Note on ‘Construction of Double Sampling s‐Control Charts for Agile Manufacturing’

He and Grigoryan (Quality and Reliability Engineering International 2002; 18 :343–355) formulated the design of a double‐sampling (DS) s control chart as an optimization problem and solved it with a genetic algorithm. They concluded that the DS s control charts can be a more economically preferable alternative in detecting small shifts than traditional s control charts. We explain that, since they only considered the average sample size when the process is in control, their conclusion is questionable. Copyright © 2006 John Wiley & Sons, Ltd.     

Dependent Mixed and Mixed Repetitive Sampling Plans for Linear Profiles

In this paper, we present two new dependent mixed sampling plans and a mixed repetitive sampling plan based on the process yield index for linear profiles. A mixed sampling plan includes two stages; the first stage is a combined test by variables and by attributes, and the second stage is tested by attributes only. The first plan is based on the traditional mixed sampling scheme without marginal quality, and the second plan is based on the modified mixed sampling scheme with marginal quality. If a lot is very bad, the probability it can be rejected with the small initial sample is higher for dependent mixed sampling with marginal quality. We compare dependent mixed plans with other types of double sampling plans; the former outperforms the others with respect to average sample number. Additionally, the number of profiles required in the first stage is much smaller than in the second stage. When the inspection is costly and destructive, a mixed repetitive sampling plan includes one stage that combines the inspection by attributes and by variables and allows resampling in some conditions. We compare the mixed repetitive sampling plan with the repetitive sampling plans by attributes and by variables. The probability of acceptance using the mixed repetitive sampling plan performs better than the repetitive sampling plans by attributes and by variables. Three examples are used to illustrate the proposed methods. Copyright © 2017 John Wiley & Sons, Ltd.     

A Single Sampling Plan Based on Exponentially Weighted Moving Average Model for Linear Profiles

The exponentially weighted moving average (EWMA) model has been successfully used in acceptance sampling plans. The EWMA model provides the quality information of the current lot and the preceding lots. In addition, a multiple dependent state (MDS) sampling plan considers the quality information of the preceding lots. In this study, we present two new sampling plans for linear profiles. One is based on EWMA model with yield index using the single sampling plan, and the other is based on EWMA model with yield index using the MDS sampling plans. The plan parameters are determined by a nonlinear optimization approach. As the smoothing parameter value equals to one, the first proposed plan becomes the traditional single sampling plan. In addition, we compare the proposed plans with the traditional single sampling plan. The results indicate that the MDS sampling plan based on EWMA model with yield index with smaller value of smoothing parameter performs better than the traditional single sampling plan and the single sampling plan based on EWMA model with yield index in terms of the sample size required. One real example is used to illustrate the proposed plan. Copyright © 2015 John Wiley & Sons, Ltd.     

Designing two mixed quick switching sampling plans for linear profiles

This study compares two proposed mixed quick switching sampling (QSS) plans for linear profiles as the quality characteristic. For the QSS plans, we recommend a binomial attribute plan for normal inspection and then a variable sampling plan for tightened inspection based on capability index C_puA of linear profiles with one-sided specifications. The difference between the two proposed QSS plans is in the tightened inspection. Tightened inspection of the first proposed plan is a single sampling using C_puA index, but tightened inspection of the second plan is a multiple dependent state repetitive (MDSR) plan based on C_puA index. The optimal parameters are obtained by nonlinear optimization. Simulation study for selecting parameters is conducted with various combinations of specified acceptable quality level (AQL), limited quality level (LQL), producer's risk, and consumer's risk. Simulation results confirm that the second proposed QSS plan which applies variable MDSR at tightened inspection performs better than another proposed plan. Hence, the approach of the second proposed plan is demonstrated in an illustrative example.     

Single Mixed Sampling Plan Based on Yield Index for Linear Profiles

Acceptance sampling plans have been widely used to decide whether an inspection lot from a supplier should be accepted or rejected. According to an economical point of view, a mixed sampling plan is better than the sampling plan by attributes. In some situations, lot sentencing can be determined by sampling plans by attributes and by variables simultaneously on the same product. In this paper, we propose a single mixed acceptance sampling plan based on the yield index for linear profiles for lot sentencing. The plan parameters are determined by minimizing sample size through a nonlinear optimization method such that the producer's risk and the consumer's risk are satisfied simultaneously for given values of acceptable quality level and limiting quality level. The results indicate that our proposed plan outperforms the single attributes sampling plan in terms of the sample size. One real example is used to illustrate the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

