International Journal of Reliability, Quality and Safety Engineering

One of the widely used NHPP models in reliability is the so-called power-law model, also known as the Duane model. A power-law model can be applied in analyzing failure data of both software and hardware systems. Nevertheless, the power-law model is no longer applicable to describe the failure behavior when a hardware/software embedded system is concerned since the failures can come from both hardware and software. How to analyze the failure data of this type is still a problem to study and a new type of model is needed to develop. In this paper, we consider the superposition of the power-law models (SPLM) as one candidate to describe the failure behaviors of hardware/software systems. The characteristics of SPLMs are thoroughly studied. It is shown that an SPLM has the intensity function that can be increasing, decreasing, increasing-then-decreasing or decreasing-then-increasing. Specifically, the identification method of the superposition of power-law processes is provided by using the TTT-plot technique. The TTT-transform of a superposition of power-law processes is DFR-like. Therefore, the conditional TTT-plot should present a convex pattern if the system failures follow a superposition process by a few power-law processes. This provides us an easy way to identify the model when the testing data is available.

In this research, we focus on covariate modelling to explore the interactions between industrial system and its enviroment in terms of the modelling fundamental characteristic — random and fuzzy uncertaity with an intention to decrease the fatal weakness of the modern dissection methodology. We extend the additive and multiplicative covariate models from these considering randomness alone into these considering both randomness and fuzziness in the sense as a mathematical extension to the existing covariate modelling. In terms of the form of logical function an engineering oriented fuzzy reliability model which could potentially count all the aspects associated with an operating system and its environment is proposed. Statistical estimation on the parameters of system fuzzy reliability is considered based on the general theory of the point processes. The impacts on the optimal plant maintenance from the engineering oriented fuzzy reliability modelling is also discussed. Finally we use an industrial example to illustrate the main theoretical developments.

The control chart based on a Poisson distribution has often been used to monitor the number of defects in sampling units. However, many false alarms could be observed due to extra zero counts, especially for high-quality processes. Therefore, some alternatives have been developed to alleviate this problem, one of which is the control chart based on the zero-inflated Poisson distribution. This distribution takes into account the extra zeros present in the data, and yield more accurate results than the Poisson distribution. However, implementing a control chart is often based on the assumption that the parameters are either known or an accurate estimate is available. For a high quality process, an accurate estimate may require a very large sample size, which is seldom available. In this paper the effect of estimation error is investigated. An analytical approximation is derived to compute shift detection probability and run length distribution. The study shows that the false alarm rates are higher than the desirable level for smaller values of the sample size. This is further supported by smaller average run length. In general, the quantitative results from this paper can be utilized to select a minimum size of the initial sample for estimating the control limits so that certain average run length requirements are met.

To ensure safety of a batch process and quality of its final product, one needs to quickly identify an assignable cause of a fault. To solve the diagnosis problem of a batch process, Cho and Kim⁶ proposed a new statistical diagnosis method based on Fisher discriminant analysis (FDA). They showed satisfactory diagnosis performance on industrial batch processes. However, the diagnosis method of Cho and Kim⁶ has a major limitation: it does not work when the fault data available for building the discriminant model are insufficient. In this work, we propose a method to handle the insufficiency of the fault data in diagnosing batch processes. The diagnosis performance of the proposed method is demonstrated using a data set from a PVC batch process. The proposed method is shown to be able to handle the data insufficiency problem, and yield reliable diagnosis performance.

Identification of important design requirements for product development is critical because it leads to successful products with shorter development time. Quality Function Deployment (QFD) is a tool to help the product development team to systematically determine the design requirements for developing a product with higher customer satisfaction. Therefore, determining the Importance rating of Engineering Characteristics should be robust and reliable. Generally, in QFD charts the relationships between Customer Attributes and Engineering Characteristics can be defined using linguistic variables that have three values: Weak, Medium and Strong. Reversing priority of results (rank reversing) is possible when various scales such as 1-3-5 or 1-3-9 are employed. In this paper, the effect of using fuzzy numbers in rank reverse reduction is studied. For this study a statistical experiment for measuring rank reverse with fuzzy numbers was designed. This experiment was replicated for 7 sets, which included symmetrical and non-symmetrical triangular and trapezoidal fuzzy sets with various degrees of fuzziness. This experiment was extended for cases involving relative importance for Customer Attributes with various fuzzy sets used for weights of importance. The results showed a major reduction in rank reversal using symmetrical membership functions. Furthermore, results did not depend on system fuzziness, and there were not any major differences between the use of triangular and trapezoidal membership functions.

A common problem encountered in product or process design is the selection of optimal parameters that involves simultaneous consideration of multi-response characteristics, called a multi-response surface (MRS) problem. There are several approaches proposed for MRS optimization (MRO), including the priority-based approach, the desirability function approach, and the loss function approach. The existing MRO approaches require that all the preference information of a decision maker be articulated prior to solving the problem. However, it is difficult for the decision maker to articulate all the preference information in advance. This paper proposes an interactive approach, called an interactive desirability function approach (IDFA), to overcome the common limitation of the existing approaches. IDFA focuses on extracting the decision maker's preference information in an interactive manner. IDFA requires no explicit tradeoffs among the responses and gives an opportunity for the decision maker to learn his/her own tradeoff space. Consequently, through IDFA, it is more likely that the decision maker finds a solution which is faithful to his/her preference structure.