International Journal of Reliability, Quality and Safety Engineering

Modeling and control of dimensional quality is one of deciding factors in current manufacturing competitions, and has always presented a great challenge to both scientists and engineers since for a multi-station machining system, the final product variation is an accumulation from all stations, and the complex non-linear relationship exits between dimensional quality and machining errors. This paper develops a linear state space model using homogeneous transformation to capture the influence of machined errors on dimensional quality, and the explicit expressions for system matrices of the model are explored. The proposed model employs a linear state space form, facilitating the use of the achievements of control theory, information technology and system engineering theory to support engineers supervisory control of physical machining processes, and it also can be used as an analytical engineering tool for efficient and effective faults diagnosis, system plan and design, and optimal sensors allocation. A real machining case illustrates the proposed model.

A "consecutive-k-out-of-m-from-n:F system" consists of n linearly or cyclically ordered components. The system fails if and only if there exist m consecutive components among them at least k ones are failed. In this paper we consider such a system with identical components and we give under some conditions a good approximation for the unreliability of the system when the number of components becomes large. More precisely, the purpose of the present paper is to show that for any failure distribution of components the limit law of the system's unreliability is always of the Weibull class. Thus we generalize here the result given in the case when the failure distribution of components is of the Weibull. We give also some numerical examples.

Cautious reliability estimates of multi-state and continuum-state systems are studied in the paper under condition that initial data about reliability of components are given in the form of interval-valued observations, measurements or expert judgments. The interval-valued information is processed by means of a set of the imprecise Dirichlet model which can be regarded as a set of Dirichlet distributions. The developed model of reliability provides cautious reliability measures when the number of observations or measurements is rather small. It can be viewed as an extension of models based on random set theory and robust statistical models. A numerical example illustrates the proposed model and an algorithm for computing the system reliability.

Reliability of a software application, its failure intensity and the residual number of faults are three important metrics that provide a quantitative assessment of the failure characteristics of an application. Ultimately, it is also necessary, based on these metrics, to determine an optimal release time at which costs justify the stop test decision. Typically, one of the many stochastic models known as software reliability growth models (SRGMs) is used to characterize the failure behavior of an application to provide estimates of the failure intensity, residual number of faults, reliability, and optimal release time and cost. To ensure analytical tractability, SRGMs assume instantaneous repair and thus the estimates of these metrics obtained using SRGMs tend to be optimistic. In practice, repair activity consumes a non trivial amount of time and resources. Also, repair may be conducted according to many policies which reflect the schedule and budget constraints of a project. A few efforts which incorporate repair into SRGMs are restrictive, since they consider only some SRGMs, model the repair process using a constant repair rate, and provide an estimate of only the residual number of faults. These efforts do not address the issue of estimating the failure intensity, reliability and optimal release time and cost in the presence of repair. In this paper we present a generic framework based on the rate-based simulation technique to incorporate repair policies into finite failure non homogeneous Poisson process (NHPP) class of SRGMs. We describe a methodology to compute the failure intensity and reliability in the presence of repair, and apply it to four popular finite failure NHPP models. We also present an economic cost model which considers explicit repair in providing estimates of optimal release time and cost. We illustrate the potential of the framework to quantify the impact of the parameters of the repair policies on the above metrics using examples. Through these examples we discuss how the framework could be used to guide the allocation of resources to achieve the desired reliability target in a cost-effective manner.

Optimal statistical designs of the multivariate CUSUM (MCUSUM) chart for multivariate individual observations based on ARL and MRL are proposed. Statistical design procedures refer to choices of the reference value, k and the control limit, H to ensure that the MCUSUM chart's performance meets certain statistical criteria. The primary criterion is the average run length (ARL) which is the most commonly used measure of a control chart's performance, while the median run length (MRL) which is the 50th percentage point of the run length distribution is suggested to be used as a potential alternative to the ARL or as a secondary criterion in the evaluation of the performance of the MCUSUM control chart. Although the MRL is used in the optimal design of the univariate EWMA and univariate CUSUM charts but the design of an optimal multivariate CUSUM chart based on MRL is not yet given in any literature. This paper also suggests a systematic approach of designing an optimal MCUSUM chart based on the average run length (ARL). The MRL profiles are considered as supplements to the ARL profiles for the control scheme. Examples of optimal designs of the MCUSUM chart based on both MRL and ARL are also presented. Tables are provided to determine the optimal chart parameters for the design of the chart based on both ARL and MRL.