Multiple Dependent State Sampling Research Articles

On control charts based on generalized multiple dependent state sampling

ABSTRACT We clarify the use of the widely used multiple dependent state sampling (MDSS) technique and its generalization (GMDSS) with control charts. We show that these rules are simple modifications of well-known supplementary runs rules. The MDSS and GMDSS rules are inefficient; however, they do not distinguish between the upper and lower warning regions. We show that the application of the more conventional supplementary runs rules, i.e. those side-sensitive with respect to the warning regions, provides significantly better performance than the MDSS and GMDSS techniques. In addition, we show that a commonly used expression for determining the average run length of the GMDSS method is incorrect and provide a Markov chain alternative approach.

Economic Design of Generalized Multiple Dependent State Sampling Plan Under Exponentiated Half Logistic Distribution

The main objective of this study is to propose an economic design of a generalized multiple dependent state sampling plan based on time truncated life test under exponentiated half logistic distribution for assuring median life. In this study, the optimal plan parameters are determined for various median ratios using the approach of two points on the operating characteristic curve. The performance of the proposed plan is compared with other sampling plans designed under exponentiated half logistic distribution. An investigation on the effect of misspecification of shape parameters on probabilities of lot acceptance is done and the industrial application of the proposed plan is explained with real time data. The results obtained from both conventional as well as economic designing show that the proposed plan outperforms the other existing sampling plans, such as multiple dependent state sampling plan, multiple dependent state repetitive group sampling plan, and single sampling plan.

Time Truncated Attribute Median Control Charts for Logistic-Exponential Process Distribution

Abstract In this article, time truncated attribute control chart is proposed for logistic-exponential distribution based on four acceptance sampling plans. The performance of the proposed control chart is evaluated in terms of average run length. Furthermore, the efficiency of the proposed attribute control chart is compared for all given acceptance sampling plans, viz., single sampling plan, repetitive sampling plan, multiple dependent state sampling plan and multiple dependent state repetitive sampling plan. Also, the application of the proposed control chart is illustrated by using real life example.

Life truncated multiple dependent state plan for imprecise Weibull distributed data

This paper aims to provide a multiple dependent state (MDS) sampling technique for light-emitting diode luminous intensities under indeterminacy by employing time truncated sampling schemes and the Weibull distribution. This indicates that ASN is significantly impacted by the indeterminacy parameter. Furthermore, a comparison is shown between the existing, indeterminate sampling plans and the recommended sample designs. The projected sampling technique is illustrated by calculating the luminous intensities of LEDs using the Weibull distribution. Based on the findings and practical example, we conclude that the suggested strategy needs a smaller sample size than SSP and the current MDS sampling plan.

Designing of multiple dependent state sampling plan for Type-II generalized half logistic distribution

Designing of multiple dependent state sampling plan for Type-II generalized half logistic distribution

Comparing the efficacy of coefficient of variation control charts using generalized multiple dependent state sampling with various run-rule control charts

This paper aimed to develop a coefficient of variation (CV) control chart utilizing the generalized multiple dependent state (GMDS) sampling approach for CV monitoring. We conducted a comprehensive examination of this designed control chart in comparison to existing control charts based on multiple dependent state sampling (MDS) and the Shewhart-type CV control chart, with a focus on average run lengths. The results were then compared to run-rule control charts available in the existing literature. Additionally, we elucidated the implementation of the proposed control chart through concrete examples and a simulation study. The findings clearly demonstrated that the GMDS sampling control chart shows significantly superior accuracy in detecting process shifts when compared to the MDS sampling control chart. As a result, the control chart approach presented in this paper holds significant potential for applications in textile and medical industries, particularly when researchers seek to identify minor to moderate shifts in the CV, contributing to enhanced quality control and process monitoring in these domains.

Application of the multiple dependent state sampling strategy to late adolescent suicide rates

A multiple dependent state sampling plan (MDSSP) is designed when the lifetimes of the variables follow New Lomax Rayleigh Distribution (NLRD). The decision to accept or reject a lot in the proposed methodology is based on the quality of the given present or previous lots. A binomial model-based operating characteristic curve (OC curve) for continuous lots of variables under similar settings in healthcare is used in finding the probability of acceptance, acceptance number, rejection number, and the number of preceding (succeeding) lots to consider. Time truncated life test based on the specified median of the NLRD is used in designing the current acceptance sampling plan. For specified values of the parameters of NLRD, quantile ratios, consumer’s risk and producer’s risk, average sampling number (ASN) and probability of acceptance of a lot are reported in tables. Real data on worldwide suicide rates of 15–19 years in the year 2019 from the World Health Organization (WHO) website is considered to illustrate this methodology. The minimum sample size required from the selected data to comment on worldwide suicide rates in late adolescents is explained with MDSSP. The results of the proposed acceptance sampling method are compared with the single-stage sampling plan.

