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While Six Sigma metrics have been studied by researchers in detail for normal distribution-based data, in this paper, we have attempted to study the Six Sigma metrics for two-parameter Weibull distribution that is useful in many life test data analyses.

In the theory of Six Sigma, most of the processes are assumed normal and Six Sigma metrics are determined for such a process of interest. In reliability studies non-normal distributions are more appropriate for life tests. In this paper, a theoretical procedure is developed for determining Six Sigma metrics when the underlying process follows two-parameter Weibull distribution. Numerical evaluations are also considered to study the proposed method.

In this paper, by matching the probabilities under different normal process-based sigma quality levels (SQLs), we first determined the Six Sigma specification limits (Lower and Upper Six Sigma Limits- LSSL and USSL) for the two-parameter Weibull distribution by setting different values for the shape parameter and the scaling parameter. Then, the lower SQL (LSQL) and upper SQL (USQL) values are obtained for the Weibull distribution with centered and shifted cases. We presented numerical results for Six Sigma metrics of Weibull distribution with different parameter settings. We also simulated a set of 1,000 values from this Weibull distribution for both centered and shifted cases to evaluate the Six Sigma performance metrics. It is found that the SQLs under two-parameter Weibull distribution are slightly lesser than those when the process is assumed normal.

The theoretical approach proposed for determining Six Sigma metrics for Weibull distribution is new to the Six Sigma Quality practitioners who commonly deal with normal process or normal approximation to non-normal processes. The procedure developed here is, in fact, used to first determine LSSL and USSL followed by which LSQL and USQL are obtained. This in turn has helped to compute the Six Sigma metrics such as defects per million opportunities (DPMOs) and the parts that are extremely good per million opportunities (EGPMOs) under two-parameter Weibull distribution for lower-the-better (LTB) and higher-the-better (HTB) quality characteristics. We believe that this approach is quite new to the practitioners, and it is not only useful to the practitioners but will also serve to motivate the researchers to do more work in this field of research.

Degraded failures and sudden critical failures are quite prevalent in industries. Degradation processes commonly belong to Weibull family and critical failures are found to follow exponential distribution. Therefore, it becomes important to carry out reliability and availability analysis of such systems. From the reported literature, it is learnt that models are available for the situations where the degraded failures as well as critical failures follow exponential distribution. The purpose of this paper is to present models suitable for reliability and availability analysis of systems where the degradation process follows Weibull distribution and critical failures follow exponential distribution.

The research uses Semi-Markov modeling using the approach of method of stages which is suitable when the failure processes follow Weibull distribution. The paper considers various states of the system and uses state transition diagram to present the transition of the system among good state, degraded state and failed state. Method of stages is used to convert the semi-Markov model to Markov model. The number of stages calculated in Method of stages is usually not an integer value which needs to be round off. Method of stages thus suffers from the rounding off error. A unique approach is proposed to arrive at failure rates to reduce the error in method of stages. Periodic inspection and repairs of systems are commonly followed in industries to take care of system degradation. This paper presents models to carry out reliability and availability analysis of the systems including the case where degraded failures can be arrested by appropriate inspection and repair.

The proposed method for estimating the degraded failure rate can be used to reduce the error in method of stages. The models and the methodology are suitable for reliability and availability analysis of systems involving degradation which is very common in systems involving moving parts. These models are very suitable in accurately estimating the system reliability and availability which is very important in industry. The models conveniently cover the cases of degraded systems for which the model proposed by Hokstad and Frovig is not suitable.

The models developed consider the systems where the repair phenomenon follows exponential and the failure mechanism follows Weibull with shape parameter greater than 1.

These models can be suitably used to deal with reliability and availability analysis of systems where the degradation process is non-exponential. Thus, the models can be practically used to meet the industrial requirement of accurately estimating the reliability and availability of degradable systems.

A unique approach is presented in this paper for estimating degraded failure rate in the method of stages which reduces the rounding error. The models presented for reliability and availability analyses can deal with degradable systems where the degradation process follows Weibull distribution, which is not possible with the model presented by Hokstad and Frovig.

