QUALITY MEASUREMENT TIME SERIES MODELING

1
QUALITY MEASUREMENTTIME SERIES MODELING
Susan Li Kasia Tepylo Lin Fang
Department of Math Stats McMaster University
2
Outline

• Introduction
• Preliminary analysis
• Model fitting
• Summary

3
Introduction

• Index of quality (AQI)
• Developed by company to monitor and assure
  product quality
• Potential use in forecasting improvement goals
• The data
• Two sequences BATCH and AQI
• Monthly data for last four years available
• Objective find temporal change pattern for
  productivity and quality

4
Preliminary Analysis

• Data feature time series
• Decomposition of time series
• Trend
• Increasing trends in BATCH and AQI, but less
  obvious in BATCH
• Seasonality
• Pronounced in BATCH less obvious in AQI
• Variation over time
• Decreasing in AQI, but not clear in BATCH

5
Seasonal decomposition of time series
Figure 1 Seasonal decomposition of BATCH
Figure 2 Seasonal decomposition of AQI
6
Removal of trend differencing by lag-1
7
Removal of seasonality differencing by lag-12
8
Model Fitting

• Model fitting strategy Box-Jenkins approach
• Plausible models
• Fitting and diagnostics
• Models BATCH W t 0.716 W t-1 0.284 W t-2
  - 0.931 W t-12
• -
  0.667 W t-13 - 0.264 W t-14 e t
• AQI Y t Y t-1 et - 0.321e t-1
• Diagnostics P-value check
• s2, log likelihood, and aic check
• Normality check
• ACF or PACF check
• Prediction BATCH AQI

9
Diagnostic Plots (BATCH)
10
Diagnostic Plots (AQI)
11
Prediction
12
Summary

• Incorporate the temporal change pattern into QC
  system
• Reliable model fitting approach
• Forecasting in quality