Time Series Modelling for Total Number of Defective Parts of Printed Circuit Boards in the Manufacturing Industry in Ghana

Abstract

For stochastic time series modelling, an essential property is the underlying statistical model that is assumed to govern the number of defective parts of printed circuit boards in a production process in the manufacturing industries in Ghana. The data was for a period spanning from 2009 to 2014. Considering time series methodology, we specify differences in the data points as a stochastic process assumed to have Markov dependency with respective state transition probabilities matrices following the identified state space (i.e. increase, decrease or remain the same). We observed that the identified states communicate, hence the chains are aperiodic and ergodic signifying the possessing of limiting distributions. We established a methodology for determining wthether the daily number of defective parts increase, decrease or remained the same. A criteria for identifying the state(s) in which production of printed circuit boards is cost effective based on least transition probabilities was also applied. The established methodology is applied to daily number of defective parts during printed circuit boards production in the manufacturing industries in Ghana. Chapman-Kolmogorov Equations and time series models were used in this study.The results showed that it was cost effective when productions are done in the first and second states since at these states least number of defective parts of printed circuit boards is recorded.The n-step probabilities were also determined by subjecting the transition matrix to powers.Autoregressive and moving average method was also applied. The data was differenced once for stationarity which was confirmed by the Augmented Dickey-Fuller Test. The model that was adjudged the best was the model with least AIC and BIC values. ARMA (1,1) model was adjudged the most ideal model for forecasting in this study since it met all the requirements of an ideal model.