Acheson J. Duncan

The Economic Design of X Charts Used to Maintain Current Control of a Process

Abstract This paper establishes a criterion that measures approximately the average net income of a process under surveillance of an X chart when the process is subject to random shifts in the process mean. The quality control rule assumed is that an assignable cause is looked for whenever a point falls outside the control limits. The criterion is for the case in which it is assumed that the process is not shut down while the search for the assignable cause is in progress, nor is the cost of adjustment or repair and the cost of bringing the process back into a state of control after the assignable cause is discovered charged to the control chart program. The paper shows how to determine the sample size, the interval between samples, and the control limits that will yield approximately maximum average net income. Numerical examples of optimum design are studied to see how variation in the various risk and cost factors affects the optimum. * The writer is greatly indebted to I. R. Savage and G. Greggory of ...

The Economic Design of -Charts When There is a Multiplicity of Assignable Causes

Abstract An earlier article by the author [4] studied the economic design of -charts used to maintain current control of a process when there is a single assignable cause occurring randomly, but with known effect. The present article extends the study to allow for the occurrence of several assignable causes the probability distribution of which is known. The initial model studied reveals the existence of readily acceptable (local minimum) solutions that are relatively stable with respect to model changes, including marked changes in the distribution of assignable causes. There were also found in some cases economically better solutions that would not be as readily acceptable as those offered by the local minima (e.g., the limits might fall at ± 6σ). The article argues that as extensions of the model approach reality, only the local-minimum solutions will remain. It then goes on to show that these can be well approximated by solutions of single-cause models. Thus in practice it may be sufficient to use sin...

The Economic Design of p-Charts to Maintain Current Control of o Process: Some Numerical Results

For two initial process levels, po ′ = 0.01 and po ′ = 0.05, minimum cost p-charts are presented for 36 sets of cost data and three degrees of shift in the process mean. Minimum cost designs are also given for other special cases. Actually minimum cost designs are derived for np-charts and converted to p-charts. The degrees of shift are expressed as 0.1, 0.5 and 1.0 multiples of the initial process standard deviation. This has some but not a full stabilizing effect. In general it is found that small shifts require larger samples taken less frequently, but generally with a lower overall intensity of sampling. It is also found that with rare exceptions charts designed to detect small shifts have acceptance limits of zero. The effects of variations in the cost parameters and in the rate of occurrence of the assignable cause are also presented in the paper and a brief comparison is made with a paper on p-charts by W. K. Chiu and another by D. C. Montgomery, J. F. Mance and R. G. Herkes.

Bulk Sampling: Problems and Lines of Attack

An attempt is made to formulate a specified type of “bulk sampling” as an abstract field for general study. Recommendations are made for definitions of terms. Populations involved are described and means are defined. The problems of randomness, bias and blending are discussed. The formulation of theoretical variance models and their use in attaining optimum sampling plans are illustrated with particular reference to fertilizer and coal. The need for large amounts of empirical research and the desirability of current controls are indicated.

Design and Operation of a Double-Limit Variables Sampling Plan

Abstract The paper presents and illustrates the use of three charts and a table for the design and operation of a double-limit variables sampling plan. Two of the charts are plots of the Lieberman-Resnikoff tables of the minimum variance unbiased estimate of the proportion of a normal universe exceeding specified limits given sample estimates of the mean and standard deviation or average range. The table is an extension of the Patnaik table of conversion factors for use of the average range in lieu of the standard deviation.

LQL Indexed Plans that are Compatible with the Structure of MIL-STD-105D

Acceptance sampling plans indexed by Limiting Quality Levels (LQLs) are derived. These plans are compatible with the structure of MIL-STD-105D. The draft table of LQL indexed plans under discussion by the International Organization for Standardization (..

Sampling by Variables to Control the Fraction Defective: Part I

Development of the theory and practice of acceptance sampling by variables to control the fraction defective is described in detail. The review starts with the initiating British papers on the subject and finishes with the British revision of MIL-STD-41..

Charts of the 10% and 50% Points of the Operating Characteristic Curves for Fixed Effects Analysis of Variance F Tests, α = 0.01 and 0.05

TABLES of the power functions for fixed effects analysis of variance F tests have been published by Tang [4 ] and Lehmer [2 ] and charts of these power functions have been presented by Pearson and Hartley [3 ] and Fox [1 ]. Pearson and Hartley offer eight charts of power curves for a = 0.01 and a = 0.05 and degrees of freedom fi from 1 to 8 and f2 from 6 to oc. They cover eight pages, one for each value of fi. Fox gives lines of constant ( (defined below) for P = 0.5, 0.7, 0.8 and 0.9 and a = 0.01 and 0.05, and values of f, from 3 to X and values of f2 from 4 to oo. Single charts are for a specified value of a and P.