The purpose of this paper is to investigate the properties of the classical goodness of fit test statistics X2, G2, GM2, and NM2 in testing quality of process represented as the…
Abstract
Purpose
The purpose of this paper is to investigate the properties of the classical goodness of fit test statistics X2, G2, GM2, and NM2 in testing quality of process represented as the trinomial distribution with dip null hypothesis and to devise a control chart for the trinomial distribution with dip null hypothesis based on demerit control chart.
Design/methodology/approach
The research involves the linear form of the test statistics, the linear function of counts since the marginal distribution of the counts in any category is binomial or approximated Poisson, in which the uniformly minimum variance unbiased estimator is the linear function of counts. A control chart is used for monitoring student characteristics in Thailand. The control chart statistics based on an average of the demerit value computed for each student as a weighted average lead to a uniformly most powerful unbiased test marginally. The two‐sided control limits were obtained using percentile estimates of the empirical distribution of the averages of the demerit.
Findings
The demerit control chart of the weight set (1, 25, 50) shows a generally good performance, robust to direction of out‐of‐control, mostly outperforms the GM2 and is recommended. The X2, NM2 are not recommended in view of inconsistency and bias. The performance of the demerit control chart of the weight set (1, 25, 50) does not dramatically change between both directions.
Practical implications
None of the multivariate control charts for counts presented in the literature deals with trinomial distribution representing the practical index of the quality of the production/process in which the classification of production outputs into three categories of “good”, “defective”, and “reworked” is common. The demerit‐based control chart presented here can be applied directly to this situation.
Originality/value
The research considers how to deal with the trinomial distribution with dip null hypothesis which no research study so far has presented. The study shows that the classical Pearson's X2, Loglikelihood, modified Loglikelihood, and Neyman modified X2 could fail to detect an “out‐of‐control”. This research provides an alternative control chart methodology based on demerit value with recommended weight set (1, 25, 50) for use in general.
Details
Keywords
This research aims to investigate the differences in designing the zero acceptance number single sampling plans using the apparent fraction of nonconforming and the binomial…
Abstract
Purpose
This research aims to investigate the differences in designing the zero acceptance number single sampling plans using the apparent fraction of nonconforming and the binomial distribution against the exact convolute compound hypergeometric distribution when both types of inspection errors are present.
Design/methodology/approach
This research presents the derivation and uses the numerical study to compare the calculated probability of acceptance and the minimum sample size when using the present design concept of binomial distribution with true fraction of nonconforming replaced with the apparent one. Under the presences of inspection errors and zero acceptance number, the probability of acceptance is alternatively derived and presented in term of a function of the probability generating function. This research uses numerical method to determine the differences in the probability of acceptance. The computation of the minimum sample sizes are presented along with the numerical results and the comparison.
Findings
When the inspection errors are present, the probability of acceptance is extremely decreased even for 1 percent of inspection errors of Type I (rejecting good product) and Type II (accepting bad product). The binomial apparent nonconforming notions yields an over‐estimation of the probability of acceptance, comparing with the exact convolute compound hypergeometric notion under the zero acceptance single sampling plans especially at low fraction of nonconforming levels, the six sigma quality levels. The differences of the calculated probabilities of acceptance and the minimum sample sizes decrease as the inspection error of Type II increases given a fixed value of Type I error and consumer risk.
Originality/value
This research alternatively presents the mathematical derivation along with numerical study to assert the over‐estimation of the probability of acceptance and the minimum sample size if the existing methodology to design the zero acceptance number single sampling plans is used. This finding will help improve the sampling design strategy of the multistage production system.
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The purpose of this paper is to apply the statistical tolerancing technique to analyze the dual responses of APFA arm height deviation with respect to next stage of disk assembly…
Abstract
Purpose
The purpose of this paper is to apply the statistical tolerancing technique to analyze the dual responses of APFA arm height deviation with respect to next stage of disk assembly process and simultaneously optimize and allocate the required tolerance of the responses onto its components at minimum cost of manufacturing and the quality loss.
Design/methodology/approach
The relationships between the dual responses of APFA heights and the geometric dimensions and tolerances of APFA components, and orientation of the assembled part with respect to disk assembly were first defined. The effects of the APFA orientation, and the component tolerances on the distributions and variations of the responses were derived and investigated in terms of resultant product/process performance, quality loss, and the cost of assembly. The tolerance cost-based objective function is then formulated as the combined manufacturing/assembly cost and the quality loss. Direct search method was used to find the best feasible tolerance solutions satisfying the required product performance at minimum cost.
Findings
The constructed relationship or transfer functions of the dual responses were probabilistic depending on the orientation of part with respect to the next assembly process. The Monte Carlo simulation is empirically suitable for the computation of the conditional distributions of the responses against the first-order linear approximation of component variances. The proposed solution of tolerance control plan increases the product performances, C pm, from 0.6 to be at least 1. The proposed tolerance allocation plans will reduce the amount of rework currently as high as 5 percent to at most 0.01 percent with minimally increased assembly cost.
Practical implications
This proposed methodology to design and allocate component tolerances is suitable and applicable to the APFA assembly process. The derived assembly functions of probabilistic type relating the responses to the process and component characteristics can represent the actual dynamic of assembled part better than a traditional single deterministic function developed under static concept. This presented methodology can be applied to other assembly cases where quality characteristic depends on the part dynamic.
Originality/value
This research simultaneously optimized the dual APFA height deviation responses with minimum cost of tolerance and quality loss using two different conditional distributions and transfer functions of the resultant deviations generated from dynamic of APFA with respect to disk.