Stability Index of Stochastic Processes: The Statistical Process Control Approach
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Alex Glushkovsky
Abstract
The article addresses the stability index of stochastic processes (time series) based on the statistical process control approach. The proposed stability index reveals the relation between assignable and common variabilities: the higher the proportion of the assignable variability, the lower the stability. It is calculated as a ratio of the average moving range to the maximum range between the time series mean and the means of the samples with the fixed end. To address sensitivity of the stability index to process changes such as mean and variance shifts, trends, seasonality, autocorrelation, and sudden changes (outliers), hundred of thousands of simulated time series are analyzed. Considering the impact of sample size, amplitude of process change, moment of process change, and type of distribution, the full factorial design of experiment has been applied. The proposed calculation of the stability index and suggested target levels serve as a guide for interpreting stability of the stochastic processes by index. A combination of stability and capability indexes emphasizes dynamic aspects of the process ability regarding specifications and are presented as a dynamic capability index.
© Heldermann Verlag
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Articles in the same Issue
- Transient Analysis of Multistage Degraded Systems with Partial Repairs of General Distribution Modeled by Erlang-k Distribution
- A Practical Procedure for Developing p-Charts
- Posterior Distribution and Loss Functions for Parameter Estimation in Weibull Processes
- Combined CUSUM–Shewhart Schemes for Binomial Data
- A Goodness of Fit Approach to NBURFR and NBARFR Classes
- Control Charts for the Log-Logistic Distribution
- Stability Index of Stochastic Processes: The Statistical Process Control Approach
- Multivariate Max-Chart
- An Optimization Methodology for Condition Based Minimal and Major Preventive Maintenance
- Multivariate Diagnostic Tests: A Review of Different Methods
- A Note on the Concept of Independence
