Inspection tables for single acceptance sampling with crisp and fuzzy formulation of quality limits

2018 ◽  
Vol 35 (9) ◽  
pp. 1755-1791 ◽  
Author(s):  
Nataliya Chukhrova ◽  
Arne Johannssen
Keyword(s):  
Sensitivity Analysis ◽  
Characteristic Function ◽  
Expert Opinion ◽  
Operating Characteristic ◽  
Test Method ◽  
Statistical Quality Control ◽  
Acceptance Sampling ◽  
Sampling Plans ◽  
Content Type ◽  
Operating Characteristic Function

Purpose The purpose of this paper is to construct innovative exact and approximative sampling plans for acceptance sampling in statistical quality control. These sampling plans are determined for crisp and fuzzy formulation of quality limits, various lot sizes and common α- and β-levels. Design/methodology/approach The authors use generalized fuzzy hypothesis testing to determine sampling plans with fuzzified quality limits. This test method allows a consideration of the indifference zone related to expert opinion or user priorities. In addition to the exact sampling plans calculated with the hypergeometric operating characteristic function, the authors consider approximative sampling plans using a little known, but excellent operating characteristic function. Further, a comprehensive sensitivity analysis of calculated sampling plans is performed, in order to examine how the inspection effort depends on crisp and fuzzy formulation of quality limits, the lot size and specifications of the producer’s and consumer’s risks. Findings The results related the parametric sensitivity analysis of the calculated sampling plans and the conclusions regarding the approximation quality provide the user a comprehensive basis for a direct implementation of the sampling plans in practice. Originality/value The constructed sampling plans ensure the simultaneous control of producer’s and consumer’s risks with the smallest possible inspection effort on the one hand and a consideration of expert opinion or user priorities on the other hand.

scholarly journals A Research Algorithm to Sentence the Lots for Costly or Destructive Products in Mixed Quality Characteristics

2019 ◽  
Vol 8 (6S4) ◽  
pp. 850-853
Keyword(s):  
Characteristic Function ◽  
Operating Procedure ◽  
Operating Characteristic ◽  
Quality Characteristics ◽  
Acceptance Sampling ◽  
Sampling Plans ◽  
Operating Characteristic Function ◽  
Acceptance Sampling Plans ◽  
Standard Quality ◽  
Selection Of

This paper deals with the new operating procedure of Acceptance Sampling Plans for costly or destructive products when the incoming lots have mixed quality characteristics. The Operating Characteristic function and other associated measures of the plan are derived and provided. The procedure is given and designing of sampling plan are indexed through standard quality levels. Tables are constructed for easy selection of the plan.Illustrations are also provided.

Improved binomial and Poisson approximations to the Type-A operating characteristic function

2019 ◽  
Vol 36 (4) ◽  
pp. 620-652 ◽  
Author(s):  
Nataliya Chukhrova ◽  
Arne Johannssen
Keyword(s):  
Operating Characteristic ◽  
Numerical Study ◽  
Type A ◽  
Computational Effort ◽  
Acceptance Sampling ◽  
Content Type ◽  
Type Approximation ◽  
Operating Characteristic Function ◽  
Wide Range ◽  
Binomial Type

PurposeIn acceptance sampling, the hypergeometric operating characteristic (OC) function (so called type-A OC) is used to be approximated by the binomial or Poisson OC function, which actually reduce computational effort, but do not provide suffcient approximation results. The purpose of this paper is to examine binomial- and Poisson-type approximations to the hypergeometric distribution, in order to find a simple but accurate approximation that can be successfully applied in acceptance sampling.Design/methodology/approachThe authors present a new binomial-type approximation for the type-A OC function, and derive its properties. Further, the authors compare this approximation via an extensive numerical study with other common approximations in terms of variation distance and relative efficiency under various conditions on the parameters including limiting cases.FindingsThe introduced approximation generates best numerical results over a wide range of parameter values, and ensures arithmetic simplicity of the binomial distribution and high accuracy to meet requirements regarding acceptance sampling problems. Additionally, it can considerably reduce the computational effort in relation to the type-A OC function and therefore is strongly recommended for calculating sampling plans.Originality/valueThe newly presented approximation provides a remarkably close fit to the type-A OC function, is discrete and needs no correction for continuity, and is skewed in the same direction by roughly the same amount as the exact OC. Due to less factorials, this OC in general involves lower powers than the type-A OC function. Moreover, the binomial-type approximation is easy to fit to the conventional statistical computing packages.

