Condition monitoring is the foundation of a condition based maintenance (CBM). To relate the information obtained from the condition monitoring to the actual state of the system, it is usually required a stochastic model. On the other hand, considering the interactions and similarities that exist between CBM and statistical process control (SPC), the integrated models for CBM and SPC have been developed. These models apply control charts as a condition monitoring technique, and the inference about the operational states of the system is based on the collected information about the quality of the produced items. Finally, it is decided whether to implement certain type of maintenance actions. This paper describes the application of Multivariate control charts as a condition monitoring technique for CBM purposes. To this end, an integrated model is developed, while it is used a chi-square control chart. Also, to determine the inspection time points, a constant hazard policy is applied.

Multivariate control chats are generally used in situations where the simultaneous monitoring or control of two or more related quality characteristics is necessary. In most processes in the real world, distribution of the process characteristics are unknown or at least non-normal, so the non-parametric or distribution-free charts are desirable. Most non-parametric statistical process-control techniques depend on ranks. In this survey, we apply the fuzzy set theory to deal with the circumstances that the values of each characteristic are presented in linguistic form, so we propose non-parametric Multivariate control charts based on sign and Wilcoxon signed-rank tests. The performance of the proposed charts is investigated in a simulation study. Numerical examples are used to demonstrate the effectiveness and performance of the proposed charts.

Using Multivariate control chart instead of univariate control chart for all variables in processes provides more time and labor advantages that are of significance in the relations among variables. However, the statistical calculation of the measured values for all variables is regarded as a single value in the control chart. Therefore, it is necessary to determine which variable(s) are the cause of the out-of-control signal. Effective corrective measures can only be developed when the causes of the fault(s) are correctly determined. The present study was aimed at determining the machine learning techniques that could accurately estimate the fault types. Through the Hotelling T2 chart, out-of control signals were identified and the types of faults affected by the variables were specified. Various machine learning techniques were used to compare classification performances. The developed model was employed in the evaluation of paint quality in a painting process. Artificial Neural Networks (ANNs) was determined as the most successful technique in terms of the performance criteria. The novelty of this study lies in its classification of the faults according to their types instead of those of the variables. Defining the faults based on their types facilitates taking effective and corrective measures when needed.

This paper is an effort to evolve Multivariate variable control charts in a fuzzy environment where each observation in each sample is assumed to be a canonical fuzzy number. To do this, a likelihood ratio test should be exploited in a fuzzy environment, because Multivariate variable control charts are constructed using this test. In this way, membership functions of likelihood ratio statistics applied to control the process mean and dispersion are obtained solving four non-linear programming problems. Using these membership functions, membership degrees of in and out of control states of both process mean and dispersion are computed. Hence contrary to the classic Multivariate variable control charts categorizing the process into just two states, i.e. in and out of control, the process can be considered in several intermediate states, based on the computed membership degrees, bringing about more flexibility in process analysis.

The familiar Multivariate process monitoring and control procedure is the Hotelling’s T2 control chart, a direct analog of the univariate shewhart  chart. But, its efficiency for detecting small to moderate shifts in the process mean is poor. To improve the power of chart, this paper presents the variable sampling intervals (VSI) scheme. It is assumed that the length of time the process remains in control has exponential distribution. The chart is modeled using Markov chains and is optimized using genetic algorithm optimization method. The results show that the T2 chart with variable ratio sampling scheme is quicker than the classical one in detecting almost all shifts in the process mean.

Many methods are applied to network surveillance for anomaly detection. Some quality control methods have been developed to monitor several quality characteristics simultaneously in different networks. In our study, we use three Multivariate process monitoring techniques such as Hotelling’, s T 2, MEWMA, and MCUSUM to compare to the prior univariate control charts in the DegreeCorrected Stochastic Block Model (DCSBM), a random network model supporting the degree of each node based on Poisson distribution. By estimating parameters in Phase I from many charts, we apply ARL and SDRL metrics for the performance evaluation of Multivariate control charts. The advantage of our method is detecting signals faster than previews ones by simulation and this is useful for defining the suitable method in different types of change. Furthermore, the quality of performance in different Multivariate methods is displayed in detecting the shifts in the DCSBM. Finally, MCUSUM shows better performance for monitoring local and global changes than other methods.