Fred A. Spiring

A New Measure of Process Capability: Cpm

A new measure of the process capability (Cpm) is proposed that takes into account the proximity to the target value as well as the process variation when assessing process performance. The sampling distribution for an estimate of Cpm (Ĉpm) and some of i..

The reflected normal loss function

The use of loss functions in quality assurance has grown steadily with the introduction of Taguchis philosophy. The quadratic loss function has been used by decision-theoretic statisticians and economists for many years. Taguchi uses a modified form of the quadratic loss function to demonstrate the need to consider proximity to the target while assessing quality. Several authors have suggested that the traditional quadratic loss function is inadequate for assessing quality and quality improvement. A new, easily understood loss function, based on a reflection of the normal density function, is presented, and some associated statistical properties discussed.

A General Class of Loss Functions with Industrial Applications

Over the last few years, loss functions have become increasingly important in quality assurance settings. In this paper, we develop a class of loss functions based on inversions of probability density functions and present industrial examples to illustr..

A Unifying Approach to Process Capability Indices

Much controversy surrounds the use of process capability indices in quality assurance programs. Some of the controversies include the indices legitimacy and consistency in monitoring improvement, their abuse by practitioners in using estimates as parame..

Assessing Process Capability: A Bayesian Approach

Abstract Quality Control Practitioners often base inferences regarding the capability of a process on a point estimate without examining the distributional qualities of the estimator used. A Bayes solution is proposed that provides good statistical analysis that can be easily used and interpreted on the manufacturing floor.

On the average run lengths of quality control schemes using a Markov chain approach

Control schemes such as cumulative sum (CUSUM), exponentially weighted moving average (EWMA) and Shewhart charts have found widespread application in improving the quality of manufactured goods and services. The run length and the average run length (ARL) have become traditional measures of a control schemes performance. Determining the run length distribution and its average is frequently a difficult and tedious task. A simple unified method based on a finite Markov chain approach for finding the run length distribution and ARL of a control scheme is developed. In addition, the method yields the variance or standard deviation of the run length as a byproduct. Numerical results illustrating the results are given.

Assessing Process Capability in the Presence of Systematic Assignable Cause

A process must be considered free from variation due to assignable cause before its capability can be determined. In those situations where variation due to an assignable cause occurs and is tolerated, process capability cannot currently be assessed. By..

Process capability: A total quality management tool

Abstract Recent developments in the assessment of process capability have fostered the principle of continuously monitoring and assessing the ability of a process to meet customer requirements. A procedure is outlined and an example provided illustrating the continuous assessment of process capability and its use as a management tool. The proposed process capability chart contains information regarding the ability of the process to meet or exceed customer requirements over the life of the process. Monitoring the behavior of the processs ability to meet customer requirements provides managers with feedback and evidence of the processs ability in terms they understand.

The inverted beta loss function: properties and applications

In this paper, a general class of loss functions based on the inversion of the standard beta probability density function (pdf) is examined. The extension of this loss function from a standard beta pdf ranging from (0, 1) to the general beta pdf ranging from (p, q) is examined through the scale invariance property under a linear transformation. An industrial application in quality assurance is used to demonstrate this general class of loss functions. Mathematical derivations are attached in the Appendices.

Some Properties of the Family of Inverted Probability Loss Functions

Abstract The concept of inverting a normal probability density function in order to provide practitioners with realistic loss functions was introduced by Spiring [2]. Further developments saw the inversion of other density functions in an attempt to provide a variety of loss functions that could be used in depicting losses associated with deviations from a target (Spiring and Yeung [3]), Leung and Spiring [1]). The recent focus has been on the development and application of particular loss functions and their associated Risk functions. In this manuscript several properties associated with the entire family of Inverted Probability Loss Functions (IPLF) are investigated and outlined. As well, several IPLFs which possess interesting and unique properties associated with assessing, and depicting losses and loss functions are discussed. Several IPLFs will be considered, some plausible conjugate distributions presented and the general performance compared numerically under homogeneous conditions. Industrial examples demonstrating economic and monetary losses are included.