Multiple Deferred State Research Articles

Optimal and economic design of multiple deferred state repetitive group sampling plan for assuring mean life under a family of lifetime distributions

In this paper, a designing methodology of the multiple deferred (dependent) state repetitive group sampling plan is developed to ensure the mean lifetime of the products under the truncated life test, which follows a family of different lifetime distributions. An approach of two points on the operating characteristic curve is followed to obtain the optimal plan parameters with the known shape parameter values for various mean life ratios under different lifetime models. The proposed sampling plan is illustrated with a numerical example. The application of the proposed sampling plan is explained with a real-life example based on Burr XII distribution. Comparison is made among the performances of the proposed sampling plan using the different lifetime distributions; these performances are also compared with a single sampling plan using Burr XII distribution based on mean life assurance. Finally, an economic design of the proposed sampling plan is discussed, along with some cost models to minimize the total cost.

Economic design of multiple deferred state sampling plan for two parameter Lindley distributed mean life assurance

In this study, we propose a multiple deferred state sampling plan under two parameter Lindley distribution based on time truncated life test. One of the principal objectives of the proposed plan is to ensure that the products have higher mean life. The procedure for determining the optimal plan parameters of the proposed plan is described by two points on the operating characteristics curve approach. Tables are constructed to select the optimal plan parameters of the proposed plan for different values of shape parameters, consumer’s risk and producer’s risk. The implementation of the proposed plan is illustrated with a real life time data. In addition, the performance of the proposed plan is evaluated by comparing the average sample number and operating characteristic curve of the proposed plan to that of single sampling plan. Finally, a mathematical model for economic design of the proposed plan is developed by considering the waiting time to reduce the total inspection cost while satisfying both the producer and consumer requirements and a sensitivity analysis is also explored.

Design of generalized fuzzy multiple deferred state sampling plan for attributes

In industry, for the quality inspection processes, acceptance sampling plans proved to be economically viable, but the unpredictability of the plan’s characteristics made the use of conventional acceptance sampling plans less reliable. The generalized fuzzy multiple deferred state sampling plan (GFMDSSP) is suggested in this study for qualities that consider the difficulty in calculating the precise value of the percentage of defectives in a batch. The strategy is created with a minimal average sample size in mind and the performance measures have already been determined. An analysis of the current fuzzy acceptance sampling plans for characteristics is conducted, and an important conclusion is drawn regarding the effectiveness of the proposed scheme. Analysis of the impact of inspection errors on the sampling process reveals a decline in plan acceptance standards that is correlated with escalating inspection errors. Finally, some numerical examples are provided to support the findings.

Designing of quality interval skip-lot sampling plan with multiple deferred state sampling plan

Designing of quality interval skip-lot sampling plan with multiple deferred state sampling plan

Design of multiple deferred state sampling inspection plan for variables

The statistical product control, also termed as, acceptance sampling, extensively used in enterprises to reach a decision on ruling of lots of manufactured products, is a definite plan that states the sampling rules to be used and the standards for acceptance or dismissal of lots submitted for inspection. In acceptance sampling, the largely used practice to minimize the testing time and cost of inspection of manufactured units is the variable sampling inspection plan, in which the sentencing of a lot of individual items is based on metrical data. One of the special purpose sampling plans, multiple deferred state sampling plan for attributes reviews the quality of current lot as well as forthcoming lots for settlement of a lot. This paper proposes a technique for designing a multiple deferred state sampling plan for variables with the quality characteristics of product following normal distribution. The optimized parameters of the proposed plan are assessed by utilizing two points on the operating characteristic (OC) curve for specific requirement to ensure upon the producer and consumer conservation, when the standard deviation is known and unknown.

Determination of new multiple deferred state sampling plan with economic perspective under Weibull distribution

ABSTRACT This study focuses on designing a new multiple deferred state sampling plan to ensure products’ mean lifetime that complies with Weibull distribution. The parameters that characterize the proposed plan are determined by considering two specified points on the operating characteristic curve. Practical applications of the proposed plan for assuring mean lifetimes of electrical appliances as well as Lithium-ion batteries are explained by using real-time data and simulated data respectively. Sensitivity analysis on testing time of the life test is done and theoretical average sample number is compared with the same obtained by simulation. By comparing the proposed plan with other existing sampling plans based on discriminating power, the number of units required for lot sentencing, it is observed that the new multiple deferred state sampling plan provides quality assurance for the products with low inspection costs compared to the other existing sampling plans. Besides, this study investigates the economic design of a new multiple deferred state sampling plan and compares the total cost needed in the proposed plan with the same required for some other existing sampling plans.

