W. L. Pearn

Distributional and Inferential Properties of Process Capability Indices

In this paper we survey and critically comment on some basic concepts and notions relevant to the methodology dealing with process capability indices (PCIs). The emphasis is on distributional and inferential aspects. The intent is to contribute to the ..

Distributional and inferential properties of the process accuracy and process precision indices

Process capability indices such as Cp, k, and Cpk, have been widely used in manufacturing industry to provide numerical measures on process potential and performance. While Cp measures overall process variation, k measures the degree of process departure. In this paper, we consider the index Cp and a transformation of k defined as Ca = 1 - k which measures the degree of process centering. We refer to Cp as the process precision index, and Ca as the process accuracy index. We consider the estimators of Cp and Ca, and investigate their statistical properties. For Cp we obtain the UMVUE and the MLE. We show that this UMVUE is consistent, and asymptotically efficient. For Ca, we investigate its natural estimator. We obtain the first two moments of this estimator, and show that the natural estimator is the MLE, which is asymptotically unbiased and asymptotically efficient. We also propose an efficient test based on the UMVUE of Cp We show that the proposed test is the UMP test.

APPLICATION OF CLEMENTS' METHOD FOR CALCULATING SECOND- AND THIRD-GENERATION PROCESS CAPABILITY INDICES FOR NON-NORMAL PEARSONIAN POPULATIONS

In this article we apply the method proposed by Clements to obtain first-approximation estimators of process capability indices (PCI) for non-normal populations to the second- and third-generation PCIs introduced by the authors in recent publications. C..

A variables sampling plan based on Cpmk for product acceptance determination

Process capability indices are useful management tools, particularly in the manufacturing industry, which provide common quantitative measures on manufacturing capability and production quality. Most supplier certification manuals include a discussion of process capability analysis and describe the recommended procedure for computing a process capability index. Acceptance sampling plans have been one of the most practical tools used in classical quality control applications. It provides both vendors and buyers to reserve their own rights by compromising on a rule to judge a batch of products. Both sides may set their own safeguard line to protect their benefits. Two kinds of risks are balanced using a well-designed sampling plan. In this paper, we introduce a new variables sampling plan based on process capability index Cpmk to deal with product sentencing (acceptance determination). The proposed new sampling plan is developed based on the exact sampling distribution hence the decisions made are more accurate and reliable. For practical purpose, tables for the required sample sizes and the corresponding critical acceptance values for various producer’s risk, the consumer’s risk and the capability requirements acceptance quality level (AQL), and the lot tolerance percent defective (LTPD) are provided. A case study is also presented to illustrate how the proposed procedure can be constructed and applied to the real applications.

One‐sided capability indices CPU and CPL: decision making with sample information

Process capability indices have been used in the manufacturing industry to provide quantitative measures on process potential and performance. The formulae for these indices are easy to understand and straightforward to apply. But, since sample data must be collected in order to calculate these indices, a great degree of uncertainty may be introduced into capability assessments due to sampling errors. Currently, most practitioners simply look at the value of the index calculated from the sample data and then make a conclusion on whether their processes meet the capability requirement. This approach is not reliable since sampling errors are ignored. Procedures for two‐sided capability indices, Cp, Cpk, and Cpm have been developed to assist practitioners to determine whether their processes meet the capability requirement based on sample information. In this paper, we first obtain unbiased estimators of CPU and CPL. We then develop a procedure similar to those of Cp, Cpk, and Cpm, for the one‐sided capability indices CPU and CPL. Practitioners can use the procedure to test whether their processes meet the capability requirement.

Capability indices for non-normal distributions with an application in electrolytic capacitor manufacturing

Abstract Process capability indices C p ( u , v ), which include the four basic indices C p , C pk , C pm and C pmk as special cases, have been proposed to measure process potential and performance. C p ( u , v ) are appropriate indices for processes with normal distributions, but have been shown to be inappropriate for processes with non-normal distributions. In this paper, we first consider two generalizations of C p ( u , v ), which we refer to as C Np ( u , v ) and C ′ Np ( u , v ), to cover cases where the underlying distributions may not be normal. Comparisons between C Np ( u , v ) and C ′ Np ( u , v ) are provided. The results indicated that the generalizations C Np ( u , v ) are superior to C ′ Np ( u , v ) in measuring process capability. We then present a case study on an aluminum electrolytic-capacitor manufacturing process to illustrate how the generalizations C Np ( u , v ) may be applied to actual data collected from the factories.

Minimising makespan on parallel batch processing machines with non-identical ready time and arbitrary job sizes

This paper considers the parallel batch processing machine scheduling problem which involves the constraints of unequal ready times, non-identical job sizes, and batch dependent processing times in order to sequence batches on identical parallel batch processing machines with capacity restrictions. This scheduling problem is a practical generalisation of the classical parallel batch processing machine scheduling problem, which has many real-world applications, particularly, in the aging test operation of the module assembly stage in the manufacture of thin film transistor liquid crystal displays (TFT-LCD). The objective of this paper is to seek a schedule with a minimum total completion time for the parallel batch processing machine scheduling problem. A mixed integer linear programming (MILP) model is proposed to optimise the scheduling problem. In addition, to solve the MILP model more efficiently, an effective compound algorithm is proposed to determine the number of batches and to apply this number as one parameter in the MILP model in order to reduce the complexity of the problem. Finally, three efficient heuristic algorithms for solving the large-scale parallel batch processing machine scheduling problem are also provided.

MULTIPROCESS PERFORMANCE ANALYSIS: A CASE STUDY

Statistical process control charts, which are essential tools to process control and improvement, have been widely used for monitoring individual factory production processes. In the multiprocess environment where a group of processes need to be monitor..

An application of non-normal process capability indices

Numerous process capability indices, including Cp, Cpk, Cpm, and Cpmk, have been proposed to provide measures of process potential and performance. In this paper, we consider some generalizations of these four basic indices to cover non-normal distributions. The proposed generalizations are compared with the four basic indices. The results show that the proposed generalizations are more accurate than those basic indices and other generalizations in measuring process capability. We also consider an estimation method based on sample percentiles to calculate the proposed generalizations, and give an example to illustrate how we apply the proposed generalizations to actual data collected from the factory.

Variables sampling plans with PPM fraction of defectives and process loss consideration

Acceptance sampling plans provide the vendor and the buyer decision rules for lot sentencing to meet their product quality needs. A problem the quality practitioners have to deal with is the determination of the critical acceptance values and inspection sample sizes that provide the desired levels of protection to both vendors and buyers. As todays modern quality improvement philosophy, reduction of variation from the target value is the guiding principle as well as reducing the fraction of defectives. The Cpm index adopts the concept of product loss, which distinguishes the product quality by setting increased penalty to products deviating from the target. In this paper, a variables sampling plan based on Cpm index is proposed to handle processes requiring very low parts per million (PPM) fraction of defectives with process loss consideration. We develop an effective method for obtaining the required sample sizes n and the critical acceptance value C0 by solving simultaneously two nonlinear equations. Based on the designed sampling plan, the practitioners can determine the number of production items to be sampled for inspection and the corresponding critical acceptance value for lot sentencing.