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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.

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.

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.

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.

In 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.

The 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.

The 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.

The 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.

The purpose of this paper is to propose a new mixed repetitive group sampling (RGS) plan based on the process capability index, C_pk, where the quality characteristics of interest follow the normal distribution with unknown mean and unknown variance. Tables are constructed to determine the optimal parameters for practical applications for both symmetric and asymmetric fraction non-conforming cases. The advantages of this proposed mixed sampling plan are also discussed. The proposed sampling plan is also compared with other existing sampling plans.

In order to determine the optimal parameters of the proposed mixed RGS plan based on C_pk, the authors constructed tables for various combinations of acceptable and limiting quality levels (LQLs). For constructing tables, the authors followed the approach of two points on the operating characteristic (OC) curve. The optimal problem is formulated as a non-linear programming where the objective function to be minimized is the average sample number (ASN) and the constraints are related to lot acceptance probabilities at acceptable quality level and LQL under the OC curve.

The proposed mixed RGS plan will be a new addition to the literature of acceptance sampling. It is shown that the proposed mixed plan involves minimum ASN with desired protection to both producers and consumers compared to other existing sampling plans. The practical application of the proposed mixed sampling plan is also explained with an illustrative real-time example.

In this paper, the authors propose a new mixed RGS plan based on the process capability index C_pk, where the quality characteristic of interest follows the normal distribution with unknown mean and unknown variance. Tables are constructed to determine the optimal parameters for practical applications. The proposed mixed sampling plan can be used in all production industries. This kind of mixed RGS plan is not available in the literature.

Lifetime data are used in many different applied sciences, like biomedicine, engineering, insurance and finance and others. The purpose of this paper is to develop a new acceptance sampling plans for Rama distribution when the mean lifetime test is truncated at a pre-determined time. The minimum sample sizes required to assert the specified life mean is obtained for a given customer’s risk. The operating characteristic function values of the sampling plans and producer’s risk are calculated.

The results are illustrated using numerical examples and a real data set is considered to illustrate the performance of the suggested acceptance sampling plans and how it can be used for the industry applications.

This paper shows a new acceptance sampling plans based on Rama distribution in the particular case when the mean life time test is truncated.

The results calculated in this paper demonstrate the differences between OC values for different distributions taken into account. In particular, OC values of Rama distribution are found to be less than the proposed distribution counterparts.

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.

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.

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.

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.

It is shown that the Quick Switching System, Tightened Normal Tightened Scheme and other switching systems emerge from the generalised two‐plan system involving normal and tightened inspection. The corresponding operating characteristic (OC) functions are also shown to emerge from generalised results. The performance of different systems is compared with reference to their OC curves. The possibility of being applied in a critical area of application (in which the single sampling plans are not possible to apply) is indicated.

The purpose of this paper is to present the single sampling attribute plan for given acceptance quality level (AQL) and limiting quality level (LQL) involving minimum sum of risks using weighted Poisson distribution.

For the given AQL and LQL, sum of producer's and consumer's risks have been attained. Based on weighted Poisson distribution, the sum of these risks has been arrived at, along with the acceptance number and the rejection number. Also, the operating characteristic function for the single sampling attribute sampling plan, using weighted Poisson distribution, has been derived.

In the final inspection, the producer and the consumer represent the same party. So, the sum these two risks should be minimized. In this paper, the sum of risks has been tabulated using weighted Poisson distribution for different operating ratios. These tabulated values are comparatively less than the sum of risks derived using Poisson distribution.

The sampling plan presented in this paper is particularly useful for testing the quality of finished products in shop floor situations.

It is shown that the quick switching system, tightened normal tightened scheme and other switching systems emerge from the generalised two‐plan system involving normal and tightened inspection. The corresponding operating characteristic (OC) functions are also shown to emerge from generalised results. The performance of different systems compared with reference to their OC curves. The possibility of being applied in a critical area of application (in which the single sampling plans are not possible to apply) is indicated.

The purpose of this paper is to provide a relatively straightforward approach of implementing standard statistical process control (SPC) concepts while instituting problem‐solving intonations in aero‐engine maintenance processes.

The inspection workflow approach is presented in order to aid in collecting and monitoring critical aero‐engine data. Observed defects are categorized according to a Pareto analysis assisted by a cause‐and‐effect diagram. A binomial process capability analysis is performed on nonconforming aero‐engines based on operating curves produced specifically for this case study. The time frame for experimental analysis is reflected in a span of six months.

It is found that a significant number of aero‐engines may be benefited by entering a more progressive maintenance program relying on predictive maintenance on the way to establishing a more effective Total Productive Maintenance scheme.

The case study showcases an approach to aero‐engine rejection statistical rates by accepting the fact that maintenance process may not be viewed as a process that may be limited to constant sampling.

For a long time, total quality management (TQM) tools have been deeply rooted in design, manufacturing and assembling of airliners and jet fighters alike. However, a comprehensive study focusing on the maintenance function of such complex machines may prove worthwhile now that an unstable global economy may prohibit extensive replacement of aging flying fleets.

With the lack of a prior practical unfolding in the field of genuine aero‐engine maintenance, this presentation aims to fill in the gap for engine rejection treatment. The variant operating curve notion introduced in the text is also a unique idea espoused for variable sampling situations when a binomial distribution is adopted.

The purpose of this paper is the determination of reliability sampling plans in the Bayesian approach assuming that the lifetime distribution is exponential.

Sampling plans are used in manufacturing companies as a tool for carrying out sampling inspections, in order to make decisions about the disposition of many finished products. If the quality characteristic is considered as the lifetime of the products, the plan is known as a reliability sampling plan. In life testing, censoring schemes are adopted in order to save time and cost of life test. The inverted gamma distribution is employed as the natural conjugate prior to the average lifetime of the products. The sampling plans are developed assuming various probability distributions to the lifetime of the products.

The optimum plans n and c are obtained for some sets of values of (p1, a, p2, ß). The selection of sampling plans is illustrated through numerical examples.

Results obtained in this paper are original and the study has been done for the first time in this regard. Reliability sampling plans are essential for making decisions either to accept or reject based on the inspection of the sample.