Economic model of [formula omitted] under non-normality and measurement errors

Abstract

This paper investigates the effect of non-normality and measurement errors on the economic design of x ̄ - control charts. The measurable quality characteristic of the product is assumed to be non-normally distributed random variable. The process is subject to a single assignable cause with exponentially distributed occurrence time. This assignable cause shifts the process from in-control state to out-of-control state. Each observation involves some deviation from true value due to measurement error. This deviation, characterized by bias and imprecision, is considered to be a normally distributed random variate. The production cycle for the process model consists of: (1 ) the in-control period, (2) the out-of-control period due to occurrence of the assignable cause, (3) the search period due to false alarm, and (4) the search and correction time due to true alarm. An expected-cost model is formulated which comprises the fixed and variable cost of sampling, the cost of searching for the assignable cause when it does and does not exist, and the adjustment and correction costs. The economic design of x - ̄ rmchart involves optimal determination of the design parameters; the sample size, the sampling interval and the control limits coefficients so as to minimize the expected total cost. The optimal value of the design parameters are obtained using a computerized search technique. Consequently the effect of non-normality parameters and measurement errors on the design parameters and on the loss-cost function is explained through numerical examples.