Economical design of multiple deferred (dependent) state repetitive group sampling plan based on truncated life test under exponentiated half-logistic distribution

The design of a multiple deferred (dependent) state repetitive group sampling plan for exponentiated half-logistic distributed percentile life assurance under time-truncated life test is considered in this article. In this research, tables are provided to choose the design parameters of the proposed plan determined for different percentile ratios using the method of two points on the operating characteristic curve with known shape parameter values. We describe the sampling procedure of the proposed multiple deferred (dependent) state repetitive group sampling plan with real-time data and discuss the effect of misspecification of the shape parameter on lot acceptance probabilities. Based on an economical design of the proposed plan, an optimal plan is determined that satisfies both producer and consumer risks with minimum cost. In addition, the performance of the proposed plan is analyzed and compared with other existing sampling plans under an exponentiated half-logistic lifetime distribution. Finally, conclusions are provided.

TIME TRUNCATED ACCEPTANCE SAMPLING PLAN FOR ODDS EXPONENTIAL LOG-LOGISTIC DISTRIBUTION

In this paper, the multiple deferred state repetitive acceptance sampling plan (MDSRASP) is proposed and designed for assuring a 50th percentile lifetime of the products under odds exponential log-logistic (OELL) distribution. The optimum parameters of the proposed plan are determined based on satisfying various blends of producer’s risk and consumer’s risk for definite quality levels in light of 50th percentile. The aim is to minimize the average sample number (ASN), though the constraints are connected with the lot acceptance probability at the acceptable and limiting quality levels. The efficiency of the proposed plan is compared with single sampling plan using ASN. Tables are formed to present the outcomes and comparison of the proposed plan with existing sampling plan is done in terms of ASN.

Multiple Deferred State Sampling Plan for Exponentiated New Weibull Pareto Distributed Mean Life Assurance

Abstract This article proposes a methodology of designing the multiple deferred state acceptance sampling plan for assuring lifetime of the products when the underlying distribution of lifetime is exponentiated new Weibull-Pareto. Inspection of the sample items is done based on attribute quality characteristics under a time truncated life test. A number of tables are constructed using attribute multiple deferred state acceptance sampling plans of some specified value for mean lifetime ratio that may be obtained under the exponentiated new Weibull-Pareto model. The consequence of misspecification of the shape parameter and the role of the number of successive lots needed for sentencing current lot are investigated. A procedure for implementing the proposed plan for life-testing applications is included. The performance of the proposed plan is compared in terms of the average sample number required as well as discriminating power.

Determination of multiple deferred state repetitive group sampling plan for life time assurance under Birnbaum–Saunders distribution

A designing methodology to determine the optimal multiple deferred state repetitive group sampling plan for assuring Birnbaum–Saunders distributed both mean and median life of the products is proposed in this paper. The operating procedure and the performance measures of the proposed sampling plan are presented in this study. One of the familiar approaches involved in sampling plan determination that is two points on the operating characteristic curve approach is used to select the optimal plan parameters, which has minimum average sample number. Tables are constructed to report the optimal plan parameters for different set of mean or median ratio and shape parameter values of Birnbaum–Saunders distribution. Further, the proposed multiple deferred (dependent) state repetitive group sampling plan is compared with other existing sampling plans using some of the performance measures.

Optimal designing of multiple deferred (dependent) state repetitive group sampling plan for variables inspection

In this paper, we propose the designing methodology of multiple deferred (dependent) state repetitive group sampling plan for lot sentencing when the quality characteristic of the product follows normal distribution. This sampling plan incorporates the features of two existing sampling plans such as multiple deferred (dependent) state sampling plan and repetitive group sampling plan. Under the proposed sampling plan, the current lot is immediately accepted if it has good quality and rejected if the lot quality is poor. But, the decision on the current lot depends on the decision of the successive/preceding lots and/or additional samples from the current lot when the current lot is of moderate quality. Two-points on the operating characteristic curve approach is used to determine the optimal plan parameters for various combinations of acceptable quality level and limiting quality level. In determination of plan parameters, two cases are considered such as standard deviation is known and unknown. An application of the proposed sampling plan in industries is discussed with real life example. The significance of the proposed plan is explained by a comparative study.

On the rectifying multiple deferred state plan in the presence of uncertain parameter

The quality of manufactured products plays a very important role in increasing consumer satisfaction. One approach to improving outgoing lot quality is applying screening method. In this paper, a multiple deferred state sampling plan is presented for

Design of multiple-deferred state sampling plans for exponentiated half logistic distribution

This paper aims to develop a multiple deferred state sampling plan for a time-truncated life test if the lifetime of the item follows exponentiated half logistic distribution. The optimal parameters of the proposed plan, such as the number of successive lots required for making the decision whether to accept or reject the current lot, sample size, the rejection and acceptance numbers are obtained using two points approach. The implementation of the proposed plan is illustrated with examples. Tables are constructed for various combinations of consumer’s and producer’s risks. Comparison is also made with existing sampling plans under exponentiated half logistic distribution.

An Attribute np Control Chart for Monitoring Mean Life Using Multiple Deferred State Sampling Based on Truncated Life Tests

In this paper, we design an attribute [Formula: see text] control chart for monitoring the mean life of the product where the lifetime follows the Pareto distribution of the second kind. The lifetime of the product is determined by time truncated life test and the multiple deferred state sampling is used to declare the status of the manufacturing process. Control limit coefficients and multiple deferred state sampling parameters such as sample size and number of successive subgroups required to declare the state of the process are determined such that the in-control average run length is as near as possible to the target average run length. Out-of-control average run lengths are calculated for the determined parameters using various shift constants. The performance of the chart is compared with other existing chart in terms of average run length.

