A unified approach to the economic aspects of statistical quality control and improvement

[摘要] ENGLISH ABSTRACT:The design of control charts refers to the selection of the parameters implied, including thesample size n, control limit width parameter k, and the sampling interval h. The design of theX -control chart that is based on economic as well as statistical considerations is presently one ofthe more popular subjects of research. Two assumptions are considered in the development anduse of the economic or economic statistical models. These assumptions are potentially critical. Itis assumed that the time between process shifts can be modelled by means of the exponentialdistribution. It is further assumed that there is only one assignable cause. Based on theseassumptions, economic or economic statistical models are derived using a total cost function perunit time as proposed by a unified approach of the Lorenzen and Vance model (1986). In thisapproach the relationship between the three control chart parameters as well as the three types ofcosts are expressed in the total cost function. The optimal parameters are usually obtained by theminimization of the expected total cost per unit time. Nevertheless, few practitioners have triedto optimize the design of their X -control charts. One reason for this is that the cost models andtheir associated optimization techniques are often too complex and difficult for practitioners tounderstand and apply. However, a user-friendly Excel program has been developed in this paperand the numerical examples illustrated are executed on this program. The optimization procedureis easy-to-use, easy-to-understand, and easy-to-access. Moreover, the proposed procedure alsoobtains exact optimal design values in contrast to the approximate designs developed by Duncan(1956) and other subsequent researchers.Numerical examples are presented of both the economic and the economic statistical designs ofthe X -control chart in order to illustrate the working of the proposed Excel optimal procedure.Based on the Excel optimization procedure, the results of the economic statistical design arecompared to those of a pure economic model. It is shown that the economic statistical designslead to wider control limits and smaller sampling intervals than the economic designs.Furthermore, even if they are more costly than the economic design they do guarantee output ofbetter quality, while keeping the number of false alarm searches at a minimum. It also leads tolow process variability. These properties are the direct result of the requirement that theeconomic statistical design must assure a satisfactory statistical performance.Additionally, extensive sensitivity studies are performed on the economic and economicstatistical designs to investigate the effect of the input parameters and the effects of varying the bounds on, a, 1-f3 , the average time-to-signal, ATS as well as the expected shift size t5 onthe minimum expected cost loss as well as the three control chart decision variables. Theanalyses show that cost is relatively insensitive to improvement in the type I and type II errorrates, but highly sensitive to changes in smaller bounds on ATS as well as extremely sensitivefor smaller shift levels, t5 .Note: expressions like economic design, economic statistical design, loss cost and assignablecause may seen linguistically and syntactically strange, but are borrowed from and usedaccording the known literature on the subject.

[发布机构] Stellenbosch University