Multidimensional Mixed Sampling Plans

Mixed sampling plans are two-stage sampling plans in which variable and attribute quality characteristics are used in deciding the acceptance or rejection of the lot. Due to modern quality control systems, mixed sampling plans are widely applied in various stages of production. Use of different sampling plans for different quality characteristics would result in loss in economy, time, and labor. Therefore an attempt has been made to design multidimensional mixed sampling plans (MDMSP). Based on multidimensional quality characteristics, a MDMSP aims at controlling overall quality of a lot or process. The design aspect of a MDMSP is given in detail based on the Poisson model (type B process) in the second stage. Tables and illustration are also provided. Suresh and Devaarul (2000) have designed mixed sampling plans with chain sampling as the attribute plan. Suresh and Devaarul (2003) have developed mixed sampling plans for maximum allowable variance. Suresh and Devaarul (2003) have combined process control and product control to reduce sampling costs. Schilling (1967) has given a method for determining the operating characteristics of a mixed sampling plan including several other measures of the plan. A multidimensional mixed sampling scheme consists of two stages in which several variable and attribute quality characteristics are considered in deciding the acceptance or rejection of the lot. The main advantage of a MDMSP over any other plan is the reduction in the sample size for the same amount of protection.     

An alternative approach to accept on zero and accept on one sampling plans

Accept on zero and accept on one sampling plans are two common approaches to determine if a manufacturing lot can be accepted or rejected. Accept on zero plans inspect fewer items than the accept on one plans. On the other hand, accept on one plans have a higher probability of accepting a lot when the defect rate is between the Acceptable and Rejectable Quality Levels. This article proposes a double sampling plan whose probability of accepting a lot resembles an accept on one plan yet inspects considerably fewer items on average.     

The Effect of Correlation on Chain Sampling Plans

The Dodge chain sampling plan (ChSP‐1) and its extensions are very useful in situations where testing is either destructive or costly. Its underlying assumption is that all units to be inspected are from the same process and the quality characteristic of interest follows an identical independent distribution. Although this assumption makes the model relatively simple and easy to implement, it may not hold for today's manufacturing processes with high production volume, in which correlation exists between products within the same process. In this paper, we propose a Markov chain model for chain sampling plans to model the dependency (correlation) between testing units. To achieve this, we assume that product units within each sample follow a Markov chain model and assume that they are independent when they are from different lots. The resulting OC curves and AOQ curves show that the discriminating power of chain sampling plans improves when there is a negative correlation between product units and deteriorates when the correlation is positive. Copyright © 2004 John Wiley & Sons, Ltd.     

A Novel Lot Sentencing Method by Variables Inspection Considering Multiple Dependent State

A good acceptance sampling plan is necessary for quality control, and different acceptance sampling plans have been developed to meet different purposes. Under a multiple dependent state (MDS) sampling plan, the lot disposition is not only based on the current sample from the lot but also on the sample results from preceding lots. This paper aims to develop a variables MDS sampling plan for normally distributed processes with two‐sided specification limits. In the proposed MDS sampling plan, the operating characteristic curve is derived based on the exact sampling distribution. The performance of the proposed plan is investigated and compared with the existing variables single sampling plan. Copyright © 2015 John Wiley & Sons, Ltd.     

Variables Sampling Plan for Resubmitted Lots in a Process with Linear Profiles

Acceptance sampling plans include a sampling scheme and a set of rules for determining whether an inspection lot from a supplier should be accepted or rejected. In some circumstances, the supplier is allowed to resubmit lots for further inspection when the original inspection result is unacceptable. In this study, two variables sampling plans based on the process‐yield index for a process with linear profiles are proposed to deal with lot sentencing. The single sampling plan is a special case of the resubmitted lots sampling plan. The plan parameters are determined using a nonlinear optimization method under the given values of producer's risk, consumer's risk, acceptable quality level, and lot tolerance percent defective. Numerous tables are provided to determine the plan parameters. One real example is used to illustrate our proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

Life-Test Sampling Plans for Two-Parameter Weibull Populations

In this paper, we give variables sampling plans for items whose failure times are distributed as either extreme-value variates or Weibull variates (the logarithms of which are from an extreme-value distribution). Tables applying to acceptance regions and operating characteristics for sample size n, ranging from 3 to 18, are given. The tables allow for Type II censoring, with censoring number r ranging from 3 to n. In order to fix the maximum time on test, the sampling plan also allows for Type I censoring.

Acceptance/rejection is based upon a statistic incorporating best linear invariant estimates, or, alternatively, maximum likelihood estimates of the location and scale parameters of the underlying extreme value distribution. The operating characteristics are computed using an approximation discussed by Fertig and Mann (1980).     