Economic design of an attribute control chart for monitoring mean life based on multiple deferred state sampling

AbstractIn this paper, we design an attribute np control chart using multiple deferred state (MDS) sampling under Weibull distribution based on time truncated life test. This chart is constructed for monitoring the variation of mean life of the product in a manufacturing process. The optimal parameters of MDS sampling and the control limit coefficients are determined so that the in‐control average run length (ARL) is as close as to the target ARL. The optimal parameters of MDS sampling are sample size and number of successive subgroups required for declaring the current state of process. Out‐of‐control ARL is considered as a measure of the performance of proposed chart and reported with determined optimal parameters for various shift constants. The out‐of‐control ARL of the proposed chart obtained under various distributions is compared with each other. The performance of proposed control chart is compared with the performance of the existing control chart designed under single sampling. In addition, the economic design of proposed chart using variable sampling interval scheme is discussed, and sensitivity analysis on expected costs is also investigated.

Fuzzy multiple deferred state variable sampling plan

Fuzzy multiple deferred state variable sampling plan

Optimal design of repetitive group sampling plans for Weibull and gamma distributions with applications and comparison to the Birnbaum–Saunders distribution

ABSTRACTIn this paper, we propose a multiple deferred state repetitive group sampling plan which is a new sampling plan developed by incorporating the features of both multiple deferred state sampling plan and repetitive group sampling plan, for assuring Weibull or gamma distributed mean life of the products. The quality of the product is represented by the ratio of true mean life and specified mean life of the products. Two points on the operating characteristic curve approach is used to determine the optimal parameters of the proposed plan. The plan parameters are determined by formulating an optimization problem for various combinations of producer's risk and consumer's risk for both distributions. The sensitivity analysis of the proposed plan is discussed. The implementation of the proposed plan is explained using real-life data and simulated data. The proposed plan under Weibull distribution is compared with the existing sampling plans. The average sample number (ASN) of the proposed plan and failure probability of the product are obtained under Weibull, gamma and Birnbaum–Saunders distributions for a specified value of shape parameter and compared with each other. In addition, a comparative study is made between the ASN of the proposed plan under Weibull and gamma distributions.

Designing a Multiple Deferred State Attribute Sampling Plan in a Fuzzy Environment

SYNOPTIC ABSTRACTIn this study, a fuzzy multiple deferred state (FMDS) attribute sampling plan is proposed when the proportion parameter (p) is uncertain. In this plan, the decision upon the acceptance of the submitted lot is based on both current lot information and future successive lots information. Then, the authors prefer to discuss the proposed plan more in a specific case designated as FMDS(0,1). Tables have been prepared to construct and determine parameters of the FMDS(0,1) plan by use of the two-point approach for determining the plan selection. In order to be fully informed, some applicable examples are given. Also, the proposed plan is compared with the existing fuzzy single, fuzzy double, and fuzzy sequential sampling plans. The obtained results show that the main advantage of the FMDS(0,1) plan is to have a minimum average sample number under the same conditions. Moreover, the authors show that the proposed plan is well-defined since it turns into a traditional case when p is crisp.

Optimal designing of multiple deferred state sampling plan for assuring percentile life under Weibull distribution

In this paper, we have proposed a multiple deferred state sampling plan for a time-truncated life test when the lifetime follows the Weibull distribution. The proposed sampling plan assures the percentile life of the products. The optimal plan parameters of the proposed plan such as the sample size, acceptance numbers, and number of successive lots required for making decision (n, c 1, c 2, m) are determined based on two points on the operating characteristic curve approach. The optimal parameters of the proposed plan are determined using an optimization problem for various combinations of producer’s risk, consumer’s risk, and percentile ratios. An illustrative example is also provided for describing the implementation of the proposed plan. Finally, we have investigated economic aspect of designing of the proposed plan under Weibull distribution.

Multiple Deferred State Sampling Plan with Fuzzy Parameter

Traditional multiple deferred state sampling plan by attribute is an inspection with crisp parameter. In this plan, in addition to using the current lot information, the future successive lots information can also be utilized on sentencing the current lot. In this study, a fuzzy multiple deferred state (FMDS) sampling plan by attribute is proposed when the proportion of defective items (p) is uncertain. So, the fuzzy probability theory is applied to construct the operating characteristic curve of mentioned plan. Then, we concentrate more on a special feature of FMDS(0,1,2) plan. We show that the proposed plan is well-defined because it converts to classic case when p is not imprecise. In order to be fully informed, some examples will also be discussed. The comparisons between the FMDS(0,1,2) plan and the existing fuzzy single sampling plan (FSSP) with zero and one acceptance number show that the proposed plan is more powerful than the FSSP in distinguishing good and bad quality of the lot. It also enjoys the least sum of the consumer and producer risks.