ENBIS18 in Nancy
2 – 25 September 2018; Ecoles des Mines, Nancy (France)
Abstract submission: 20 December 2017 – 4 June 2018
My abstracts
The following abstracts have been accepted for this event:

Hierarchical Models for Reliability Verification
Authors:
Nikolaus Haselgruber (CIS Consulting in Industrial Statistics GmbH)
Primary area of focus / application:
Reliability
Secondary area of focus / application:
Modelling
Keywords: Reliability, Hierarchical Bayesian models, Verification, Sampling plans
Submitted at 6Mar2018 12:03 by Nikolaus Haselgruber
Accepted
(view paper)
4Sep2018 09:00 Hierarchical Models for Reliability Verification
In a development process of a complex technical product, such as a vehicle or a wind turbine, the verification of reliability targets is an important mission. It decides about release of systems and components. If the product can be considered as a repairable system composed of (subsystems built up from) nonrepairable components, the verification process starts on component level and ends up with the release of the final product based on system testing. Depending on reliability and lifetime requirements, the verification process may be expensive in terms of resources and time. Thus, effective sampling plans can help to minimize the sample size and simultaneously control the risk of releasing unreliable products. This talk discusses several ways to design reliability verification plans. Starting from the classical binomial approach which is wellknown from quality engineering, several alternatives are introduced, such as a Bayesian variant with Beta prior on the failure probability or an a priori known shape parameter for Weibull distributed lifetime. Applications of hierarchical Bayesian models to derive sampling plans for reliability verification for nonrepairable as well as repairable objects are presented in addition. Advantages and potential problems of the different alternatives are discussed by looking realworld examples from the automotive industry, e.g. head lamps of passenger cars.

A New Age and StateDependent Degradation Process with Possibly Negative Increments
Authors:
Massimiliano Giorgio (Università della Campania "Luigi Vanvitelli"), Gianpaolo Pulcini (Istituto Motori, National Research Council (CNR))
Primary area of focus / application:
Other: Statistical methods for degradation data
Keywords: Degradation, Wiener process, Age and state dependent degradation increments, Maximum likelihood estimation
Submitted at 7Mar2018 14:46 by massimiliano Giorgio
Accepted
5Sep2018 10:50 A New Age and StateDependent Degradation Process with Possibly Negative Increments
A new age and statedependent degradation process is proposed that can be used in the case the degradation phenomenon under study is not necessarily monotonic increasing. In particular, the degradation increments of the proposed model are assumed to be possibly dependent on each other and negative. The model is obtained by generalizing the wellknown and largely applied Wiener process and partially preserves the mathematically tractability of the Wiener process. In the paper, the main features and properties of the proposed model are first discussed and the maximum likelihood estimators of its parameters are derived. An applicative example is finally developed which shows the feasibility and the effectiveness of the proposed approach.

Textbooks on response surface methodology emphasize the importance of lackoffit tests when fitting response surface models and stress that, to be able to test for lack of fit, designed experiments should have replication and allow for pureerror estimation. In this paper, we show how to obtain pureerror estimates and how to carry out a lackoffit test when the experiment is not completely randomized, but a blocked experiment, a splitplot experiment, or any other multistratum experiment. Our approach to calculating pureerror estimates is based on residual maximum likelihood (REML) estimation of the variance components in a full treatment model (sometimes also referred to as a cell means model). It generalizes the approach suggested by Vining et al. (2005) in the sense that it works for a broader set of designs and for replicates other than centerpoint replicates. Our lackoffit test also generalizes the test proposed by Khuri (1992) for data from blocked experiments because it exploits replicates other than centerpoint replicates and works for splitplot and other multistratum designs as well. We provide analytical expressions for the test statistic and the corresponding degrees of freedom and demonstrate how to perform the lackoffit test in the SAS procedure MIXED. We reanalyze several published data sets and discover a few instances in which the usual response surface model exhibits significant lack of fit.

Design of a Multivariate Control Chart Using a Support Vector Machine
Authors:
Paria Soleimani (Department of Industrial Engineering, South Tehran branch, Islamic Azad University, Tehran, Iran), Amir Azar (Department of Industrial Engineering, South Tehran branch, Islamic Azad University, Tehran, Iran)
Primary area of focus / application:
Process
Keywords: Statistical process control, Multivariate control chart, Support vector machine, Kernel functions, Average run length
Submitted at 12Mar2018 09:35 by Amir Azar
Accepted
(view paper)
3Sep2018 15:50 Design of a Multivariate Control Chart Using a Support Vector Machine
The current research has designed and developed a control chart based on a oneclass support vector machine and has generalized it to the nonlinear state using kernel functions. The proposed method, taking into account the distribution of data, can create the complex structures as the control limits. In this research with the help of other decision functions, the possibility of discovering out of control variable is also possible that, this feature is not available in most traditional charts.
In order to make a correct comparison, the average run length criterion in a controlled state by adjusting the control limits has been set to 200. Consequently, the control superspace is achieved. Regarding to the degree of kernel function used in the design of the chart, control limits can be converted from the control circle to the control ellipse and ultimately converted to the ellipses of one side (bean shape).
Following are the comparisons between the designed chart and the traditional Hotelling T2chart indicating that, the proposed method has better performance in terms of the average run length. In addition, the discovery of the uncontrolled variable is also evaluated by the proposed method that in this context, the control chart based on support vector machine with polynomial kernel function has been superior.

Estimating Latent Variable by Generalized Kalman Recursions
Authors:
Sadeq Kadhim (Université de Lorraine), Joseph NgatchouWandji (Université de Lorraine)
Primary area of focus / application:
Modelling
Secondary area of focus / application:
Quality
Keywords: Generalized Kalman recursions, Generalized state space models, Multicategorical longitudinal data, Latent variables, Particle filters, EM algorithm
Submitted at 16Mar2018 09:54 by Sadeq KADHIM
Accepted
We consider state space models, relate observed time series to unobserved time series by a system of two equations. The first equation is called the observation equation and the second equation is called the state equation. In this work, we consider generlaized state space models in which the associated functions can be nonlinear and the noises of nonGaussian models. We estimate the states of these models using generalized Kalman recursions, the particle filters and the EM algorithm. Our work is focused on estimating the latent trait in quality of life where the questionnaires are considered as observations and latent variables as states. Concrete examples of latent variables are: the patient health, the business confidence, the morale of customers, the level of anxiety of machine or robot users in factories. Our approach is both an alternative to existing literature work and its generalization. In our work, we are interested in the latent variables Xi (t) produced by an individual i, (i = 1, · · · , n), at time t, (t = 1, · · · , T ). Xi (t) may be the patient’s health, a latent trait, etc. Only Yi (t) is observed instead of Xi (t), the Yi (t) are individuals’ responses to the questionnaire. These results are illustrated by numerical simulations and an application to real data in the quality of life of patients surged for breast cancer.

Most survival analyzes are based on exact failure times and right censored observations, using widely used statistical methods such as the KaplanMeier (KM) method. In medical studies the failure times (e.g. disease or relapse) are observed in the visits that pacients do to medical centers and this situation induces that the interval censoring arises. When interval censoring is present in data, it is necessary to use the Turnbull's method to estimate the survival function, however in practice the imputation of the failure time in this type of censoring is often done using the midpoint of the interval, the right end of the interval or a random point generated within the interval using the uniform distribution. This work through simulation studies the effect of the three types of imputation on the estimation of the survival curve compared to the Turnbull's method. Different simulation scenarios were analyzed based on sample size and time between visits. In all simulation scenarios, the functions estimated using data imputation differ significantly from the true survival function S(t).