Some Recent Advances in Forecasting and Control

TLDR

Statistical quality control charting and discrete stochastic control models are introduced, emphasizing their relevance to chemical and parts manufacturing industries and their suitability for digital computer implementation. The control strategy balances adjustment costs, deviation penalties, and stochastic disturbances, with a justification distinct from previous approaches. An example demonstrates that the optimal action resembles Roberts’ modification of a Shewhart chart.

Abstract

A brief discussion of Statistical Quality Control Charting procedures is first presented with special reference to the relevance of the objectives and assumptions. An approach to the design of discrete feedforward and feedback control schemes, which are of great importance for example, in the chemical industry, is then given. This approach to control employs discrete stochastic and dynamic models discussed in Part I of this paper (Box and Jenkins, 1968) and has a close link with the forecasting problems discussed there. The control algorithms obtained are ideally suited to discrete digital computer control. However, for common simple situations the algorithms may be represented by suitable charts or nomograms which may be employed to obtain improved manual control. The paper ends with a discussion of a problem typical of that arising in the parts manufacturing industry. Here, attention must be given to the cost of making an adjustment to the machine as well as to the cost of being off target and to the stochastic nature of the disturbance. An example is given where the appropriate form of action is like that required by Roberts's modification of a Shewhart chart. However, the justification required to make such action appropriate is very different from that previously given.