Producer's Risk Research Articles

Group Acceptance Sampling Plans for Life Tests Based on Half Normal Distribution

In this article, a group acceptance sampling plan is developed based on truncated lifetimes when the lifetime of an item follows a half normal distribution. For a given group size, the minimum number of groups and the acceptance number required are determined for specified consumer's risk and the test termination time. The values of operating characteristic function for various quality levels are calculated and the minimum ratios of the true average life to the specified life at given producer's risk are obtained. The results are illustrated by examples. DOI: http://dx.doi.org/10.4038/sljastats.v15i3.7799

A Method of Positional Quality Control Testing for 2D and 3D Line Strings

AbstractThis article presents a positional quality acceptance control method for 2D and 3D line strings based on a statistical hypothesis test. Two statistical models are applied together: a Binomial Model is applied over a Base Model. By means of the Base Model the method can be applied to any parametric or non‐parametric error model. The Base Model represents the hypothesis about the error behavior. The Binomial Model is fixed and consists of counting the number F of fail events in a sample of a determined size. The π parameter of the Binomial Model is derived from the Base Model by means of a desired tolerance. By comparing the probabilities associated to F and π a statistical acceptance/rejection decision is achieved. This method allows us to know and control the user's and producer's risk of acceptance/rejection. An example using a 2D line string data set from a commercial product is presented. The extension of the method to the 3D line string case is also presented. In order to facilitate the application of the method, some tables linking π with F and the control sample sizes are presented.

Mixed Acceptance Sampling Plans for Product Inspection Using Process Capability Index

ABSTRACTIn this article, a mixed acceptance sampling plan, which is the combination of an attribute plan and a variable plan based on , is proposed when the quality characteristic follows the normal distribution. The plan parameters are determined using a nonlinear optimization method such that producer's risk and consumer's risk are satisfied simultaneously for given values of acceptable quality level and limiting quality level. Symmetric and asymmetric cases are considered to design the proposed plan. The performance of the proposed plan over the attribute and variable sampling plans is discussed. Tables of plan parameters and examples are given to illustrate the plan developed here.

Planning Progressive Type-I Interval Censoring Life Tests With Competing Risks

In this article, we investigate some reliability and quality problems when the competing risks data are progressive type-I interval censored with binomial removals. The failure times of the individual causes are assumed to be statistically independent and exponentially distributed with different parameters. We obtain the estimates of the unknown parameters through a maximum likelihood method, and also derive the Fisher's information matrix. The optimal lengths of the inspection intervals are determined under two different criteria. The reliability sampling plans are established under given producer's and customer's risks. A Monte Carlo simulation is conducted to evaluate the performance of the estimators, and also some numerical results are presented.

Acceptance sampling by variables with life-test objectives

Sampling plans by variables with special references to life-test problems based on Weidull distribution are obtained. The life-test is terminated at the r-th failure. The sampling plan is such that a lot is accepted with a reassigned(high)probability when the specified mean life can be established. OC functions of the plans are obtained and Producer's risk is also discussed. A method of obtaining minimum sample size has been proposed so as to obtain the require number of failures with a prescribed time limit with a given probability .

Acceptance Sampling Plans: Size Biased Lomax Model

A new probability model size biased Lomax is considered for a life time random variable. The problem of acceptance sampling when the life test is truncated at a pre-assigned time is discussed with a known shape parameter. For various acceptance numbers, confidence levels and values of the ratio of the fixed experimental time to the specified mean life, the minimum sample size necessary to assure the specified mean life time is evaluated. The operating characteristic functions of the sampling plans are derived. Producer's risk is also discussed. A table for the ratio of true mean life to a specified mean life that ensure acceptance with a pre-assigned probability is provided. The results are given by an example.

Repetitive Group Sampling Plan Based on Truncated Tests for Weibull Models

This study proposes a new repetitive group sampling plan by attributes based on truncated life test under the Weibull distributions with known shape parameter. The constrained optimization problem is formulated as a nonlinear integer programming to determine the sample size and the acceptance criterion of the proposed plan. The objective function to be minimized is the average sample number, whereas the constraints are related to the lot acceptance probabilities at the acceptable and limiting quality levels. Tables containing the optimal design parameters are constructed for various values of the Weibull shape parameter and the results are explained with several examples. Minimum producer's and consumer's risks are also determined. The proposed sampling plan reduces significantly the average sample number as compared with the traditional single sampling plan. The effect of the mis-specification of shape parameters is also discussed.

Hybrid Group Acceptance Sampling Plan Based on Size Biased Lomax Model

In this paper, a hybrid group acceptance sampling plan is introduced for a truncated life test if life times of the items follow size biased Lomax model. The minimum number of testers and acceptance number are obtained when the consumer's risk and the test termination time and group size are pre-specified. The operating characteristic values, minimum ratios of the true mean life to the specified mean life for the given producer's risk are also derived. The results are discussed through an example, a comparative study of proposed sampling plan with existing sampling plan are elaborated.

