Thomas P. McWilliams

Economic control chart policies for monitoring variables

In this paper, we compare the costs of an economically designed CUSUM control chart and a common Shewhart control chart, the X–bar chart for many configurations of parameters. Our results indicate that there are identifiable regions where there is an overwhelming cost advantage to using CUSUM charts. Additionally, we find that there are identifiable regions where an X–bar chart can be employed without any substantial economic disadvantage. Finally, we identify regions where a regular search policy is less costly than a policy of using either a CUSUM or X–bar chart.

Economic-Statistical Design of X̄ and R or X̄ and S Charts

In this paper we present a comprehensive FORTRAN program that can be used to jointly determine the parameters of X̄ charts used in combination with either R or S charts. The parameters are determined using economic, statistical, or economic- statistical design criteria. The general cost model due to Lorenzen and Vance (1986) is used in economic and economic-statistical designs.

Baseball players with the initial “K” do not strike out more often

It has been claimed that baseball players whose first or last name begins with the letter K have a tendency to strike out more than players whose initials do not contain the letter K. This “result” was achieved by a naive application of statistical methods. We show that this result is a spurious statistical artifact that can be reversed by the use of only slightly less naive statistical methods. We also show that other letters have larger and/or more significant effects than the letter K. Finally, we show that the original study applied the wrong statistical test and tested the hypothesis incorrectly. When these errors are corrected, most of the letters of the alphabet have a statistically significant strikeout effect.

On the Design of Single Sample Acceptance Sampling Plans

Abstract In this paper we provide a method of finding exact designs for single sample acceptance sampling plans. The method uses an algorithm that allows determination of plans based on the hypergeometric, binomial or Poisson distributions. Designs can be found for specified OC curves of either Type A or Type B.

The Design of Truncated Sequential Test Plans Based on Attributes Data

Abstract This study investigates the effect of the choice of a truncation strategy on sequential test plan performance for test plans based on attributes data. We present numerical results that demonstrate the effect of varying the truncation sample size m and reject value R for plans having essentially equivalent Type I and Type II error probabilities. The results show that the choice of m and R should not be taken lightly, as both parameters have a significant effect on test performance.

Economic Advantages of CUSUM Control Charts for Variables

CUSUM charts are usually recommended to be used to monitor the quality of a stable process when the expected shift is small. Here, a number of authors have shown that the average run length (ARL) performance of the CUSUM chart is better than that of the standard Shewhart chart. In this paper we address this question from an economic perspective. Specifically we consider the case where one is monitoring a stable process where the quality measurement is a variable and the underlying distribution is normal. We compare the economic performance of CUSUM and \( \bar X\) charts for a wide range of cost and system parameters in a large experiment using examples from the literature. We find that there are several situations in which CUSUM control charts have an economic advantage over \( \bar X\) charts. These situations are: 1. when there are high costs of false alarms and high costs of repairing a process; 2. when there are restrictions on sample size and sampling interval; 3. when there are several components of variance, and; 4. when there are statistical constraints on ARL.

Students with the initial “A” don’t get better grades

It has been claimed that students whose first or last name begins with the letters A or B have higher grade point averages than students whose first or last name begins with the letters C or D. This “result” was achieved by a naive and incoherent application of statistical methods. We correctly analyze the problem using a new dataset and conclude that the claim is completely unsupported.

Economic Control Chart Policies for Monitoring Variables When There Are Two Components of Variance

When controlling a process mean one can achieve optimal performance in terms of the criterion of average run length (ARL) by using a CUSUM control chart rather than a Shewhart control chart, although for very large shifts the Shewhart control chart is equivalent to a CUSUM chart. Using cost as a criterion, several authors have shown that the ARL dominance of the CUSUM chart does not translate to a cost dominance unless the fixed cost of sampling is very small and some other configurations of the input parameters are met. Additionally, because of the simplicity of the Shewart chart in terms of user training, ease of design and ease of use it may be preferable to a CUSUM chart in these situations. Here, using a large experiment, we investigate the cost advantages of the CUSUM chart versus a common Shewhart control chart, the \(\overline{X}\) chart, in the situation when one is monitoring a process mean and there are two components of variance. Our results are similar to the single component of variance results in that there are predictable regions where there is a large cost advantage to using CUSUM charts and there are also predictable regions where one can use an \(\overline{X}\) without incurring any large increase in cost.

An algorithm for the design of group sequential triangular tests for single‐arm clinical trials with a binary endpoint

Consider the problem of testing H(0):p ≤ p(0) vs H(1):p > p(0), where p could, for example, represent the response rate to a new drug. The group sequential TT is an efficient alternative to a single-stage test as it can provide a substantial reduction in the expected number of test subjects. Whitehead provides formulas for determining stopping boundaries for this test. Existing research shows that test designs based on these formulas (WTTs) may not meet Type I error and/or power specifications, or may be over-powered at the expense of requiring more test subjects than are necessary. We present a search algorithm, with program available from the author, which provides an alternative approach to triangular test design. The primary advantage of the algorithm is that it generates test designs that consistently meet error specifications. In tests on nearly 1000 example combinations of n (group size), p(0), p(1), α, and β the algorithm-determined triangular test (ATT) design met specified Type I error and power constraints in every case considered, whereas WTT designs met constraints in only 10 cases. Actual Type I error and power values for the ATTs tend to be close to specified values, leading to test designs with favorable average sample number performance. For cases where the WTT designs did meet Type I error and power constraints, the corresponding ATT designs also had the advantage of providing, on average, a modest reduction in average sample numbers calculated at p(0), p(1), and (p(0) + p(1))/2.

Statistical CUSUM designs with minimum sampling cost

ABSTRACT We develop a method of designing CUSUM control charts that yields minimum sampling costs while meeting statistical constraints on the average time to signal when there is no assignable cause and the average time to signal when there is an assignable cause. We call this method statistical CUSUM design with minimum sampling costs. Numerical examples are given which show the dominance of this method over the usual statistical design method with the only disadvantage being the small additional effort to estimate sampling costs. The designs we compute are compared to recommended CUSUM statistical designs as well as economic statistical designs.