Economically Optimal Design of Inline Equation\( \bar X\)-Control Charts Assuming Gamma Distributed In-Control Times

  • M. A. Rahim
Chapter

Abstract

This paper is motivated by the idea of perfect switching of a repairable equipment adherent to statistical process control. The problem can be viewed as a combination of the inspection policy and the control policy. The state of the randomly failing equipment can only be determined by sampling inspection. The output of the product quality is assumed to be normally distributed and monitored by an \(\bar{x}\)-control chart. The paper determines economically optimum design parameters of \(\bar{x}\)-control charts. A gamma distribution of the in-control periods having an increasing hazard rate is assumed, an age-dependent salvage value of the equipment is introduced. The possibility of an early replacement of the equipment before its failure is considered. The hazard rate is defined to be the probability density of failure at time t to given survival up to that time. Results of using both truncated and non-truncated production cycles are shown. A truncated production cycle begins when a new component of the equipment is installed. It ends with a repair or after a specified number of sampling intervals, whichever occurs first. A non-truncated production cycle is defined in the usual way. It begins when a new component is installed and ends after a shift due to component failure is detected. The process is brought back to the in-control state only by replacement. A single assignable cause model is assumed. Minimizing the expected cost per hour, the optimal values of the design parameters (i.e., sample size, sampling intervals, control limit coefficient and number of inspection intervals) are determined under five different inspection schemes. The sensitivity of the model is examined. Economic benefits of truncated/non-truncated non-uniform schemes are shown.

Key words

economic design of control charts gamma shock models increasing hazard rates variable inspection scheme truncated production cycle 
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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • M. A. Rahim
    • 1
  1. 1.University of New BrunswickFrederictonCanada

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