Darwin Davis

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A linear-time method for computing the ANOS of Bernoulli and Poisson CUSUM charts

Quality and Reliability Engineering International

The average number of observations to signal (ANOS) is an important measure of the effectiveness ... more The average number of observations to signal (ANOS) is an important measure of the effectiveness of Bernoulli or Poisson cumulative sum (CUSUM) control charts. Being able to quickly and accurately calculate an ANOS vector facilitates effective control chart design. We present a linear-time method for computing the ANOS of Bernoulli CUSUM charts and generalize to Poisson CUSUM charts. This method overcomes computation challenges associated with previously existing methods. KEYWORDS average number of observations to signal (ANOS), Bernoulli CUSUM, high side and low side, LU factorization, Markov chain, statistical process control

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Using Shewhart and CUSUM Charts for Diagnosis with Count Data in a Vendor Certification Study

Journal of Quality Technology, 2009

Problem: We present a case study concerned with the problem of reducing errors by vendors who pro... more Problem: We present a case study concerned with the problem of reducing errors by vendors who process credit card applications for a large credit card bank. More specifically, we show the results of a process performance evaluation and process capability analysis that was used to help identify and solve the problem of excess variability. These tasks are sometimes called Phase I studies. We conclude with a discussion of implications for process monitoring and subsequent process improvements, sometimes called Phase II studies. Approach: Quality of the credit card processing task was measured with count data and the counts were low; this is typical of many service operations today. Our approach was to use sequence plots and CUSUM sequence plots of the data and Shewhart np and CUSUM control charts to explore the count data drawn from the four vendors that process credit card applications for this bank. We found that using both Shewhart and CUSUM methods helped us to better accomplish the Phase I study. Results: The results of our analysis indicated differences in quality between vendors and within vendors over time. Subsequent analysis showed that the differences were related directly to training and workers' experience. Two interventions were made subsequent to the process capability analysis; these were improved training and interventions to reduce turnover.

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Economic-Statistical Design ofX̄and R orX̄and S Charts

Journal of Quality Technology, 2001

In this paper w~present a comprehensive FORTRAN program that can be used to jointly determine the... more In this paper w~present a comprehensive FORTRAN program that can be used to jointly determine the parameters of X 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.

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Economic, Statistical, and Economic-Statistical Design of Attribute Charts

Journal of Quality Technology, 1995

We present a FORTRAN program that can be used to determine the economic, statistical, or economic... more We present a FORTRAN program that can be used to determine the economic, statistical, or economicstatistical design of a fraction defective or defects per unit chart. In the economic design approach, the general Lorenzen-Vance cost function is minimized. In statistical design, we find designs which meet constraints on average run length while in control and while in a variety of out-of-control states. Economicstatistical designs are based on Saniga's approach, which minimizes the cost function subject to statistical constraints.

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Statistical CUSUM designs with minimum sampling cost

Quality Technology & Quantitative Management, 2016

ABSTRACT We develop a method of designing CUSUM control charts that yields minimum sampling costs... more 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.

$Research paper thumbnail of Characteristics of Economically Designed CUSUM and $$\bar{X}$$ Control Charts$

Characteristics of Economically Designed CUSUM and $$\bar{X}$$ Control Charts

Frontiers in Statistical Quality Control 11, 2015

In this paper we investigate the characteristics of economic control chart designs for both Shewh... more In this paper we investigate the characteristics of economic control chart designs for both Shewhart ($\bar{X}$) and CUSUM control charts. Authors in the past have made some suggestions regarding the design of these charts, where design is defined as finding the values of sample size, intersample interval and control limit (Shewhart chart) or control parameters (k and h) for the CUSUM chart. Here, we run a large number of experiments consisting of many configurations of the parameters and describe and model the results in terms of the actual economic designs.

Column: Computer Programs: Economic-Statistical Design of X-Bar and R or X-Bar and S Charts

[Author's abstract.] In this paper we present a comprehensive FORTRAN program that can be use... more

The Economic and Statistical Designs of Control charts for Censored and Non-Normal Data

In this research, we are dealing with constructing the statistical design (SD) and economic stati... more

Statistical Design of Attribute Charts for Monitoring and Continuous Improvement When Count Levels Are Low

Frontiers in Statistical Quality Control 7, 2004

... Design of Attribute Charts for Monitoring and Continuous Improvement When Count Levels Are Lo... more

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

Frontiers in Statistical Quality Control 10, 2012

When controlling a process mean one can achieve optimal performance in terms of the criterion of ... more 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.

Economic Advantages of CUSUM Control Charts for Variables

Frontiers in Statistical Quality Control 8

CUSUM charts are usually recommended to be used to monitor the quality of a stable process when t... more 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.

Detecting improvement using Shewhart attribute control charts when the lower control limit is zero

IIE Transactions, 2006

In this paper, we present a method to monitor count data so as to be able to detect improvement w... more In this paper, we present a method to monitor count data so as to be able to detect improvement when the counts are low enough to cause the lower limit to be zero. The method, which is proposed as an add-on to the conventional Shewhart control chart, consists in counting the number of samples in which zero defectives or zero

On the Design of Single Sample Acceptance Sampling Plans

Economic Quality Control, 2001

ABSTRACT We provide a method of finding exact designs for single sample acceptance sampling plans... more

A Primer on SPC and Web Data

Frontiers in Statistical Quality Control 12, 2018

In this chapter we compare the website visitor data generated by a variety of commercially availa... more In this chapter we compare the website visitor data generated by a variety of commercially available analytics packages and discuss issues of data accuracy, consistency and unavailability of some important measures. We also discuss some common and perhaps new SPC methods for monitoring website effectiveness using this data.

$Research paper thumbnail of Characteristics of Economically Designed CUSUM and $$\bar{X}$$ Control Charts$

Characteristics of Economically Designed CUSUM and $$\bar{X}$$ Control Charts

by E. Saniga and Darwin Davis

Frontiers in Statistical Quality Control 11, 2015

In this paper we investigate the characteristics of economic control chart designs for both Shewh... more In this paper we investigate the characteristics of economic control chart designs for both Shewhart (X) and CUSUM control charts. Authors in the past have made some suggestions regarding the design of these charts, where design is defined as finding the values of sample size, intersample interval and control limit (Shewhart chart) or control parameters (k and h) for the CUSUM chart. Here, we run a large number of experiments consisting of many configurations of the parameters and describe and model the results in terms of the actual economic designs.

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On the Design of Single Sample Acceptance Sampling Plans

by E. Saniga and Darwin Davis

Economic Quality Control, 2001

In this paper we provide a method of finding exact designs for single sample acceptance sampling ... more 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.

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The Economic and Statistical Designs of Control charts for Censored and Non-Normal Data

by E. Saniga and Darwin Davis

Using Shewhart and CUSUM charts for diagnosis with count data in a vendor certification study

by E. Saniga and Darwin Davis

Economic, statistical, and economic-statistical design of attribute charts

by E. Saniga and Darwin Davis

Statistical Design of Attribute Charts for Monitoring and Continuous Improvement When Count Levels Are Low

by E. Saniga and Darwin Davis

Frontiers in Statistical Quality Control 7, 2004

... Design of Attribute Charts for Monitoring and Continuous Improvement When Count Levels Are Lo... more

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