Selection of single sampling plans by attributes under the conditions of zero-inflated Poisson distribution

2014 ◽  
Vol 31 (9) ◽  
pp. 1002-1011 ◽  
Author(s):  
Loganathan Appaia ◽  
Shalini Kandaswamy
Keyword(s):  
Design Methodology ◽  
Operating Characteristic ◽  
Manufacturing Processes ◽  
Sampling Plans ◽  
Content Type ◽  
Numerical Examples ◽  
Number Of Zeros ◽  
Operating Characteristic Function ◽  
First Time ◽  
Selection Of

Purpose – The purpose of this paper is to determine single sampling plans (SSPs) by attributes when the number of nonconformities is distributed according to a zero-inflated Poisson (ZIP) distribution. Design/methodology/approach – Manufacturing processes have now-a-days been aligned properly and are monitored well, so that the occurrence of nonconformities would be a rare phenomenon. The information related to number of nonconformities per product will have more number of zeros. Under such circumstances, the appropriate probability distribution of the number of nonconformities is a ZIP distribution. The operating characteristic function of the sampling plan is derived. Findings – Parameters of the sampling plans are obtained for some sets of values of (p 1, α, p 2, β). Numerical examples are given to illustrate the selection of SSPs under ZIP distribution and to study its advantages over Poisson SSP. Originality/value – Results obtained in this paper are original and has been done for the first time in this regard. Parameters of the sampling plans are essential to make decisions either to accept or reject the lots based on the inspection of the samples.

Acceptance Sampling Plans Based on Truncated Lifetime Tests for Transmuted Inverse Rayleigh Distribution

2016 ◽  
Vol 31 (2) ◽  
Author(s):  
Amer I. Al-Omari
Keyword(s):  
Sample Size ◽  
Operating Characteristic ◽  
Rayleigh Distribution ◽  
Acceptance Sampling ◽  
Sampling Plans ◽  
Confidence Levels ◽  
Operating Characteristic Function ◽  
Acceptance Sampling Plans ◽  
Mean Lifetime ◽  
Predetermined Level

AbstractIn this paper, we propose acceptance sampling plans for transmuted inverse Rayleigh distribution when the lifetime time is truncated at a predetermined level. We consider various characteristics of the acceptance sampling plans such as confidence levels, acceptance numbers, ratio of the experimental time to such a specified average, minimum requisite sample size to affirm a certain mean lifetime assuming transmuted inverse Rayleigh distribution. The minimum sample size, the operating characteristic function values of the new sampling plans as well as the producer’s risk are obtained and the results are illustrated by examples.

New Acceptance Sampling Plans Based on Percentiles for Exponentiated Fréchet Distribution

2016 ◽  
Vol 31 (1) ◽  
Author(s):  
Gadde Srinivasa Rao ◽  
Kanaparthi Rosaiah ◽  
Mothukuri Sridhar Babu ◽  
Devireddy Charanaudaya Sivakumar
Keyword(s):  
Operating Characteristic ◽  
Real Data ◽  
Acceptance Sampling ◽  
Producer’S Risk ◽  
Data Set ◽  
Sampling Plans ◽  
Fréchet Distribution ◽  
Acceptance Sampling Plans ◽  
Characteristic Values ◽  
Frechet Distribution

AbstractIn this article, acceptance sampling plans are developed for the exponentiated Fréchet distribution based on percentiles when the life test is truncated at a pre-specified time. The minimum sample size necessary to ensure the specified life percentile is obtained under a given customer's risk and producer's risk simultaneously. The operating characteristic values of the sampling plans are presented. One example with real data set is also given as an illustration.

