Estimating Low Process Average by Inverse Binomial Sampling

Abstract

Traditional methods of estimating the `process average` detect rate of a manufacturing process involves selecting a fixed number of items from the process and using the sample defective proportion as its estimate. If the estimate is required to have a precision proportional to the true process average defect rate, the sample size required is dependent on that true process average. When prior knowledge about the process average is uncertain and its value is low, as in most modern production situations, this binomial sampling scheme often fails to meet the predetermined precision specifications or results in an unnecessarily large number of observations. A well-known sequential estimation method called inverse negative binomial sampling is considered as a potentially more efficient alternative to the traditional binomial fixed sample size approach. particularly under such circumstances. Several existing estimators for the method are presented and compared, from which derives a general estimator whose closed form expressions permit simple determination of moments for estimators fitting this general form. A new estimator is then derived from the general estimator and is shown to he more efficient than the existing ones The precision of the sequential estimation method using the new estimator is shown to be virtually insensitive to a. prior knowledge of the true process average, thereby avoiding the need to provide an initial estimate of it, and therefore making it potentially attractive in practical applications.