DESINGING DSP (0, 1) ACCEPTANCE SAMPLING PLANS BASED ON TRUNCATED LIFE TESTS UNDER VARIOUS DISTRIBUTIONS USING MINIMUM ANGLE METHOD

In this paper DSP (0, 1) sampling plans for truncat ed life tests are developed using minimum angle met hod, when the life time of the items follows some selected distributions. The desi gn parameters of the sampling plan are determined f or pre-determined acceptance number by satisfying two risks at the specified qua lity levels simultaneously. The tables of design pa rameters are provided for various test termination time and mean ratio for some selec ted distributions. The operating characteristic val ues are also provided in the table. Some comparisons are made among the selected distributions. The results are explained with exam ples. Acceptance sampling is a inspecting procedure appli ed in statistical quality control. Acceptance sampling is a part of operations management and service quality maintenance. It is important for industrial, but also for business pur poses helping the decision - making process for the purpose of qu ality management. In a time- truncated sampling plan, a random sample is selected from a lot of products and put o n the test where the number of failures is recorded until the pre - specified time. If the number of failures observed is not greater than the specified acceptance number, then the lot will be accepted. Two risks are always attached to an ac ceptance sampling. The probability of rejecting the good lot is known as the type - 1 error (producer's risk) and it is deno ted by α. The probability of accepting the bad lot is known as th e type - 2 error (consumer's risk) and it is denoted by β. An acceptance sampling plan should be designed so that both risks are smaller than the required values. An acceptance sam pling plan involves quality contracting on product orders betw een the producer's risk and consumer's risk. In many pract ical situations, an important quality characteristic is the lifetime of the product that is, the time over which it fulfill s its task. Sampling plans to determine acceptability of a prod uct based on the number of failures recorded until the pre-sp ecified time are called time-truncated sampling plans.

Inspection of Batches Through Skip-R Lot Sampling Plan

In this paper, we present a new lot acceptance policy for batch inspection from a continuous process called the skip-lot sampling plan of type R (SkSP-R). The proposed plan is the extension of the SkSP-2 sampling plan and SkSP-V sampling plan by utilizing resampling. We formulate the optimization problem of minimizing the average sample number to determine the plan parameters of the proposed SkSP-R sampling plan. The constraints are to satisfy the producer's risk at the acceptable quality level and the consumer’s risk at the limiting quality level. The tables are presented and the results are explained with an example. The proposed plan is more efficient than the single sampling plan, SkSP-2 sampling plan, and SkSP-V sampling plan in terms of the average sample number.

Acceptance Sampling Plan Based on Truncated Life Tests for Three Parameter Kappa Distribution

This paper considers the problem of an acceptance sampling plan for a truncated life test when the lifetime follows the three parameter Kappa distribution. For different acceptance numbers, confidence levels and values of the ratio of the fixed experiment time to the specified lower bound of the mean lifetime, the minimum sample sizes necessary to ensure a specified mean lifetime are obtained. The operating characteristic function values of the suggested sampling plans and the corresponding producer's risk are stated. Tables are provided so that the plans can be easily applied in practice.

Bayesian Binomial Assurance Tests for System Reliability Using Component Data

This paper illustrates the development of Bayesian assurance test plans for system reliability assuming that binomial data will be collected on the system and that previous information is available from component testing. The posterior consumer's and producer's risks are used as the criteria for developing the test plan. Using the previous component information reduces the number of tests needed to achieve the same levels of risk. The proposed methodology is illustrated with two examples.

Repetitive variable acceptance sampling plan for one-sided specification

In this paper, a variable repetitive group sampling plans based on one-sided process capability indices is proposed to deal with lot sentencing for one-sided specifications. The parameters of the proposed plans are tabulated for some combinations of acceptance quality levels with commonly used producer's risk and consumer's risk. The efficiency of the proposed plan is compared with the Pearn and Wu [Critical acceptance values and sample sizes of a variables sampling plan for very low fraction of defectives. Omega – Int J Manag Sci. 2006;34(1):90–101] plan in terms of sample size and the power curve. One example is given to illustrate the proposed methodology.