A new multiple dependent state sampling plan based on one-sided process capability indices

A new multiple dependent state sampling plan based on one-sided process capability indices

Improving Multiple Dependent State Sampling Plan Based on Capability Index S^T_pk

Improving Multiple Dependent State Sampling Plan Based on Capability Index S^T_pk

Designing Adaptive Multiple Dependent State Sampling Plan for Accelerated Life Tests

A novel adaptive multiple dependent state sampling plan (AMDSSP) was designed to inspect products from a continuous manufacturing process under the accelerated life test (ALT) using both double sampling plan (DSP) and multiple dependent state sampling plan (MDSSP) concepts. Under accelerated conditions, the lifetime of a product follows the Weibull distribution with a known shape parameter, while the scale parameter can be determined using the acceleration factor (AF). The Arrhenius model is used to estimate AF when the damaging process is temperature-sensitive. An economic design of the proposed sampling plan was also considered for the ALT. A genetic algorithm with nonlinear optimization was used to estimate optimal plan parameters to minimize the average sample number (ASN) and total cost of inspection (TC) under both producer’s and consumer’s risks. Numerical results are presented to support the AMDSSP for the ALT, while performance comparisons between the AMDSSP, the MDSSP and a single sampling plan (SSP) for the ALT are discussed. Results indicated that the AMDSSP was more flexible and efficient for ASN and TC than the MDSSP and SSP plans under accelerated conditions. The AMDSSP also had a higher operating characteristic (OC) curve than both the existing sampling plans. Two real datasets of electronic devices for the ALT at high temperatures demonstrated the practicality and usefulness of the proposed sampling plan.

A generalized multiple dependent state sampling chart based on ridge penalized likelihood ratio for high-dimensional covariance matrix monitoring

Online monitoring of high-dimensional processes variability in which the number of variables is larger than the sample size is a challenging issue for quality practitioners because the sample covariance matrix is not invariable. To deal with this challenge, a generalized multiple dependent state sampling (GMDS) chart based on ridge penalized likelihood ratio (RPLR) statistic is developed for Phase II monitoring of multivariate process variability under high-dimensional setting. The developed control chart benefits from three advantages: (1) departing from the conventional covariance matrix charts, it can be efficiently employed for both spars and non-spars covariance matrices; (2) it is able to detect spars shift patterns in which only a few covariance matrix elements are deviated from their nominal values; and (3) it outperforms the detectability of the RPLR chart in terms of average run length (ARL) and standard deviation of run length (SDRL). The performance of RPLR, MDS-RPLR, and GMDS-RPLR charts are compared using extensive simulation studies by considering different diagonal and/or off-diagonal covariance matrix disturbance. Moreover, sensitivity analysis are provided to analyze how the number of process variables and GMDS parameter affect the run length properties of the developed chart.

Generalized multiple dependent state sampling plan for quality inspection in ocean dataset

The present article develops the generalized multiple dependent state sampling plan for testing the quality of the ocean data. The plan parameters for the inspection of the ocean data are selected through the optimization process. The operational procedure for the inspection of ocean data is given under the proposed sampling scheme. The efficiency of the proposed plan is compared with the existing plan used for the inspection of the quality of ocean data in terms of sample size. From the comparative study, it is concluded that the proposed plan is efficient than the existing plan in an inspection of the ocean data.

Monitoring Using X-Bar Control Chart Using Neutrosophic-Based Generalized Multiple Dependent State Sampling with Application

In this article, an enhanced X-bar control chart using generalized multiple dependent state (GMDS) sampling under neutrosophic statistics is presented. The joint advantages of GMDS sampling and the neutrosophic statistics have been recycled for the efficient monitoring of the average quality characteristic of any production process. The efficiency of the proposed chart has been evaluated using the average run length values under different ranges of the parameters under study. The comparison of the proposed chart with the existing control chart has been discussed. The comparison shows that the proposed chart is better than the existing chart. Results reveal the superiority of the proposed neutrosophic-based GMDS sampling chart. In addition, an example has also been included for the practical implementation of the proposed methodology.

Equivalences between multiple dependent state sampling, chain sampling, and control chart runs rules

Multiple dependent state sampling (MDSS) is a feature that was recently proposed for acceptance sampling plans. In addition, it is increasingly recommended to use this technique, and its generalization, with quality control charts. In our paper, we show that the MDSS feature is an extension of chain sampling in acceptance sampling applications. In addition, we show that use of the MDSS feature with control charts is equivalent to the use of standard supplementary runs rules. Analytical methods based on Markov chains for determining the performance of control charts with runs rules can also be applied to MDSS acceptance sampling applications. Additionally, we provide a derivation approach for some of the formulas for the performance measures for the MDSS charts and point out some incorrect derivations.

Sampling Inspection Plan to Test Daily COVID-19 Cases Using Gamma Distribution under Indeterminacy Based on Multiple Dependent Scheme.

The purpose of this paper is to develop a multiple dependent state (MDS) sampling plan based on time-truncated sampling schemes for the daily number of cases of the coronavirus disease COVID-19 using gamma distribution under indeterminacy. The proposed sampling scheme parameters include average sample number (ASN) and accept and reject sample numbers when the indeterminacy parameter is known. In addition to the parameters of the proposed sampling schemes, the resultant tables are provided for different known indeterminacy parametric values. The outcomes resulting from various sampling schemes show that the ASN decreases as indeterminacy values increase. This shows that the indeterminacy parameter plays a vital role for the ASN. A comparative study between the proposed sampling schemes and existing sampling schemes based on indeterminacy is also discussed. The projected sampling scheme is illustrated with the help of the daily number of cases of COVID-19 data. From the results and real example, we conclude that the proposed MDS sampling scheme under indeterminacy requires a smaller sample size compared to the single sampling plan (SSP) and the existing MDS sampling plan.

