scholarly journals Designing a Repetitive Group Sampling Plan for Weibull Distributed Processes

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Aijun Yan ◽  
Sanyang Liu
Keyword(s):  
Quality Parameter ◽  
Sampling Plan ◽  
Quality Characteristic ◽  
Quality Level ◽  
Sample Number ◽  
Distributed Processes ◽  
Acceptance Sampling Plans ◽  
Limiting Quality Level ◽  
Important Quality ◽  
Repetitive Group Sampling

Acceptance sampling plans are useful tools to determine whether the submitted lots should be accepted or rejected. An efficient and economic sampling plan is very desirable for the high quality levels required by the production processes. The process capability indexCLis an important quality parameter to measure the product quality. Utilizing the relationship between theCLindex and the nonconforming rate, a repetitive group sampling (RGS) plan based onCLindex is developed in this paper when the quality characteristic follows the Weibull distribution. The optimal plan parameters of the proposed RGS plan are determined by satisfying the commonly used producer’s risk and consumer’s risk at the same time by minimizing the average sample number (ASN) and then tabulated for different combinations of acceptance quality level (AQL) and limiting quality level (LQL). The results show that the proposed plan has better performance than the single sampling plan in terms of ASN. Finally, the proposed RGS plan is illustrated with an industrial example.

scholarly journals Optimal Designing of Variables Chain Sampling Plan by Minimizing the Average Sample Number

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
S. Balamurali ◽  
M. Usha
Keyword(s):  
Operating Characteristic ◽  
Characteristic Curve ◽  
Sampling Plan ◽  
Quality Level ◽  
Sample Number ◽  
Acceptable Quality ◽  
Acceptable Quality Level ◽  
Limiting Quality Level ◽  
Optimal Designing ◽  
Average Sample

We investigate the optimal designing of chain sampling plan for the application of normally distributed quality characteristics. The chain sampling plan is one of the conditional sampling procedures and this plan under variables inspection will be useful when testing is costly and destructive. The advantages of this proposed variables plan over variables single sampling plan and variables double sampling plan are discussed. Tables are also constructed for the selection of optimal parameters of known and unknown standard deviation variables chain sampling plan for specified two points on the operating characteristic curve, namely, the acceptable quality level and the limiting quality level, along with the producer’s and consumer’s risks. The optimization problem is formulated as a nonlinear programming where the objective function to be minimized is the average sample number and the constraints are related to lot acceptance probabilities at acceptable quality level and limiting quality level under the operating characteristic curve.

VARIABLES QUICK SWITCHING SYSTEM WITH DOUBLE SPECIFICATION LIMITS

2012 ◽  
Vol 19 (02) ◽  
pp. 1250008 ◽  
Author(s):  
S. BALAMURALI ◽  
M. USHA
Keyword(s):  
Characteristic Curve ◽  
Quality Characteristic ◽  
Quality Level ◽  
Switching System ◽  
Sampling System ◽  
Sample Number ◽  
Specification Limits ◽  
Acceptable Quality ◽  
Acceptable Quality Level ◽  
Limiting Quality Level

This paper investigates a variables quick switching sampling system when a measurable quality characteristic has double specification limits beyond which an item is considered to be a nonconforming. The quality characteristic of interest is assumed to follow a normal distribution. The optimal parameters of the variables quick switching system are determined for both known and unknown standard deviations which satisfy the producer's and consumer's risks at the corresponding specified quality levels. Symmetric and asymmetric cases based on the fraction nonconforming by the lower and the upper specification limits are also considered. The problem is formulated as a nonlinear programming where the objective function to be minimized is the average sample number and the constraints are related to a lot of acceptance probabilities at acceptable quality level and limiting quality level under the operating characteristic curve.

Optimal designing of SkSP-2 skip-lot sampling plan for normally distributed quality characteristics

2017 ◽  
Vol 40 (7) ◽  
pp. 2240-2248 ◽  
Author(s):  
Saminathan Balamurali ◽  
Jambulingam Subramani
Keyword(s):  
Sampling Plan ◽  
Quality Characteristic ◽  
Optimal Parameters ◽  
Optimal Plan ◽  
Sample Number ◽  
Sampling Plans ◽  
Sampling Schemes ◽  
The Cost ◽  
Optimal Designing ◽  
Average Sample

Skip-lot sampling plans have been widely used in industries to reduce the inspection efforts on products that have an excellent quality history. These skip-lot sampling schemes are economically advantageous and useful to minimize the cost of the inspection of the final lots. Also, the skip-lot concept is sound and useful in the design of sampling plans. In this paper, we propose a designing methodology to determine the optimal parameters of a skip-lot sampling plan of type SkSP-2 when the quality characteristic under study follows a normal distribution. The optimal plan parameters are determined to minimize the average sample number subject to satisfying the producer’s and consumer’s risks simultaneously at the acceptable and limiting quality levels, respectively. An optimization problem is formulated in order to construct tables for determining the optimal parameters of the proposed sampling plan for both known and unknown standard deviation cases and the results are compared with the variables single sampling plans.