Estimation of the Stress-Strength Reliability for Exponentiated Pareto Distribution Using Median and Ranked Set Sampling Methods

In reliability analysis, the stress-strength model is often used to describe the life of a component which has a random strength (X) and is subjected to a random stress (Y). In this paper, we considered the problem of estimating the reliability R=P [Y<X] when the distributions of both stress and strength are independent and follow exponentiated Pareto distribution. The maximum likelihood estimator of the stress strength reliability is calculated under simple random sample, ranked set sampling and median ranked set sampling methods. Four different reliability estimators under median ranked set sampling are derived. Two estimators are obtained when both strength and stress have an odd or an even set size. The two other estimators are obtained when the strength has an odd size and the stress has an even set size and vice versa. The performances of the suggested estimators are compared with their competitors under simple random sample via a simulation study. The simulation study revealed that the stress strength reliability estimates based on ranked set sampling and median ranked set sampling are more efficient than their competitors via simple random sample. In general, the stress strength reliability estimates based on median ranked set sampling are smaller than the corresponding estimates under ranked set sampling and simple random sample methods.     

Developing a variables multiple dependent state sampling plan with simultaneous consideration of process yield and quality loss

Acceptance sampling plans have been utilised predominantly for the inspection of outgoing and incoming lots; these plans provide effective rules to vendors and buyers for making decisions on product acceptance or rejection. Multiple dependent state (MDS) sampling plans have been developed for lot sentencing and are shown to be more efficient than traditional single sampling plans. The decision criteria of MDS sampling plans are based on sample information not only from the current lot but also from preceding lots. In this study, we develop a variables MDS sampling plan for lot sentencing based on the advanced process capability index, which was developed by combining the merits of the yield-based index and loss-based index. The operating characteristic function of the developed plan is derived based on the exact sampling distribution. The determination of plan parameters is formulated as an optimisation model with non-linear constraints, where the objective is to minimise the sample size required for inspection and the constraints are set by the vendor and the buyer to satisfy the desired quality levels and allowable risks. The performance of the developed plan is examined and compared with traditional sampling plans. A step-by-step procedure is provided, and the parameters of the plan under various conditions are tabulated for practical applications.     

Erratum

Erratum to Quality and Reliability Engineering International, Volume 20 Issue 4, ‘Setting Reliability Requirements Based on Minimum Failure‐free Operating Periods’, by M. T. Todinov, 273–287, 2004.     

New Synthetic Control Charts for Monitoring Process Mean and Process Dispersion

A statistical quality control chart is widely recognized as a potentially powerful tool that is frequently used in many manufacturing and service industries to monitor the quality of the product or manufacturing processes. In this paper, we propose new synthetic control charts for monitoring the process mean and the process dispersion. The proposed synthetic charts are based on ranked set sampling (RSS), median RSS (MRSS), and ordered RSS (ORSS) schemes, named synthetic‐RSS, synthetic‐MRSS, and synthetic‐ORSS charts, respectively. Average run lengths are used to evaluate the performances of the control charts. It is found that the synthetic‐RSS and synthetic‐MRSS mean charts perform uniformly better than the Shewhart mean chart based on simple random sampling (Shewhart‐SRS), synthetic‐SRS, double sampling‐SRS, Shewhart‐RSS, and Shewhart‐MRSS mean charts. The proposed synthetic charts generally outperform the exponentially weighted moving average (EWMA) chart based on SRS in the detection of large mean shifts. We also compare the performance of the synthetic‐ORSS dispersion chart with the existing powerful dispersion charts. It turns out that the synthetic‐ORSS chart also performs uniformly better than the Shewhart‐R, Shewhart‐S, synthetic‐R, synthetic‐S, synthetic‐D, cumulative sum (CUSUM) ln S², CUSUM‐R, CUSUM‐S, EWMA‐ln S², and change point CUSUM charts for detecting increases in the process dispersion. A similar trend is observed when the proposed synthetic charts are constructed under imperfect RSS schemes. Illustrative examples are used to demonstrate the implementation of the proposed synthetic charts. Copyright © 2014 John Wiley & Sons, Ltd.     

