and inspection costs. Methods of finding the optimal process mean and lower screening limit are presented and numerical examples are given.