Most of the existing software reliability models assume time between failures to follow an exponential distribution. Develops a reliability growth model based on non‐homogeneous Poisson process with intensity function given by the power law, to predict the reliability of a software. Several authors have suggested the use of the non‐homogeneous Poisson process to assess the reliability growth of software and to predict their failure behaviour. Inference procedures considered by these authors have been Bayesian in nature. Uses an unbiased estimate of the failure rate for prediction. Compares the performance of this model with Bayes empirical‐Bayes models and a time series model. The model developed is realistic, easy to use, and gives a better prediction of reliability of a software.

Develops the joint economic designs of • and S² control charts under four operating policies to monitor the process in a situation where the occurrence of the assignable cause follows a general distribution with an increasing hazard rate. The four operating policies can be chosen by quality controllers to cope with the specific process situation. Policy I and policy II assume that the process performs the preventive maintenance programme at equal and decreasing sampling time intervals, respectively. Policy III and policy IV in turn merely take samples using the non‐uniform and uniform sampling interval schemes without preventive maintenance. The derivation of the four models is not very difficult, so it can be used to derive another model. Offers numerical examples to compare the economic designs and the total expected costs per hour of the four models. Finds, from the computational results, policy II is the best for adoption in the design of • and S² control charts. The results also show that the proposed solution procedure is more accurate and better than Rahim et al.’s and Chung and Chen’s procedures. Concludes with remarks and some advantages of introducing the periodic preventive maintenance policy into a process.

The purpose of this study is to propose the time series decomposition approach to analyze and predict the failure data of the repairable systems.

This study employs NHPP to model the failure data. Initially, Nelson's graph method is employed to estimate the mean number of repairs and the MCRF value for the repairable system. Second, the time series decomposition approach is employed to predict the mean number of repairs and MCRF values.

The proposed method can analyze and predict the reliability for repairable systems. It can analyze the combined effect of trend‐cycle components and the seasonal component of the failure data.

This study only adopts simulated data to verify the proposed method. Future research may use other real products' failure data to verify the proposed method. The proposed method is superior to ARIMA and neural network model prediction techniques in the reliability of repairable systems.

Results in this study can provide a valuable reference for engineers when constructing quality feedback systems for assessing current quality conditions, providing logistical support, correcting product design, facilitating optimal component‐replacement and maintenance strategies, and ensuring that products meet quality requirements.

The time series decomposition approach was used to model and analyze software aging and software failure in 2007. However, the time series decomposition approach was rarely used for modeling and analyzing the failure data for repairable systems. This study proposes the time series decomposition approach to analyze and predict the failure data of the repairable systems and the proposed method is better than the ARIMA model and neural networks in predictive accuracy.

Analyzing and forecasting reliability is increasingly important for enterprises. An accurate product reliability forecasting model cannot only learn and track a product's reliability and operational performance, but can also offer useful information that allows managers to take follow‐up actions to improve the product's quality and cost. The Generalized Autoregressive Conditional Heteroskedastic (GARCH) model is already extensively used to analyze and forecast time series data. However, the GARCH model has not been used to analyze and forecast the failure data of repairable systems. Based on these concerns, this study proposes the GARCH model to analyze and forecast the field failure data of repairable systems.

This paper proposes the GARCH model to analyze and forecast the field failure data of repairable systems. Empirical results from electronic systems designed and manufactured by suppliers of the Chrysler Corporation are presented and discussed.

The proposed method can analyze and forecast failure data for repairable systems. Not only can this method analyze failure data volatility, it can also forecast the future failure data of repairable systems.

Advanced progress in the field of reliability prediction estimation can benefit engineers or management authorities by providing important decision support tools in which the prediction accuracy suggests financial and business outcomes as well as other outcome application results.

