DETERMINATION OF OPTIMAL DESIGN PARAMETERS FOR X CONTROL CHART WITH TRUNCATED WEIBULL IN-CONTROL TIMES

Control charts play an important role in monitoring the quality of a production process. Usually in designing the control charts it is assumed that the in-control times (the time to occurrence of an assignable cause) follow exponential or two parameter Weibull distribution. The three parameter Weibull distribution includes exponential, two parameter Weibull distributions as limiting cases. With suitable cost considerations the optimal values of the design parameters viz. sample size ‘n', the sampling interval ‘h' and control limits ‘k' subject to constraints on type I and type II error probabilities are obtained. The sensitivity analysis of the statistical economic design of control chart with respect to model parameters and costs is also studied. It was found that the economic design of chart is greatly influenced by the distributional assumptions. This design is also extended to the case of random out of control times.