An optimal construction of yield-based EWMA repetitive multivariate sampling plan

In this paper, a variable repetitive group sampling (VRGS) plan is proposed based on the exponentially weighted moving average (EWMA) statistic with yield index for inspection of mutually independent and multivariate normally distributed characteristics. Plan parameters are found optimally based on asymptotic distribution of using a non linear optimization. A simulation study indicates that the reported parameters can thoroughly warrant determined risks for finite sample sizes. This work also extends application of the proposed plan to the class of correlated characteristics. The obtained findings show that the proposed plan significantly reduces required average sample number compared to the existing modified VRGS plan, single, double, and multiple dependent state sampling plans with yield-based EWMA statistic. Two industrial examples are presented to illustrate the application of the proposed plan in real world.

Multiple dependent state repetitive sampling plans for exponentiated half logistic distribution

ABSTRACT In the textile and packing industries, the lifetime of the items is exhibited by some statistical distribution. This paper aims to develop a multiple dependent state repetitive (MDSR) sampling plan by assuming that the lifetime of an item comes from an exponentiated half logistic distribution (EHLD). The MDSR sampling plan will be more economical than the other sampling plans on hand such as the multiple dependent state sampling schemes, the repetitive sampling plan, the single sampling plan, and the resubmitted sampling plan concerning the size of the sample required to test the lot. The design parameters for the developed sampling plans are obtained by minimizing the average sample number when both the consumer’s and producer’s risks are satisfied at corresponding quality levels. Tables are given for practical use. The proposed MDSR sampling plan is compared with the single sampling plan and some examples are also provided.

Product Acceptance Determination Based on EWMA Yield Index Using Repetitive and MDS Sampling Schemes

In this manuscript, we present a repetitive group sampling plan and a multiple dependent state sampling plan based on the EWMA (exponentially weighted moving average) yield index for product acceptance. The proposed plans utilize the current and the previous information through EWMA statistic to reach a decision of lot sentencing. A non-linear optimization model is developed to determine the plan parameters of the proposed plans for various specified conditions. The performance of the proposed plans over several existing sampling plans is analyzed, which shows that the proposed plans are efficient in reducing the sample size for lot sentencing. For industrial application, a real example is given to demonstrate the implementation of the proposed plans.

A Novel Multiple Dependent State Sampling Plan Based on Time Truncated Life Tests Using Mean Lifetime

The design of a new adaptive version of the multiple dependent state (AMDS) sampling plan is presented based on the time truncated life test under the Weibull distribution. We achieved the proposed sampling plan by applying the concept of the double sampling plan and existing multiple dependent state sampling plans. A warning sign for acceptance number was proposed to increase the probability of current lot acceptance. The optimal plan parameters were determined simultaneously with nonlinear optimization problems under the producer’s risk and consumer’s risk. A simulation study was presented to support the proposed sampling plan. A comparison between the proposed and existing sampling plans, namely multiple dependent state (MDS) sampling plans and a modified multiple dependent state (MMDS) sampling plan, was considered under the average sampling number and operating characteristic curve values. In addition, the use of two real datasets demonstrated the practicality and usefulness of the proposed sampling plan. The results indicated that the proposed plan is more flexible and efficient in terms of the average sample number compared to the existing MDS and MMDS sampling plans.

Comparing the Performance of C pk and X Control Charts With the Generalized Multiple Dependent State Sampling Supplementary Signaling Rule

The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C_{pk}$ </tex-math></inline-formula> index was originally created to measure the ability of the processes to produce products meeting specifications but, more recently, Rao and team proposed the use of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C_{pk}$ </tex-math></inline-formula> index to control processes. In reality, they investigated the performance of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C_{pk}$ </tex-math></inline-formula> chart with the GMDS (Generalized Multiple Dependent State Sampling) supplementary signaling rule. With the GMDS supplementary run rule, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C_{pk}$ </tex-math></inline-formula> chart signals when a point falls in the action region or when a point falls in the warning region after a sequence of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> points, with less than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> , in the central region. The points on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C_{pk}$ </tex-math></inline-formula> chart are the estimated values of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C_{pk}$ </tex-math></inline-formula> index obtained with the mean and the variance of the samples. Rao and team obtained the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ARLs</i> of the GMDS <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C_{pk}$ </tex-math></inline-formula> chart by simulation; reminding the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ARL</i> is the average number of samples the chart requires to signal a change in the process. This present work uses the Markov chain approach to obtain the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ARLs</i> , once this approach leads to exact results. The main conclusion is that the GMDS <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\bar {X}$ </tex-math></inline-formula> chart is not only simpler to use than the GMDS <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C_{pk}$ </tex-math></inline-formula> chart, but it is also more sensitive to process changes.