Chien-Wei Wu

Variables sampling inspection scheme for resubmitted lots based on the process capability index Cpk

This paper attempts to develop a sampling inspection scheme by variables based on process performance index for product acceptance determination, which examines the situation where resampling is permitted on lots not accepted on original inspection. The equations for plan parameters, the required sample size and the corresponding critical value, are derived based on the exact sampling distribution rather than an approximation approach hence the decisions made are more accurate and reliable. Moreover, the efficiency of the proposed variables resubmitted sampling plan is evaluated and compared with the existing variables single sampling plan. For illustrative purpose, an example is presented to demonstrate the use of the derived results for making a decision on product acceptance determination.

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.

Monitoring Multivariate Process Variability for Individual Observations

Most of the existing control charts for monitoring multivariate process variability are based on subgroup sizes greater than one. In many practical applications, however, only individual observations are available and the usual control charts are not applicable in these cases. In this paper, two new control charts are proposed to monitor multivariate process variability for individual observations. The proposed control charts are constructed based on the traces of the estimated covariance matrices derived from the individual observations. When there is only one quality characteristic, these two charts respectively reduce to the exponentially weighted mean squared deviation and exponentially weighted moving variance charts. It is shown based on the simulation studies that the proposed charts are superior to the existing ones in detecting increases in variance and changes in correlation. An example from the semiconductor industry is also presented to illustrate the applicability of the proposed charts.

A multivariate EWMA control chart for monitoring process variability with individual observations

A control chart is proposed to effectively monitor changes in the population variance-covariance matrix of a multivariate normal process when individual observations are collected. The proposed control chart is constructed based on first taking the exponentially weighted moving average of the product of each observation and its transpose. Appropriate statistics which are based on square distances between estimators and true parameters are then developed to detect changes in the variances and covariances of the variance-covariance matrix. The simulation studies show that the proposed control chart outperforms existing procedures in cases where either the variances or correlations increase or both increase. The improvement in performance of the proposed control chart is particularly notable when variables are strongly positively correlated. The proposed control chart is applied to a real-life example taken from the semiconductor industry.

Decision-making in testing process performance with fuzzy data

Over the years, numerous process capability indices (PCIs) have been proposed to the manufacturing industry to provide numerical measures of process performance. Most research efforts have focused on developing and investigating PCIs that assess process capability by precise measurements of output quality. However, real observations of continuous quantities are not precise numbers; in practice, they are more or less imprecise. Since observations of continuous random variables are imprecise the values of related test statistics become imprecise. Therefore, decision rules for statistical tests have to be adapted to this situation. This article presents a set of confidence intervals that produces triangular fuzzy numbers for the estimation of Cpk index using Buckleys approach with some modification. Additionally, a three-decision testing rule and step-by-step procedure are developed to assess process performance based on fuzzy critical values and fuzzy p-values. This concept is also illustrated with an example for testing process performance.

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.

Assessing process capability based on Bayesian approach with subsamples

Abstract Process capability indices (PCIs) have been widely used to measure the actual process information with respect to the manufacturing specifications, and become the common language for process quality between the customer and the supplier. Most of existing research works for capability testing are based on the traditional frequentist point of view and statistical properties of the estimated PCIs are derived based on the assumption of one single sample. In this paper, we consider the problem of estimating and testing process capability using Bayesian approach based on subsamples collected over time from an in-control process. The posterior probability and the credible interval for the most popular index C pk under a non-informative prior are derived. The manufacturers can use the presented approach to perform capability testing and determine whether their processes are capable of reproducing product items satisfying customers’ stringent quality requirements when a daily-based or weekly-based production control plan is implemented for monitoring process stability.

A resubmitted sampling scheme by variables inspection for controlling lot fraction nonconforming

The paper attempts to develop a resubmitted sampling scheme by variables inspection for controlling lot fraction nonconforming when the quality characteristic follows a normal distribution and has two-sided specification limits. In this paper, the plan parameters are determined by the classical two-point condition on the operating characteristic curve, which will satisfy the quality requirements and allowable risks by the producer and the consumer simultaneously. The behaviour of the proposed sampling plan is discussed and compared with the conventional single sampling plan by variables. The proposed plan requires smaller sample size for inspection with the same protection to the producer and the consumer especially when the quality of the submitted lot is good enough. Tables of the plan parameters under several selected quality requirements and risks are provided for practical applications, and the operating procedure is also presented and illustrated with an example.

Developing a variables repetitive group sampling plan based on process capability index C pk with unknown mean and variance

In this paper, variables repetitive group sampling plans are developed based on the process capability index C pk when the quality characteristic follows a normal distribution with unknown mean and variance. The sampling plan parameters such as the sample size and the acceptance constant are determined to minimize the average sample number. Symmetric and asymmetric cases, in percent defectives due to two specification limits, are dealt with for specified combinations of acceptable quality level and limiting quality level. Tables are provided and examples are given to use proposed plans in practice.

An efficient approach to determine cell formation, cell layout and intracellular machine sequence in cellular manufacturing systems

Cellular manufacturing systems (CMS) are used to improve production flexibility and efficiency. They involve the identification of part families and machine cells so that intercellular movement is minimized and the utilization of the machines within a cell is maximized. Previous research has focused mainly on cell formation problems and their variants; however, only few articles have focused on more practical and complicated problems that simultaneously consider the three critical issues in the CMS-design process, i.e., cell formation, cell layout, and intracellular machine sequence. In this study, a two-stage mathematical programming model is formulated to integrate the three critical issues with the consideration of alternative process routings, operation sequences, and production volume. Next, because of the combinatorial nature of the above model, an efficient tabu search algorithm based on a generalized similarity coefficient is proposed. Computational results from test problems show that our proposed model and solution approach are both effective and efficient. When compared to the mathematical programming approach, which takes more than 112h (LINGO) and 1139s (CPLEX) to solve a set of ten test instances, the proposed algorithm can produce optimal solutions for the same set of test instances in less than 12s.