Process control and lot disposition for destructive sampling plans with predictable and unpredictable sampling accuracy

Modern manufacturing facilities are highly sophisticated, and are designed to produce lots of large sizes. Producing quality items of all types, electronic, mechanical, etc. requires effective techniques of sampling and testing. The impact of manufacturing a large number of defective items, can be very costly for both the consumer and the producer, especially if the search for the cause(s) of inaccuracies requires shutting down the facility for an unspecified period of time. In most cases inaccuracies occur due to bias, imprecision, and failure to predict the mean time before failure for items that perform in a satisfactory condition for a short period of time. In this paper all the variables specified were modified by considering all possible causes of inaccuracies that are critical in classifying the items manufactured as quality items. The Bayesian mathematical form of the cost equation was formulated as a function of the upper and lower limits relative to the quality characteristic X under investigation, the mean of X which was assumed as a variable, the variance of X, and the cost parameters. Both possibilities of predictable and unpredictable sampling accuracy were considered. The cost function was optimized to estimate the optimal sample size. The sample size was implemented together with the distribution of the fraction defective, and the two types of error I and II to estimate a set of decision points, and to construct the X~ chart for testing and for lot disposition.