Ecomonic Design Of Statistical Quality Control Chart Research

Control charts are widely used to establish and maintain statistical control of process. They are also effective devices for estimating process parameters, particularly in process capability studies. The use of a control chart requires that the engineer or analyst select a sample size, a sampling frequency or interval between samples, and the control limits for chart. Selection of these three parameters is usually called the design of the control chart.Traditionally, control charts have been designed with respect to statistical criteria only. This usually involves selecting the sample size and control limits such that the average run length of the chart to satisfy some conditions.The frequency of sampling is rarely treated analytically, and usually the practitioner is advised to consider such factors as the production rate, the expected frequency of shifts to an out-of-control state, and the possible consequences of such process shifts in selecting the sampling interval. The use of statistical criteria and practical experience has led, in many cases, to general guidelines for the design of control charts. Many of these guidelines, as well as the approach used in developing them, have been discussed for specific types of control charts in many literature.The design of a control chart has economic consequences in that the costs of sampling and testing, costs associated with investigating out-of-control signals and possibly correcting assignable causes, and costs of allowing nonconforming units to reach the consumer are all affected by the choice of the control chart parameters. Therefore, it is logical to consider the design of a control chart from an economic viewpoint.We present two basic models for the optimal economic design of control charts. One is Duncan's model proposed by Duncan in 1956,another is Lorenzen&Vance's model with a unified approach proposed by Lorenzen&Vance in 1986.Based on the economic model interested in, we incorporate Taguchi's loss function in the econominc design of control chart; we discuss economic statistical design approach that takes statistical properties into account while designing control charts economically. Statistical constraints based on average run length (ARL) is used in formulating a model for the economic statistical design of (X|-) chart for controlling process means. Cost comparisons between optimal economic designs and optimal economic statistical designs show relatively small cost increases when imposing statistical constraints on the cost model. we also study the statistical properties and the economic design of (X|-) chart with asymmetric control limits. It has been found thatthe ARL₀ depend heavily on the probability of an upward or downward shift in theprocess mean. finally , we discuss the economic designs of CUSUM and EWMA control charts.