Monitoring Process Mean and Process Variance Using Collani's Statistic
-
Osiris Turnes
Abstract
In this paper the use of Collani's 
statistic for monitoring simultaneously process mean and process variance is investigated by a comparison with the more popular 
chart and 
chart, respectively. The comparison is performed by means of an economic design of the charts assuming two different situations with respect to the occurrence of assignable cause. The criteria used for the comparison are the average total cost (ATC) and the average run lengths (ARLs), where the latter make sense only for equal sample sizes. Various cases with respect to the economic parameters and the distribution parameters are considered omitting the case of constant process variance, because in such a case a simple 
-chart is in any case superior. It turns out that a chart based on Collani's statistic is by far superior than the two popular charts. In order to have the superiority documented the numerical results are displayed in numerous tables.
© Heldermann Verlag
Articles in the same Issue
- 2005 - The Jakob Bernoulli Year 350th Anniversary of Jakob's Birth and 300th Anniversary of Jakob's Death
- Six Sigma the “Breakthrough Management Strategy”?
- Determining the Parameters of a Multinomial Distribution: The Fiducial Approach
- Some Group Inspection Based Multi-Attribute Control Charts to Identify Process Deterioration
- On Cumulative Conforming Type of Control Charts for High Quality Processes Under Sampling Inspection
- Monitoring Process Mean and Process Variance Using Collani's Statistic
- Ratio of Logistic and Bessel Random Variables
- Weibull Extension of a Bivariate Exponential Regression Model
- Weighted Least Squares Estimators for a Change-Point
- A Note on the Appropriateness of Taguchi's Loss Function
- Acceptance Sampling Based on the Inverse Rayleigh Distribution
- An Alternative Simple Proof of a Result Useful in Reliability Shock Models
- Draft International Standard ISO/DIS 2210: Milk and Milk Products
Articles in the same Issue
- 2005 - The Jakob Bernoulli Year 350th Anniversary of Jakob's Birth and 300th Anniversary of Jakob's Death
- Six Sigma the “Breakthrough Management Strategy”?
- Determining the Parameters of a Multinomial Distribution: The Fiducial Approach
- Some Group Inspection Based Multi-Attribute Control Charts to Identify Process Deterioration
- On Cumulative Conforming Type of Control Charts for High Quality Processes Under Sampling Inspection
- Monitoring Process Mean and Process Variance Using Collani's Statistic
- Ratio of Logistic and Bessel Random Variables
- Weibull Extension of a Bivariate Exponential Regression Model
- Weighted Least Squares Estimators for a Change-Point
- A Note on the Appropriateness of Taguchi's Loss Function
- Acceptance Sampling Based on the Inverse Rayleigh Distribution
- An Alternative Simple Proof of a Result Useful in Reliability Shock Models
- Draft International Standard ISO/DIS 2210: Milk and Milk Products