Describes a probabilistic methodology for fracture assessments of flawed structures constructed of ferritic steels using the research code WSTRESS. The probabilistic formulation for cleavage fracture implements a multiaxial form of the weakest link model which couples the macroscopic fracture behavior with a micromechanics model based on the statistics of microcracks. The Weibull stress, σ_w, emerges as a suitable near‐tip parameter to provide a connection between the microregime of failure and remote loading (J). WSTRESS builds on an iterative procedure to incorporate a 3‐D finite element description of the crack‐tip stress field and measured values of fracture toughness to calibrate the Weibull modulus, m, and the scale parameter, σ_u. Specific features of the code include statistical inference of Weibull parameters based on uncensored and censored models (with maximum likelihood method), construction of confidence intervals, several definitions for the near‐tip fracture process zone and other general facilities such as spatial integration of the stress field (to incorporate the random orientation of microcracks) and stochastic simulation of fracture data using the Monte Carlo method. The code also includes a convenient free‐form command language and a seamless interface with finite element results files stored in Patran binary or ASCII format.

The purpose of this paper is to investigate maintenance performance of a gasification process unit by identifying reliability, failure and hazard rate. The prediction on the number of preventive maintenance (PM) activities and size of labour are being analysed.

The study collects maintenance data for 4,000 hours operation to perform Weibull analysis in order to determine two key factors which are beta shape factor, β and characteristic life, η.

The results for estimation of failure, reliability and hazard rate show that the pump was most likely contributed to the biggest failure. On the other hand, reaction chamber was able to maintain the longest operation among other components. It is estimated that the total PM activities should be within 20-50 activities per month for whole processing plant. Meanwhile, the estimation of size of labour should be within the range of 60-130 numbers of workers per month for all components.

The method of Weibull analysis for investigating current maintenance performance has been analysed using real case study data. The data collection is obtained from a typical gasification process unit.

Due to the limitation of experimental conditions and budget, fatigue data of mechanical components are often scarce in practical engineering, which leads to low reliability of fatigue data and reduces the accuracy of fatigue life prediction. Therefore, this study aims to expand the available fatigue data and verify its reliability, enabling the achievement of life prediction analysis at different stress levels.

First, the principle of fatigue life probability percentiles consistency and the perturbation optimization technique is used to realize the equivalent conversion of small samples fatigue life test data at different stress levels. Meanwhile, checking failure model by fitting the goodness of fit test and proposing a Monte Carlo method based on the data distribution characteristics and a numerical simulation strategy of directional sampling is used to extend equivalent data. Furthermore, the relationship between effective stress and characteristic life is analyzed using a combination of the Weibull distribution and the Stromeyer equation. An iterative sequence is established to obtain predicted life.

The TC4–DT titanium alloy is selected to assess the accuracy and reliability of the proposed method and the results show that predicted life obtained with the proposed method is within the double dispersion band, indicating high accuracy.

The purpose of this study is to provide a reference for the expansion of small sample fatigue test data, verification of data reliability and prediction of fatigue life data. In addition, the proposed method provides a theoretical basis for engineering applications.

The purpose of this paper is to estimate the required number of robots consisting of some non-repairable components, by employing a renewal model. Considering the importance of the availability of standby autonomous robots for reducing and preventing down-times of advanced production systems, which imposes a considerable loss, the present research tries to introduce a practical model for the determination of the required number of autonomous robots.

Most of the available research on the estimation of the required standby components based on the reliability characteristics of components has not considered the environmental factors influencing the reliability characteristics. Therefore, such estimations are not accurate enough. In contrast, this paper focuses on the influence of the environmental and human factors (e.g. the operators’ skill) on the robot reliability characteristics.

A model based on the Weibull renewal process combined with the cold standby strategy is developed for reliability evaluation of the system. The effectiveness of the proposed integrated reliability evaluation model is worked out in some cases.

Determining a required number of robots is an important issue in availability and utilization of a complex robotic production system. In an advanced production system, while the estimation process of a required number of robots can be performed through different approaches, one of the realistic estimation methods is based on the system’s reliability that takes into consideration the system operating environment. To forecast the required number of robots for an existing production system, in some cases, the assumption of a constant failure rate does not differ much from the assumption of a non-constant failure rate and can be made with an acceptable error.