A two-stage group acceptance sampling plan based on life tests for half logistic distribution

In this paper, a group acceptance sampling plan using weighted binomial is developed for a truncated life test when the lifetime of an item follows Inverse Rayleigh and Log - Logistic distributions. The minimum number of groups required for a given group size and the acceptance number is determined when the consumer's risk and the test termination time are specified. The operating characteristic values according to various quality levels are obtained. The results are explained with examples.

Acceptance sampling plans are specific rules used in statistical quality control to reach a decision on acceptance or rejection of lots of manufactured products submitted for inspection subject to the quality requirements of the sampled units. In order to reduce the inspection time and cost, the variable sampling plans are used as it needs comparatively small sample size. The multiple dependent state sampling plan is one of the conditional sampling plans which acquires the sample information from present lot as well as the prior lots for disposition of a lot. The MDS plan is applicable in the situations where lots are submitted for inspection in sequence of production from a process having a constant proportion non-conforming. MDS plan under the assumption of normality are found in literature. In this article, a multiple dependent state sampling plan is developed for sentencing lots of products whose quality characteristics follows a Logistic distribution. The proposed plan is designed by considering the two points on the OC curve, by formulating it as a non-linear optimization problem, when standard deviation is known and unknown. The tables are constructed for the selection of the proposed plan parameters. The proposed plan is compared with the single variable sampling plan based on Logistic distribution.

Time to failure due to fatigue is one of the common quality characteristics in material engineering applications. In this article, acceptance sampling plans are developed for the Birnbaum–Saunders distribution 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. The operating characteristic values (and curves) of the sampling plans as well as the producer's risk are presented. The R package named spbsq is developed to implement the developed sampling plans. Two examples with real data sets are also given as illustration.

ABSTRACTAn acceptance sampling plan (ASP) is a commonly used tool in quality assurance that allows business partners to make decisions about lot disposition. To enhance the efficiency and applicability of inspection, various ASPs have been constructed to meet different circumstances in practical applications. One of these ASPs is the skip‐lot sampling plan (SkSP), which reduces inspection time and cost for a series of product lots from a supplier with excellent quality records. Based on the structure of the SkSP, we propose an improved variables SkSP that uses a repetitive group sampling (RGS) plan based on the most commonly used capability index Cpk as the reference plan, designated as Cpk‐based SkSP‐RGS. This plan is optimized using a model that ensures the operating characteristic function meets a two‐point condition and minimizes the average sample number (ASN). Additionally, two main performance measures of sampling plans, ASN and discriminatory power, are investigated. The results reveal the superiority of the proposed plan over conventional Cpk‐based sampling plans. Lastly, a case study from the liquid crystal module industry is demonstrated using the proposed plan to show its applicability and practicality.

During the manufacturing process of a product, the manufacturer is very careful from the initial raw material to the final stage of the product. He always tries to enhance the quality level of the product. But if even the product is manufactured using the same machines, in the same laboratory, using the same manpower and environment and at the same temperature level, there may be still variation in the lifetime/failure time of the product. These failure times or lifetimes of the product are always fitted to some statistical distributions. Failure and repair times of electronic components are random and unpredictable in nature. But, the failure time of an electronic component can be modeled using statistical distributions and they are used in acceptance sampling. Distribution theory plays an important role in life testing of products. Many lifetime distributions have been widely used in the areas of quality control, reliability analysis and acceptance sampling plans which include such distributions as Birnbaum–Saunders distribution, Burr type XII distribution, generalized Birnbaum–Saunders distribution, generalized exponential distribution, generalized Rayleigh distribution, inverse Rayleigh distribution, inverse Gaussian distribution, log-logistic distribution and lognormal distribution. In this chapter, we will focus on these distributions to develop the acceptance sampling plans based on truncated life tests.

This research reveals a group acceptance sampling plan (GASP) for lot resubmitting is designed for conditions wherein an item life is taken from the size biased Lomax distribution (SBLD). The plan parameters of the GASP are obtained by fulfilling the prefixed producer’s and consumer’s risks as per the test completion time and the number of testers. The projected plan needs a minimal sample size in comparison with the standard GASP. This proposed plan is justified with an example.

The Garima distribution is proposed as a model for lifetime. The problem of acceptance sampling plan when the life test is truncated at a predetermined time is studied. For various acceptance numbers, different confidence levels, and different values of the ratio of the fixed experiment time to the specified average life, the tables of the minimum sample sizes required to assert the specified life mean are obtained. The producer’s risk and the operating characteristic function values of the suggested sampling plans are calculated. The results are illustrated using numerical examples. An application of a real data set reveals that the proposed acceptance sampling plans can be used in the industry.

In this article, acceptance sampling plans are developed for the log-logistic distribution 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. The operating characteristic values (and curves) of the sampling plans as well as the producer's risk are presented. Two examples with real data sets are also given as illustration.