The Effect of Autocorrelation on the Hotelling T2 Control Chart

One of the basic assumptions for traditional univariate and multivariate control charts is that the data are independent in time. For the latter, in many cases, the data are serially dependent (autocorrelated) and cross‐correlated because of, for example, frequent sampling and process dynamics. It is well known that the autocorrelation affects the false alarm rate and the shift‐detection ability of the traditional univariate control charts. However, how the false alarm rate and the shift‐detection ability of the Hotelling T² control chart are affected by various autocorrelation and cross‐correlation structures for different magnitudes of shifts in the process mean is not fully explored in the literature. In this article, the performance of the Hotelling T² control chart for different shift sizes and various autocorrelation and cross‐correlation structures are compared based on the average run length using simulated data. Three different approaches in constructing the Hotelling T² chart are studied for two different estimates of the covariance matrix: (i) ignoring the autocorrelation and using the raw data with theoretical upper control limits; (ii) ignoring the autocorrelation and using the raw data with adjusted control limits calculated through Monte Carlo simulations; and (iii) constructing the control chart for the residuals from a multivariate time series model fitted to the raw data. To limit the complexity, we use a first‐order vector autoregressive process and focus mainly on bivariate data. © 2014 The Authors. Quality and Reliability Engineering International Published by John Wiley & Sons Ltd.     

A Novel Multiple Dependent State Sampling Plan Based on Time Truncated Life Tests Using Mean Lifetime

The design of a new adaptive version of the multiple dependent state (AMDS) sampling plan is presented based on the time truncated life test under the Weibull distribution. We achieved the proposed sampling plan by applying the concept of the double sampling plan and existing multiple dependent state sampling plans. A warning sign for acceptance number was proposed to increase the probability of current lot acceptance. The optimal plan parameters were determined simultaneously with nonlinear optimization problems under the producer’s risk and consumer’s risk. A simulation study was presented to support the proposed sampling plan. A comparison between the proposed and existing sampling plans, namely multiple dependent state (MDS) sampling plans and a modified multiple dependent state (MMDS) sampling plan, was considered under the average sampling number and operating characteristic curve values. In addition, the use of two real datasets demonstrated the practicality and usefulness of the proposed sampling plan. The results indicated that the proposed plan is more flexible and efficient in terms of the average sample number compared to the existing MDS and MMDS sampling plans.     

Sampling plans for the zero‐inflated negative binomial distribution in the food industry

In this paper, we propose 3 new sampling plans, including resubmitted single sampling plan (RSSP), repetitive group sampling (RGS) plan, and multiple dependent state (MDS) sampling plan to study the zero‐inflated negative binomial distribution in microbiological food safety and quality assurance practices. The unity value approach is used to find optimal plan parameters. The proposed plans are compared with the single sampling plan (SSP). We found that degree of clustering and excess of zeros counts affect the performance of all sampling plans. The MDS plan outperforms the SSP, RSSP, and RGS plans with respect to minimum average sample number in most cases. Both RGS and MDS plans show a comparable performance. The average run length is calculated to evaluate the rejection capability of the plans and signal the deterioration of the quality of lots. An example from 9 Irish abattoirs is used to illustrate the application of the proposed methods.     

Reducing sample size by tightening test conditions

The inspection of measurement devices according to statistical sampling plans allows conclusions to be drawn about the reliability of a whole population of devices. However, confirming high reliability levels requires large sample sizes and is thus expensive or even infeasible. For example, a reliability of 99.5% can only be guaranteed with 90% confidence by inspecting each item in a population of 280 (see ISO 2859‐2). When reliability is judged by not exceeding a certain threshold, this research provides a convenient solution allowing considerably more efficient sampling plans. Under certain distributional assumptions, in particular, we have proved that if 100q% of a population meets a tighter threshold Δ/γ, then at least 100p% of the population meets threshold Δ(with p>q, γ>1). The importance and effect of different distributional assumptions are demonstrated and relevant scenarios for the parameters (p,q,γ) presented. Verifying that a smaller portion of devices comply requires smaller sample sizes. Costs may thus decrease when more stringent specifications are verified. For example, up to 98% of utility meters in Germany are required to measure correctly at inspections, to ensure a reliability of 95% in the future. Instead of applying costly sampling plans to meters in use to demonstrate these high reliability levels, this research enables the sample size to be reduced, eg, by half.     

A variables multiple dependent state sampling plan based on a one-sided capability index

Acceptance sampling plan has been considered as one of most practical tools for quality assurance applications. While various types of acceptance sampling plans have been developed for different purposes, single acceptance sampling plan is the most popular because it is simple to administrate. However, a new concept called multiple dependent state sampling has gained the attention of scholars in recent years. The underlying principle is that the acceptance of a submitted lot should not only depend on the quality of the current lot but also consider the quality of the preceding lots. This research develops a variables multiple dependent state sampling plan (VMDSSP) for unilateral specification limit based on a one-sided capability index. The operating characteristic (OC) curve is prepared based on the exact sampling distribution. The plan parameters are determined by minimizing the average sample number while satisfying the quality levels demanded by both the producer and the consumer. The performance of the proposed plan is compared with the traditional variables single sampling plan (VSSP) and is examined in a case study.