Volume 17, Issue 2

This case study is concerned with the determination of the specifications of tensile strengths of castings. Thus far, the company has relied on the tensile strength of the test bars as certified by the foundries. Recently, it has bought a tensometer. This machine requires small specimen, which can be machined out of the casting itself. Regression analysis was used to obtain specification limits. A designed experiment enabled the apportioning of variation. It was found that ladle-to-ladle variation was significant.

In this paper we propose an extension of the problem to determine the economic design of a Type I continuous sampling plan (CSP-1 plan) and the economic manufacturing quantity (EMQ) under imperfect quality investigated in Chen et al. (Economic Quality Control 15: 137-146, 2000), where the economic objective equals the total inventory cost including the set-up cost, the holding cost and the expected quality loss. The extension refers to the economic specification limits. The problem can be formulated as a non-linear mixed-integer minimization problem. By solving it, the required level of product quality is obtained at minimum total inventory cost. A numerical example is given to illustrate the solution procedure.

Neyman prediction and measurement procedures have been discussed by E.v. Collani, M. Dumitrescu and their co-workers since 1999. These procedures offer optimal, however, computational rather intensive ways for predicting with respect to the future outcome of a random variable and measuring with respect to the actual value of a deterministic variable under the realistic condition that the range of variability of any involved variable is bounded. This paper presents an algorithm for constructing Neyman prediction and complete measurement procedures for the variance of a normal distribution (with known or unknown mean). A comparison with the traditional shortest confidence intervals is presented by means of a numerical example. The main advantages of the Neyman approach are the following: 1. the unrealistic assumption of maximal and, hence, generally unbounded range of variability is abandoned, 2. the measurements (= confidence intervals) are necessarily subsets of the bounded range of variability, and, therefore, unreasonable results are impossible, 3. the point estimation is necessarily meaningful because it is associated with a confidence interval and a specified confidence level.

We study a nonparametric sequential detection procedure, which aims at detecting the first time point where a drift term appears in a stationary process, from a Bayesian perspective. The approach is based on a nonparametric model for the drift, a nonparametric kernel smoother which is used to define the stopping rule, and a performance measure which determines for each smoothing kernel and each given drift the asymptotic accuracy of the method. We look at this approach by parameterizing the drift and putting a prior distribution on the parameter vector. We are able to identify the optimal prior distribution which minimizes the expected performance measure. Consequently, we can judge whether a certain prior distribution yields good or even optimal asymptotic detection. We consider several important special cases where the optimal prior can be calculated explicitly.

In this paper mixed acceptance sampling procedures are analyzed which combine methods of process control and acceptance sampling for arriving at an efficient and cost-reduced way of performing the control of outgoing or incoming lots of product. The resulting plans are called mixed sampling plans.

In the first part of this paper [Wild and von Collani, Economic Quality Control 17: 113-122, 2002] the Bruceton method and the underlying model assumptions for assessing the sensitivity of explosives were critically examined resulting in the recommendation not to use the Bruceton method. The second part describes an alternative model and method for analyzing the sensitivity of explosive materials. The resulting procedure is applied for comparing the explosive sensitivity of two different kinds of hexogen and for analyzing the sensitivity of a number of other popular explosives.

In this paper, a modification is proposed to the tightened three level continuous sampling plan. The tightened three level plan is one of the three tightened multi-level continuous sampling plans of Derman et. al. (Annals of Mathematical Statistics 28: 395-404, 1957) with three sampling levels and is designated as MLP – T – 3. Using a Markov chain model, expressions for the performance measures of the modified MLP – T – 3 plan are derived. The modified MLP – T – 3 plan is shown to be identical to the MLP – T – 3 plan and CSP – T plan, where CSP – T plan is a special case of MLP – T – 3 plan. Tables are also presented for the selection of a modified MLP – T – 3 plan when the AQL or LQL and AOQL are specified.

This note investigates the problem of minimizing the average fraction inspected ( AFI ) for a CSP – V plan. A solution procedure is developed to find the sampling plan parameters that meet the average outgoing quality limit ( AOQL ) requirement, while minimizing the AFI when the process average (> AOQL ) is known.