The reliability of computer software is of prime importance for all developers of software. The complicated nature of detecting and removing faults from software has led to a plethora of models for reliability growth. One of the most basic of these is the Jelinski Moranda model, where it is assumed that there are N faults in the software, and that in testing, bugs (or faults) are encountered (and removed when defected) according to a stochastic process at a rate which at a given point in time is proportional to the number of bugs remaining in the system. In this research, we consider the possibility that imperfect repair may occur in any attempt to remove a detected bug in the Jelinski Moranda model. We let p represent the probability that a fault which is discovered or detected is actually perfectly repaired. The possibility that the probability p may differ before and after release of the software is also considered. The distribution of both the number of bugs detected and perfectly repaired in a given time period is studied. Cost models for the development and release of software are investigated, and the impact of the parameter p on the optimal release time minimizing expected costs is assessed.

Starting with the meaning of the word quality, diverse concepts connoted by the term are examined. Instead of a bathtub curve, the desirable shape of a failure rate covering the entire life of a good product, which might be called hockey-stick line, is introduced. From the hockey-stick line and the definition of reliability, two measurements are extracted. The terms reliability, failure rate, product life, and durability are explained. From the customer's standpoint, the concept of product quality is classified in five factors, according to related technology: performance, reliability, conformance to specifications, customer perception, and fundamentals advantage. The correlation of the five factors for a first-class product is discussed, Since the market share of a company is determined as the competition result of its product value, defined as product quality and price, the market share increase is derived mathematically from the increment of product value. The market share increase, $\Delta$S, can be calculated from the present market share, S, and the oriented relative value increment of new product, R, to the current product in the same company for the same market target: $\Delta$S : $\Delta$(1-S). R/(1+S.R). Finally, the importance of separating warranty cost from the profit equation for the durables is explained.

The estimation of mean lifetimes in presence of interval censoring with mixed replacement procedure is examined when the distributions of lifetimes are exponential. It is assumed that, due to physical restrictions and/or economic constraints, the number of failures is investigated only at several inspection times during the lifetime test; thus there is interval censoring. The maximum likelihood estimator is found in an implicit form. The Cramor-Rao lower bound, which is the asymptotic variance of the estimator, is derived. The estimation of mean lifetimes for competing failures model has been expanded.

The failure rate functions between successive failures are of concatenated form. We allow the parameters of failure rate function change after a certain failure and its fixing. We confine out attention to a model wherein the interfailure times are described by its failure rate function. We suggest an adaptive failure rate function with a change-point under the assumption that interfailure times are record value statistics from a Weibull distribution. The proposed model will be applied through a practical example of software failure data.

Computer-based simulation and analysis is used extensively in engineering for a variety of tasks. Despite the steady and continuing growth of computing power and speed, the computational cost of complex high-fidelity engineering analyses and simulations limit their use in important areas like design optimization and reliability analysis. Statistical approximation techniques such as design of experiments and response surface methodology are becoming widely used in engineering to minimize the computational expense of running such computer analyses and circumvent many of these limitations. In this paper, we compare and contrast five experimental design types and four approximation model types in terms of their capability to generate accurate approximations for two engineering applications with typical engineering behaviors and a wide range of nonlinearity. The first example involves the analysis of a two-member frame that has three input variables and three responses of interest. The second example simulates the roll-over potential of a semi-tractor-trailer for different combinations of input variables and braking and steering levels. Detailed error analysis reveals that uniform designs provide good sampling for generating accurate approximations using different sample sizes while kriging models provide accurate approximations that are robust for use with a variety of experimental designs and sample sizes.