Optimising use of the x-chart

Younger, N., 1998. Optimising use of the x-chart. PhD, Nottingham Trent University.

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This thesis begins with a review of the development and use of the control chart in the manufacturing industry. The review reveals scope for investigating the effects of important parameters of the production environment on control chart design parameters and the penalty incurred when suboptimal parameter values are used. The design parameters are sample size (n), sampling interval (h), and control limit coefficient (k).

A subsequent review of the economic design of the x-chart reveals that objective expected cost per time unit (ECPTU) functions can be minimised in order to determine optimum values of n, h and k. In this thesis we use a special case of Lorenzen and Vance's [51] model to extend the previous literature by studying the limiting behaviour of a system of control which is based on the x-chart; quantifying the response of x-chart design parameters to changes in the production environment; and investigating the penalty for use of suboptimal parameter values.

ECPTU functions are minimised with respect to the x-chart's design parameters. When compared with the heuristic design, the primary benefit of use of an economic design as presented in this thesis is the increased probability of detecting the OOC state. The study confirms the need to change the value of the design parameters in response to changes in the values of other process parameters such as the hourly cost of operating the process when it is out of control and the shift coefficient. Average values of the percentage changes are given.

Generally in the literature the time spent identifying and removing the assignable cause has not been regarded as a stochastic variable. In this thesis we generalise the model used to derive ECPTU functions to allow for a distribution of total time spent searching for and removing the assignable cause. Explicitly accounting for restoration time as a stochastic variate which is correlated with the period of surveillance by the x-chart increases the optimum value of sampling interval. A reduction in the value of the penalty for use of suboptimal values is also observed.

The research also explores the practical issues related to production which must be addressed in order to facilitate successful implementation of the ECPTU function.

Item Type: Thesis
Creators: Younger, N.
Date: 1998
ISBN: 9781369323320
Divisions: Schools > Nottingham Business School
Record created by: Linda Sullivan
Date Added: 02 Oct 2020 08:07
Last Modified: 27 Sep 2023 10:27
URI: https://irep.ntu.ac.uk/id/eprint/41089

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