scholarly journals Mixed Variables-Attributes Test Plans for Single and Double Acceptance Sampling under Exponential Distribution

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Yan Li ◽  
Xiaolong Pu ◽  
Dongdong Xiang
Keyword(s):  
Exponential Distribution ◽  
Operating Characteristic ◽  
Acceptance Sampling ◽  
Sample Sizes ◽  
Sample Number ◽  
Sampling Plans ◽  
Average Sample Number ◽  
Mixed Variables ◽  
Average Sample

The mixed variables-attributes test plans for single acceptance sampling are proposed to protect “good lots” from attributes aspect and to optimize sample sizes from variables aspect. For the single and double mixed plans, exact formulas of the operating characteristic and average sample number are developed for the exponential distribution. Numerical illustrations show that the mixed sampling plans have some advantages over the variables plans or attributes plans alone.

scholarly journals Acceptance Sampling Plans for Finite and Infinite Lot Size under Power Lindley Distribution

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 496
Author(s):  
Saman Shahbaz ◽  
Khushnoor Khan ◽  
Muhammad Shahbaz
Keyword(s):  
Operating Characteristic ◽  
Acceptance Sampling ◽  
Lot Size ◽  
Characteristic Curves ◽  
Sampling Plans ◽  
Lindley Distribution ◽  
Product Life ◽  
Power Lindley Distribution ◽  
Acceptance Sampling Plans ◽  
Lot Sizes

In this paper, we have developed single and double acceptance sampling plans when the product life length follows the power Lindley distribution. The sampling plans have been developed by assuming infinite and finite lot sizes. We have obtained the operating characteristic curves for the resultant sampling plans. The sampling plans have been obtained for various values of the parameters. It has been found that for a finite lot size, the sampling plans provide smaller values of the parameters to achieve the specified acceptance probabilities.

Integrating Human Factors Models into Statistical Quality Control

1976 ◽  
Vol 20 (1) ◽  
pp. 1-5 ◽  
Author(s):  
C. G. Drury
Keyword(s):  
Quality Control ◽  
Operating Characteristic ◽  
Statistical Quality Control ◽  
Control Field ◽  
Sampling Plans ◽  
Statistical Quality ◽  
Input Quality ◽  
Human Inspection

Recent progress in the Statistical Quality Control field has led to the design of Sampling plans which do not assume perfect inspection. Simple methods now exist for analyzing the effect of inspector error on the operating characteristic (OC) curve of a plan and further for re-designing the plan so that a predetermined OC curve is obtained. However, the usual assumption made about human inspection error is that it is constant. Many studies show that Type 1 and Type 2 inspector error change systematically with many variables such as input quality, complexity of item inspected, type of fault, standards, individual differences, etc. This paper develops a methodology for including an explicit human inspector model into the sampling plan design. A particular model integrating visual search and decision making (proposed earlier by the author) is used to demonstrate the feasibility of including explicit human inspector data in the design process. The applications of this model to single and double sampling plans are discussed, together with evidence for the validity of the model under laboratory and field conditions.

scholarly journals A Two-Parameter Quasi Lindley Distribution in Acceptance Sampling Plans from Truncated Life Tests

2019 ◽  
pp. 39-47
Author(s):  
Amer Ibrahim Al-Omari ◽  
Amjad Al-Nasser
Keyword(s):  
Life Time ◽  
Acceptance Sampling ◽  
Average Life ◽  
Sampling Plans ◽  
Lindley Distribution ◽  
Confidence Levels ◽  
Operating Characteristic Function ◽  
Acceptance Sampling Plans ◽  
Life Tests ◽  
Two Parameter

In this paper, acceptance sampling plans are developed when the life test is truncated at a pre-assigned time. For different acceptance numbers, confidence levels and values of the ratio of the fixed experiment time to the specified average life time, the minimum sample sizes required to ensure the specified average life are calculate assuming that the life time variate of the test units follows a two-parameter Quasi Lindley distribution (QLD(2)). The operating characteristic function values of the new sampling plans and the corresponding producer's risk are presented.

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