An Explanatory Study on the Non-Parametric Multivariate T2 Control Chart

Most control charts require the assumption of normal distribution for observations. When distribution is not normal, one can use non-parametric control charts such as sign control chart. A deficiency of such control charts could be the loss of information due to replacing an observation with its sign or rank. Furthermore, because the chart statistics of T2 are correlated, the T2 chart is not a desire performance. Non-parametric bootstrap algorithm could help to calculate control chart parameters using the original observations while no assumption regarding the distribution is needed. In this paper, first, a bootstrap multivariate control chart is presented based on Hotelling’s T2 statistic then the performance of the bootstrap multivariate control chart is compared to a Hotelling’s T2 parametric multivariate control chart, a multivariate sign control chart, and a multivariate Wilcoxon control chart using a simulation study. Ultimately, the bootstrap multivariate control chart is used in an empirical example to study the process of sugar production

A Statistical Model for Determination of the Type of Knowledge Management Approach Based on Organization Processes

Knowledge management is vital to organization management and is done by pursuing different strategies, which are mainly based on two basic knowledge management approaches called the explicit-oriented approach and the tacit-oriented approach. In this paper, we have tried to consider the type of knowledge strategy of organizations in a new classification including organizations with routine or non-routine processes. Thus, the two important knowledge strategies of organizations, the explicit-oriented and the tacit-oriented strategy, are evaluated using a questionnaire completed by 64 companies of either the type with routine or the type with non-routine processes. Then, the relation between the state of knowledge in the companies and the types of companies was determined by using logistic regression and it was found that the companies which use explicit knowledge operate more routinely and vice versa, the companies which use tacit knowledge operate less routinely

Change Point Estimation of a Process Variance with a Linear Trend Disturbance

When a change occurs in a process, one expects to receive a signal from a control chart as quickly as possible. Upon the receipt of signal from the control chart a search for identifying the source of disturbance begins. However, searching for assignable cause around the signal time, due to the fact that the disturbance may have manifested itself into the rocess sometimes back, may not always lead to successful identification of assignable cause(s). If process engineers could identify the change point, i.e. the time when the disturbance first manifested itself into the process, then corrective actions could be directed towards effective elimination of the source of disturbance. In this paper we develop a maximum likelihood estimator (MLE) for process change point designed to detect changes in process variance of a normal quality characteristic when the change follows a linear trend. We describe how this estimator can be used to identify the change point when a Shewhart S-control chart signals a change in the process variance. Numerical results reveal that the proposed estimator outperforms the MLE designed for step change when a linear trend disturbance is present

Identifying the period of a step change in high-yield processes

Quality control charts have proven to be very effective in detecting out-of-control states. When a signal is detected a search begins to identify and eliminate the source(s) of the signal. A critical issue that keeps the mind of the process engineer busy at this point is determining the time when the process first changed. Knowing when the process first changed can assist process engineers to focus efforts effectively on eliminating the source(s) of the signal. The time when a change in the process takes place is referred to as the change point. This paper provides an estimator for a period of time in which a step change in the process non-conformity proportion in high-yield processes occurs. In such processes, the number of items until the occurrence of the first non-conforming item can be modeled by a geometric distribution. The performance of the proposed model is investigated through several numerical examples. The results indicate that the proposed estimator provides a reasonable estimate for the period when the step change occurred at the process non-conformity level. Copyright © 2009 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/64306/1/1007_ftp.pd

Modeling and Analysis of Effective Ways for Improving the Reliability of Second-hand Products Sold with Warranty

Often, customers are uncertain about the performance and durability of the used/second-hand products. The warranties play an important role in reassuring the buyer. Offering the warranty implies that the dealer incurs additional costs to service any claims made by the customers. Reducing warranty costs is an issue of great interest to dealers. One way of improving the reliability and reducing the warranty servicing cost for second-hand items is through actions such as overhaul and upgrade which are carried out by the dealer or a third party. Improving actions allow the dealer to offer better warranty terms and to sell the item at a higher price. This paper deals with two effective approaches (virtual age approach and screening test approach) to decide on the reliability improvement strategies for second-hand products sold under various warranty policies (failure-free, rebate warranty, and a combination of free replacement and lump sum). A numerical example illustrates that from a dealer’s point of view, it is beneficial to carry out an improvement action only if the reduction in the warranty servicing cost is greater than the extra cost incurred due to this improvement action

Linear Profile Monitoring in the Presence of Non-Normality and Autocorrelation

In an increasing number of practical situations, the quality of a process or product can be effectively characterized and summarized by a profile. A profile is usually a functional relationship between a response variable and one or more explanatory variables which can be modeled frequently using linear or nonlinear regression models. In this paper, we study the effect of non-normality on profile monitoring in Phase II when within or between autocorrelation is present. Different levels of autocorrelation and skewed and heavy-tailed symmetric non-normal distributions are used in our study to evaluate the performance of three existing monitoring schemes numerically. Simulation results indicate that the non-normality and autocorrelation can have a significant effect on the in-control performances of the considered schemes. Results also indicate that the out-of-control performances of the schemes are not very sensitive to low and moderate levels of autocorrelation in moderate and large shifts

Bayesian change point estimation in Poisson-based control charts

Precise identification of the time when a process has changed enables process engineers to search for a potential special cause more effectively. In this paper, we develop change point estimation methods for a Poisson process in a Bayesian framework. We apply Bayesian hierarchical models to formulate the change point where there exists a step change, a linear trend and a known multiple number of changes in the Poisson rate. The Markov chain Monte Carlo is used to obtain posterior distributions of the change point parameters and corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the well-known c-, Poisson exponentially weighted moving average (EWMA) and Poisson cumulative sum (CUSUM) control charts for different change type scenarios. We also apply the Deviance Information Criterion as a model selection criterion in the Bayesian context, to find the best change point model for a given dataset where there is no prior knowledge about the change type in the process. In comparison with built-in estimators of EWMA and CUSUM charts and ML based estimators, the Bayesian estimator performs reasonably well and remains a strong alternative. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.</p

Monitoring Multinomial Logit Profiles via Log-Linear Models (Quality Engineering Conference Paper)

In certain statistical process control applications, quality of a process or product can be characterized by a function commonly referred to as profile. Some of the potential applications of profile monitoring are cases where quality characteristic of interest is modelled using binary,multinomial or ordinal variables. In this paper, profiles with multinomial response are studied. For this purpose, multinomial logit regression (MLR) is considered as the basis.Then, the MLR is converted to Poisson GLM with log link. Two methods including Multivariate exponentially weighted moving average (MEWMA) statistics, and Likelihood ratio test (LRT) statistics are proposed to monitor MLR profiles in phase II. Performances of these three methods are evaluated by average run length criterion (ARL). A case study from alloy fasteners manufacturing process is used to illustrate the implementation of the proposed approach. Results indicate satisfactory performance for the proposed method

A general framework for multiresponse optimization problems based on goal programming

Setting of process variables to meet a required specification of quality characteristic (or response variable) in a process, is one of the common problems in the process quality control. But generally there are more than one quality characteristics in the process and the experimenter attempts to optimize all of them simultaneously. Since response variables are different in some properties such as scale, measurement unit, type of optimality and their preferences, there are different approaches in model building and optimization of MRS problems. This study propose a general framework in MRS problems according to some existing works and some types of related decision makers and attempts to aggregate all of characteristics in one approach. The proposed framework contains four non-desirability parts of bias, response variation, errors in predictions and separation from responses' specific region. We demonstrate the proposed framework with two examples of the literature and the results has been discussed with comparing of mentioned existing works.