Designing of Variables Repetitive Group Sampling Plan Involving Minimum Average Sample Number

2005 ◽  
Vol 34 (3) ◽  
pp. 799-809 ◽  
Author(s):  
S. Balamurali ◽  
Heekon Park ◽  
Chi-Hyuck Jun ◽  
Kwang-Jae Kim ◽  
Jaewook Lee
Keyword(s):  
Sampling Plan ◽  
Sample Number ◽  
Average Sample Number ◽  
Repetitive Group Sampling ◽  
Average Sample

scholarly journals Optimization of Bayesian repetitive group sampling plan for quality determination in Pharmaceutical products and related materials

2022 ◽  
Vol 13 (1) ◽  
pp. 31-42 ◽  
Author(s):  
Velappan Kaviyarasu ◽  
Palanisamy Sivakumar
Keyword(s):  
Poisson Model ◽  
Pharmaceutical Products ◽  
Sampling Plan ◽  
Good Decision ◽  
Sample Number ◽  
Number Of Zeros ◽  
Pharmaceutical Industries ◽  
Excess Number ◽  
Quality Of Products ◽  
Repetitive Group Sampling

Sampling plans are extensively used in pharmaceutical industries to test drugs or other related materials to ensure that they are safe and consistent. A sampling plan can help to determine the quality of products, to monitor the goodness of materials and to validate the yields whether it is free from defects or not. If the manufacturing process is precisely aligned, the occurrence of defects will be an unusual occasion and will result in an excess number of zeros (no defects) during the sampling inspection. The Zero Inflated Poisson (ZIP) distribution is studied for the given scenario, which helps the management to take a precise decision about the lot and it can certainly reduce the error rate than the regular Poisson model. The Bayesian methodology is a more appropriate statistical procedure for reaching a good decision if the previous knowledge is available concerning the production process. This article proposed a new design of the Bayesian Repetitive Group Sampling plan based on Zero Inflated Poisson distribution for the quality assurance in pharmaceutical products and related materials. This plan is studied through the Gamma-Zero Inflated Poisson (G-ZIP) model to safeguard both the producer and consumer by minimizing the Average Sample Number. Necessary tables and figures are constructed for the selection of optimal plan parameters and suitable illustrations are provided that are applicable for pharmaceutical industries.

Design and Construction of Plan for Exponential Distribution Using Repetitive Sampling

2016 ◽  
Vol 13 (10) ◽  
pp. 6568-6575
Author(s):  
Muhammad Aslam ◽  
Ali Hamed S Algarni ◽  
Ramsha Saeed
Keyword(s):  
Exponential Distribution ◽  
Linear Optimization ◽  
Sampling Plan ◽  
Design Parameters ◽  
Sample Number ◽  
Sampling Plans ◽  
Industrial Data ◽  
Repetitive Group Sampling ◽  
Average Sample

In this paper, sampling plan using exact and approximated approaches is presented when the quality of interest follows the exponential distribution. The designing both presented using the repetitive group sampling plan. The design parameters of the proposed sampling plans are determined through non-linear optimization. The efficiency of proposed sampling plans is compared with the existing sampling plans in terms of average sample number. The application of the proposed plans is discussed by industrial data.

scholarly journals Bayesian Two-sided Complete Group Chain Sampling Plan for Binomial Distribution using Beta Prior through Quality Regions

2021 ◽  
Vol 21 (No.1) ◽  
pp. 51-69
Author(s):  
Waqar Hafeez ◽  
Nazrina Aziz
Keyword(s):  
Binomial Distribution ◽  
Sampling Plan ◽  
Design Parameters ◽  
Quality Level ◽  
Acceptance Sampling ◽  
Consumer’S Risk ◽  
Complete Group ◽  
Acceptable Quality Level ◽  
Limiting Quality Level ◽  
Estimate Quality

Acceptance sampling is a technique for statistical quality assurance based on the inspection of a random sample to decide the lot disposition: accept or reject. Producer’s risk and consumer’s risk are inevitable in acceptance sampling. Most conventional plans only focus on minimizing the consumer’s risk. This study focused on minimizing both producer’s and consumer’s risks through the quality region. Experts from available historical knowledge concurred that Bayesian is the best approach to make the correct decision. In this study, a Bayesian two-sided complete group chain sampling plan (BTSCGChSP) was proposed for the average probability of acceptance. The binomial distribution was used to derive the probability of lot acceptance, and the beta distribution was used as the prior distribution. For selected design parameters in BTSCGChSP, the acceptable quality level and limiting quality level were considered to estimate quality regions that were directly associated with producer’s and consumer’s risks, respectively. Four quality regions: (i) quality decision region , (ii) probabilistic quality region (PQR), (iii) limiting quality region, and (iv) indifference quality region, were evaluated. To compare with the existing Bayesian group chain sampling plan (BGChSP), operating characteristic curves were used for the same parameter values and probability of lot acceptance. The findings explained that BTSCGChSP provided a smaller proportion of defectives than BGChSP for the same probability of acceptance. If quality regions were found for the same values of consumer and producer risks, then the BTSCGChSP region would contain fewer defectives than in the BGChSP region. Therefore, for industrial practitioners, the proposed plan is a better substitute for existing BGChSP and other conventional plans.

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