To facilitate the derivation, two-stage fraction non-conforming acceptance sampling plans (with their operations characteristics curves passing through two predetermined points) were traditionally derived under conditions that restricted the relationships between the sample sizes and acceptance numbers of both stages. Removing those restrictions, and applying computerized search procedures in the solution space, improved sampling plans were derived with lower average sample sizes. The reduction in the average sample sizes amounted up to 31.41% and averaged around 7.48%. To facilitate the use of improved average-sample-number reduced sampling plans for unpublished parameter combinations, approximation formulas were developed using regression analysis. Their use allows a reduction of 4% in the Average Sample Number.

From quality and reliability perspectives, acceptance sampling plans play a significant role in manufacturing and industries in order to minimize the defect in the process. It is essential that the final product received by the customers, either external or internal, to be defect-free. In this regard, this paper presents the special case of acceptance sampling plan referred to as quick switching sampling (QSS) plan in the context of failure censoring reliability tests by considering the information from lifetime performance index (LPI). Unlike the common process capability indexes, LPI is usually appropriate for processes with non-negative quality characteristics. It is assumed that the lifetime of items follows Weibull distribution. Derivations of the operating characteristic curves are developed and a mathematical model is presented which determines the optimal parameters of the QSS plan. In order to see the effectiveness of proposed QSS, a real example is presented. In addition, different sensitivity analyses are conducted which the results indicate that proposed QSS plan can significantly decrease the costs of the life testing and sampling in comparison with a single sampling plan.

The concept of acceptance sampling plans ensures the quality of products and materials used in highway construction. These acceptance sampling plans require the testing of each and every individual lot of products for the highway construction and materials. This approach of sampling is applicable and appropriate if the supplier or contractor is unreliable. If the contractor is consistent and reliable, then instead of inspecting each and every lot of products, skip-lot sampling system can be utilized where only a fraction of the lots are inspected after assuring the quality and after a certain number of conforming lots is obtained. Skip-lot sampling plan can be used for reducing the amount of inspection on product that has an excellent quality history. Thus, skip-lot sampling plans are designed to reduce inspection costs. Moreover, skip-lot concept is sound and useful and it is economically advantageous in the design of sampling plans. Hence, this paper presents an improved system of skip-lot sampling plans designated as SkSP-V plan for the application of highway construction and materials. Advantages of this plan over the existing skip-lot plan and AASHTO’s lot-by-lot sampling plan are also discussed. The efficiency of this new plan is also investigated.

Acceptance sampling is a statistical quality control technique whereby the final decision to accept or reject a lot is based on the outcome from the inspection of its sample. A recent development in acceptance sampling includes the group chain acceptance sampling plan (GChSP) to rectify the problems with the single acceptance sampling plans (SSP) and chain acceptance sampling plans (ChSP). To date, the GChSP has been developed using two different approaches: minimizing the consumer’s risk (CR) and balancing both the CR and producer’s risk (PR) via minimum angle method. For both approaches, the GChSP has been developed by applying exponential distribution to the sampling plans. However, previous researchers only developed GChSP using these approaches without comparing their performance. Therefore, this article compares the performance of the GChSP using both approaches but considering the CR only. Both the GChSPs are developed via the same phases: (i) identifying the design parameters, (ii) developing operating procedures, (iii) deriving the probability of lot acceptance, (iv) deriving the probability of zero or one defective, (v) selecting lifetime distribution and (vi) measuring performance. The results reveal two interesting findings. The first finding shows that at the lower value of a, the minimum angle method has better protection for the consumer. The second finding shows that when the value of a increases, both approaches actually protect the consumer at the same level.

Acceptance sampling is one of the imperative methods used in statistical quality control through judgement a lot concerning its quality of 100% inspection and no inspection. Acceptance sampling plan is able to minimise the inspection cost and sampling error. It is a technique that deals with accepting or not the lot to be found on sampling inspection that delivers the quality of products manufactured by industries. This paper portrays designing procedure and development of skip-lot sampling plan of type SkSP-T with special type double sampling plan (STDSP) as reference plan which is designated as SkSTDSP-T. Operating characteristics and performance measures are derived, evaluated and tables involving incoming and outgoing quality levels are constructed for SkSTDSP-T plan. Tables are simulated by changing various parametric values of SkSP-T and STDSP plan. Table values are calculated, operating characteristic curve is drawn by using R (programming) language. Additionally, the efficiency of the proposed plan is discussed.

An instantaneous replenishment model under the effect of a sampling policy for defective items

Acceptance sampling plan is a product control technique, which plays a vital role in industries to inspect the quality of the raw materials processing at various stages of manufacturing and finished products at the specified quality levels. Various methods are used for monitoring and maintaining the quality of the products and services. Using acceptance sampling techniques, the quality of the products and services are decided, whether to accept or reject the finished product. In this situation the interest is to keep away from wrong selections, which is accepting the product of bad quality and rejecting the product of good quality. Accordingly, the usual objective in these cases is to use the overall risk of a wrong decision as optimization criteria. This situation is called as Minimum Risks Sampling Plan. In this paper, Hurdle Poisson distribution has been used to select the parameters of Repetitive Group Sampling Attribute Plan involving minimum sum of producer’s and consumer’s risks for specified Acceptable Quality Level and Limiting Quality Level.