A Computer Program to Calculate Two-Stage Short-Run Control Chart Factors for (X,MR) Charts

This paper is the second in a series of two papers that fully develops two-stage short-run (X, MR) control charts. This paper describes the development and execution of a computer program that accurately calculates first- and second-stage short-run control chart factors for (X, MR) charts using the equations derived in the first paper. The software used is Mathcad. The program accepts values for number of subgroups, alpha for the X chart, and alpha for the MR chart both above the upper control limit and below the lower control limit. Tables are generated for specific values of these inputs and the implications of the results are discussed. A numerical example illustrates the use of the program.

Second Stage Short Run (X,vc) and (X,sc) Control Charts

In their'70 paper titled "Mean and Variance Control Chart Limits Based on a Small Number of Subgroups" (Journal of Quality Technology, Volume 2, Number 1, pp. 9-16), Yang and Hillier originally derived equations for calculating the factors required to determine second stage short run control limits for ) v,X c( and )s ,X( c charts. Two issues have restricted the applicability of this particular control chart methodology. These are the limited tabulated values of factors Yang and Hillier present and no example to illustrate the use of the methodology. This paper addresses the first issue by presenting a computer program that accurately calculates the factors regardless of the values of the required inputs. An example shows how to incorporate the methodology into a two stage short run control charting procedure. The computer program is available at http://program.20m.com.

Two-Stage Short-Run (X, MR) Control Charts

This article is the first in a series of two articles that applies two-stage short-run control charting to (X, MR) charts. Theory is developed and then used to derive the control chart factor equations. In the sequel, the control chart factor calculations are computerized and an example is presented

A Computer Program to Calculate Two-Stage Short-Run Control Chart Factors for (X,MR) Charts

This paper is the second in a series of two papers that fully develops two-stage short-run (X, MR) control charts. This paper describes the development and execution of a computer program that accurately calculates first- and second-stage short-run control chart factors for (X, MR) charts using the equations derived in the first paper. The software used is Mathcad. The program accepts values for number of subgroups, α for the X chart, and α for the MR chart both above the upper control limit and below the lower control limit. Tables are generated for specific values of these inputs and the implications of the results are discussed. A numerical example illustrates the use of the program

A Methodology to Improve PCI Use in Industry

This article presents the development of a methodology using decision trees to resolve issues in industry with using process capability indices (PCIs). The methodology forms the structure of a prototype decision support system (PDSS) for PCI selection, calculation, and interpretation. Download instructions for the PDSS are available at http://program.20m.com

Second Stage Short Run (X,vc) and (X,sc) Control Charts

In their 1970 paper titled "Mean and Variance Control Chart Limits Based on a Small Number of Subgroups" (Journal of Quality Technology, Volume 2, Number 1, pp. 9-16), Yang and Hillier originally derived equations for calculating the factors required to determine second stage short run control limits for ) v,X c( and )s ,X( c charts. Two issues have restricted the applicability of this particular control chart methodology. These are the limited tabulated values of factors Yang and Hillier present and no example to illustrate the use of the methodology. This paper addresses the first issue by presenting a computer program that accurately calculates the factors regardless of the values of the required inputs. An example shows how to incorporate the methodology into a two stage short run control charting procedure. The computer program is available at http://program.20m.com

Estimating Task Duration in PERT using the Weibull Probability Distribution

The Weibull probability distribution can be used as an alternative model for task time estimates in the PERT estimating methodology. It has the same advantages as the traditional beta distribution for this application. It has additional benefits, however, that make it a preferred option

Delete and Revise Procedures for Two-Stage Short-Run Control Charts

This article investigates the effect different delete and revise procedures have on the performance of twostage short-run control charting methodology in the second stage of its two stage procedure. Five variables control chart combinations, six delete and revise procedures, and various out-of-control situations in both stages are considered

Two New Unbiased Point Estimates Of A Population Variance

Two new unbiased point estimates of an unknown population variance are introduced. They are compared to three known estimates using the mean-square error (MSE). A computer program, which is available for download at http://program.20m.com, is developed for performing calculations for the estimates