Selection of Minimum Sample Size Tightened-Normal-Tightened Sampling Inspection Schemes

Abstract Acceptance sampling schemes are frequently used when finished products or materials are supplied by the producer for making decisions about individual lots or group of lots by examining sample information of such products or material. A sampling scheme is a set of plans that are usually specified by certain parameters such as sample size(s) and acceptance number(s). The tightened-normal-tightened (TNT) sampling scheme is a scheme that incorporates two single sampling plans called normal and tightened sampling plans, having the same sample size, but with different acceptance numbers along with the rules for switching between the plans. The determination of parameters of a sampling scheme for specified requirements on its operating characteristic curve providing protection to the producer and consumer is termed as designing of the scheme. This paper presents an iterative procedure for designing TNT schemes for two specified points on the operating characteristic curve, namely, acceptable quality level and limiting quality level associated with the producer's risk and the consumer's risk, respectively. Tables providing the parameters of the schemes for various values of acceptable quality level and limiting quality level under the conditions of binomial and Poisson distributions are developed and presented. The efficiency of such schemes over the schemes developed by the unity value approach is demonstrated with illustrations.

Skip-Lot Sampling Plan of Type SkSP-2 with Two-Stage Group Acceptance Sampling Plan as Reference Plan

This article deals with the optimal designing of skip-lot sampling plan of type SkSP-2 based on time-truncated life tests by considering two-stage group sampling plan as the reference plan under Burr type X and XII distributions. The optimal plan parameters are determined such that the specified producer's risk and consumer's risk are satisfied for given values of experiment time, percentile ratios, and percentile values. Extensive tables are also provided for various values of shape parameters. Examples reveal the use of the plan in laboratory experiments.

A new lot inspection procedure based on exponentially weighted moving average

In this manuscript a new variable sampling plan based on the exponentially weighted moving average (EWMA) statistic is proposed assuming that the quality characteristic follows the normal distribution. The plans are proposed when the standard deviation of the normal distribution is known or unknown. The plan parameters for both cases are determined such that the given producer's risk and consumer's risk are satisfied. The proposed plan includes the ordinary variable single sampling plan as a special case and its advantage over the single sampling plan is discussed in terms of the sample size. Extensive tables are provided for industrial use.

Assessing a Binary Measurement System With Varying Misclassification Rates When a Gold Standard Is Available

In manufacturing, we often use a binary measurement system (BMS) for 100% inspection to protect customers from receiving nonconforming product. We can assess the performance of a BMS by estimating the consumer's and producer's risks, the two misclassification rates. Here, we consider assessment plans and their analysis when a gold standard system (GSS) is available for the assessment study but is too expensive for everyday use. We propose a random-effects model to allow for variation in the misclassification rates within the populations of conforming and nonconforming parts. One possibility, here denoted the standard plan, is to randomly sample n parts and measure them once with the GSS and r times with the inspection system. We provide a simple analysis and planning advice for standard plans. In practice, the misclassification rates are often low and the underlying process has high capability. This combination of conditions makes the assessment of the BMS challenging. We show that we need a very large number of measurements with the standard plan in order to get precise estimators of the average misclassification rates and the true process performance. We consider an alternate design, here denoted the conditional assessment plan, where we select random samples from the sets of previously passed and failed parts. The sampled parts are measured once with the GSS and r times with the inspection system. When we augment the data from the conditional plans with available baseline information on the overall pass rate, we show that we can precisely estimate the parameters of interest with many fewer measurements. In the online supplementary materials, we provide R code to find maximum likelihood estimates and corresponding approximate standard errors, and to find the asymptotic standard deviation of the estimators with a selected plan size and assumed parameter values for both the standard and the conditional sampling plans.

Optimal Design of Skip Lot Group Acceptance Sampling Plans for the Weibull Distribution and the Generalized Exponential Distribution

ABSTRACT The present article proposes the skip lot sampling plan of type SkSP-2 using a group acceptance sampling plan for a time-truncated experiment as the reference plan, called SkGSP-2, when the lifetime of a product follows either the Weibull distribution or the generalized exponential distribution. The percentile life is used as the product quality in the proposed plan because assuring the percentile life is more practical than assuring the mean lifetime. The plan parameters such as the number of groups and the acceptance number are determined such that the specified values of producer's risk and consumer's risk are satisfied simultaneously. Extensive tables are provided for the selection of plan parameters according to various values of experiment time, percentiles ratios, and group size. Real-life examples are also given to illustrate the operation of the proposed plan.

Two-Stage Group Acceptance Sampling Plan for Burr Type X Percentiles

Abstract A two-stage group acceptance sampling plan for the percentile of lifetimes which have the Burr type X distribution is discussed under the time truncated life test. The sampling plan parameters for the two-stage sampling plan are determined such that the producer's risk and consumer's risk are satisfied simultaneously for the given tester size and experiment time. The advantage of the proposed two-stage sampling plan over the single-stage sampling plan is also discussed. Useful tables are given for practical purpose.

Selection of single sampling attribute plan for given AQL and LQL involving minimum risks using weighted Poisson distribution

PurposeThe 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.Design/methodology/approachFor 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.FindingsIn 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.Originality/valueThe sampling plan presented in this paper is particularly useful for testing the quality of finished products in shop floor situations.