Michael H. Peters

Use of Curtailed Sampling Plans in the Economic Design of np-Control Charts

An expected-cost model is developed for the np-control chart when curtailed sampling procedures are followed. The total expected cost consists of the cost of sampling, the cost of investigating and possibly correcting the process when an out-of-control signal is received, and the cost of producing defectives. A Hook–Jeeves search procedure is used to identify the minimum-cost sampling policy as a function of three design variables: rejection number, maximum sample size, and intersample interval. Numerical examples are presented, and comparisons are made to corresponding complete sampling policies. These results indicate that curtailed sampling plans provide cost improvements over traditional complete sampling plans and are, therefore, to be recommended whenever it is appropriate to use them.

Economic Design of Quality Monitoring Efforts for Multi-Stage Production Systems

Abstract A model is developed for locating quality monitoring stations in a multi-stage production system and determining the parameters of the np-chart (sample size, acceptance number and sampling interval) used at each quality monitoring station. Each production stage can shift to an out-of-control state associated with an assignable cause. Various cost, profit and time elements are included in the derivation of the net profit per unit function. Dynamic programming and direct search techniques are used to maximize this expected net profit per unit function across the production system. Numerical examples and sensitivity analysis of the model are presented.

Economic design of an attributes control system for a multistage serial production process

A model for the economic design of an np-control system integrated within a multiple stage serial production process is presented. The total expected quality control cost includes the costs of sampling, the costs of investigating an out-of-control alarm and possibly correcting an assignable cause(s), and the costs associated with the production of non-conforming items. The model is represented as a directed network with decision variables of sample size, rejection number and frequency of sampling occurring at each stage of the process. A combination of dynamic programming and direct search techniques is applied to determine the set of sampling policies which yield minimum total expected cost. Numerical examples and results of a sensitivity analysis are reported.

Time-dependent demand in requirements planning: An exploratory assessment of the effects of serially correlated demand sequences on lot-sizing performa

Abstract The problem of determining the appropriate stock replenishment quantity within a time-phased requirements planning environment has received considerable research attention in recent years. Relative performance characteristics of lot-sizing policies have been assessed as a function of the cost structure, the demand pattern, the product structure, forecast error, the length of the planning horizon, and the interaction between replenishment quantities and sequencing decisions. In particular, the relationship between lot sizing behavior and variability in the requirements profile has been intensely investigated. However, despite these efforts, the empirical evidence linking lotsizing performance with demand variability remains inconclusive. This article suggests that, in part, some of the ambiguity in the literature may be an artifact of a failure to adequately control for other important dimensions of simulated demand sequences. The features that have been thought to describe “lumpy” requirements profiles are discussed and the characteristic of periodicity or time-dependency in the demand entries is identified as a variable that has been insufficiently controlled in prior work. A reanalysis of the demand sequences originally published by Kaimann, and subsequently used in a number of comparative lot-sizing studies, reveals that the patterns differ not only in variability as measured by the coefficient of variation, but also in terms of correlation structure as described by the autocorrelation function. Alternative methods for simulating demand sequences are reviewed and a correlation transfer technique, which has the capability to simultaneously control both the degree of variability and correlation, is suggested as an improved method for the generation of synthetic sequences of “lumpy” demand. Using this technique, five of Kaimanns original sequences are rearranged, resulting in three sets of sequences differing only in the strength of serial correlation. Four lot-sizing procedures are applied to each of these sets to discern if the correlation structure has any appreciable effect on lot-sizing performance. Results indicate that, on average, higher total inventory costs are experienced when the demand environment is characterized by randomness. Economic order quantity and part-period balancing achieve lowest average costs when confronted with highly autocorrelated demand or patterns of few runs; conversely, minimum cost per period and Wagner-Whitin perform best under conditions of many runs. Both economic order quantity and part-period balancing perform most favorably in comparison to Wagner-Whitin when runs are few. In addition, there appears to be a potential interaction between the level of demand variability and the degree of serial correlation. This finding is somewhat disconcerting since high variability demand sequences used in some prior research were also characterized by relatively high levels of autocorrelation; hence it becomes most difficult to identify and decompose the unique influences of each demand pattern dimension on lot-sizing behavior. Because of this phenomenon, it is suggested that future studies direct greater attention to the demand simulating methodology than has heretofore been accorded.

Economic design of fraction nonconforming control charts with multiple state changes

A number of models for the economic design of fraction nonconforming control charts have been presented. When multiple out-of-control states exist, a common assumption has been that at most a single assignable cause may affect the state of the productio..

Constructing and maintaining a Beta process distribution for Bayesian quality audit systems

Abstract The process distribution of a manufacturing process which reflects past experience with the quality levels of outgoing lots is an indispensible input of the Bayesian quality audit systems. A distance-method estimator for the process distribution is developed and shown to be superior to the commonly used method-of-moments estimator. In a continuous manufacturing process, the process distribution needs to be updated after each new lot is inspected. Several updating procedures including the posterior distribution, the exponential smoothing method, the moving window method and the all periods method are proposed and compared by a simulation study.

Evaluation of an integrated supplier-buyer quality-control system

In this article, a quality-control design framework that employs information for the supplier-buyer system is modeled. Significant operational savings may be obtained by using the integrated plans developed under this framework. This is especially true when the cost of a defective is high, and the variable sampling and rework costs are low. Analysis of the interaction of defective, rework, and variable sampling costs reveals that the savings are the result of a shift of control effort from the process-control to the lot-acceptance stage, which is the consequence of tradeoffs involving both stages. The managerial impact of adopting integrated plans is discussed.

A multivariate utility function approach to stochastic capacity planning

Abstract The problem being considered is the expansion of a single capacity when the installation cost is large and there are neither absolescence nor spatial effects on the expansion. Demand is assumed to follow an evolving process; in particular, the demand increments are normally distributed with linearly increasing mean and variance in time (i.e., a Wiener process). Selecting the optimum size and timing of capacity additions in the face of uncertain demand forecasts involves both the minimization of cost as well as the minimization of risk. For the situation where demand acts as a Wiener process, Kang and Park have derived the expectation of the “equivalent cost rate.” Using the standard deviation of the equivalent cost rate as a measure of the risk of expansion, Kang and Park then minimized an objective function that was a linear combination of cost and risk. The purpose of this paper is to extend this line of research. Using standard decision analysis procedures, a multiattribute utility function is constructed that reflects the decision makers trade-off for cost and risk. A significant advantage of the utility function approach is that it allows for nonlinear trade-offs of cost and risk.

Economic Design of Fraction Defective Control Charts: Simplification of the Multiple Assignable Causes Situation

Several models for the economic design of p- and np-charts have been developed where the process can be disturbed by more than one assignable cause. It has been speculated that this multiple causes situation can be converted to the simpler single cause version that yields a matching solution. In this paper, heuristics are developed for determining the matching single cause problem for two multiple causes models. These new heuristics are compared with previously suggested heuristics across a wide range of values for a variety of model parameters.

An Economic Evaluation of an Alternative Supplier Customer Quality Control System

In the recent literature much attention has been given to the establishment of a “co-maker” relationship between the customer and the manufacturer (supplier) of a commodity. Under a co-maker relationship, the supplier is viewed as an “upstream extension of the customer’s process” [1]. Although much has been written about certain aspects of co-maker relationships, little research has been done to investigate and evaluate their economic impact. In this research, an analysis is made of the potential economic benefits of a co-maker relationship relative to quality control efforts. The total quality control costs under the traditional supplier-customer relationship are compared to the total quality control costs under a co-maker relationship.