Nonconforming Items Research Articles

Integrating delayed buffering-monitoring policy and spare parts management with incremental discount for imperfect two-machine series systems

ABSTRACT This paper presents a methodology for the inventory planning of a two-machine series system, wherein the first and second machines are designated as the upstream and downstream machines, respectively. The upstream machine commences production in the in-control state, and after a period of time, it may transition into an out-of-control state. In such circumstances, the rate of non-conforming items rises significantly. In consideration of the mechanical nature of the process, the time-to-shift variable is presumed to follow a Weibull distribution. Therefore, the upstream machine needs to be overhauled after a set time. During the implementation of overhaul activity, the upstream machine ceases to operate. A delayed buffering-monitoring policy is developed with three goals: (1) The creation of an intermediate buffer between two machines serves to prevent the interruption of the production line utilized by the downstream machine; (2) the reduction of the manufacturing costs, particularly the buffer inventory holding cost; and (3) the shift detection in the upstream machine through successive inspections. Furthermore, a restoration activity is implemented with the objective of returning the upstream machine condition to an in-control state. To do this, one spare part is consumed, which can be purchased under an incremental discount policy.

Development and Design of an Online Quality Inspection System for Electric Car Seats.

As the market share of electric vehicles continues to rise, consumer demands for comfort within the vehicle interior have also increased. The noise generated by electric seats during operation has become one of the primary sources of in-cabin noise. However, the offline detection methods for electric seat noise severely limit production capacity. To address this issue, this paper presents an online quality inspection system for automotive electric seats, developed using LabVIEW. This system is capable of simultaneously detecting both the noise and electrical functions of electric seats, thereby resolving problems associated with multiple detection processes and low integration levels that affect production efficiency on the assembly line. The system employs NI boards (9250 + 9182) to collect noise data, while communication between LabVIEW and the Programmable Logic Controller (PLC) allows for programmed control of the seat motor to gather motor current. Additionally, a supervisory computer was developed to process the collected data, which includes generating frequency and time-domain graphs, conducting data analysis and evaluation, and performing database queries. By being co-located with the production line, the system features a highly integrated hardware and software design that facilitates the online synchronous detection of noise performance and electrical functions in automotive electric seats, effectively streamlining the detection process and enhancing overall integration. Practical verification results indicate that the system improves the production line cycle time by 34.84%, enabling rapid and accurate identification of non-conforming items in the seat motor, with a detection time of less than 86 s, thereby meeting the quality inspection needs for automotive electric seats.

Multivariate process capability analysis with decision-maker preferences

Multivariate process capability analysis with decision-maker preferences

Assessing the economic-statistical performance of an attribute SVSSI-np control chart based on genetic algorithms

Assessing the economic-statistical performance of an attribute SVSSI-np control chart based on genetic algorithms

Weighted-Likelihood-Ratio-Based EWMA Schemes for Monitoring Geometric Distributions

Monitoring the parameter of discrete distributions is common in industrial production. Also, it is often crucial to monitor the parameter of geometric distribution, which is often regarded as the nonconforming item rate. To enhance the detection of nonconforming item, we designed an exponentially weighted moving average (EWMA) scheme based on the weighted likelihood ratio test (WLRT) method, and this scheme is denoted as the EWLRT scheme, specifically designed for monitoring the increase of the parameter in geometric distribution. Moreover, the optimal statistical design of the EWLRT scheme is presented when the shift is known. Results from numerical comparisons through Monte Carlo simulations indicates that the EWLRT scheme performs better than the competing schemes in some scenarios. Additionally, the designed scheme is characterized by its simplicity and ease of use, making it ideally suited for scenarios involving single observation. An example is illustrated to demonstrate the effectiveness of the EWLRT scheme.

The economic production quantity model for an imperfect production process by control chart design

The Economic Production Quantity (EPQ) plays a crucial role in the manufacturing process. The traditional EPQ model operates under the assumption that Non-Conforming (NC) items are not produced, and the process remains under control. However, real-world scenarios often involve the production of NC products, leading to process deviations. This study introduces a model that optimizes the design of a control chart to incorporate NC products into the EPQ model. The model integrates inventory and quality-related costs to minimize the expected total cost by determining EPQ, sample size, and control limit. The solution methodology employs direct search techniques to solve this problem. The sensitivity analysis results demonstrate the significant cost reduction achieved by the proposed model compared to the classical EPQ model. The numerical examples presented in the study show an average cost reduction of approximately 21 percent, highlighting the potential effectiveness of the model in cost reduction efforts.

A design methodology based on two dimensional fuzzy linguistic variables for attribute control charts with real case applications

A design methodology based on two dimensional fuzzy linguistic variables for attribute control charts with real case applications

The economic production quantity model with optimal single sampling inspection

Abstract This paper derives an inspection policy for an economic production quantity (EPQ) model under the assumption that a process may produce non-conforming (NC) items. In various stages of a production process, a department receiving an order uses a single sampling inspection policy to detect NC items. Under such a policy, a lot is accepted if the number of NC items in the inspected sample is equal to or less than the acceptance number. The proposed model considers both EPQ- and quality-related costs. Moreover, economic production order quantity, sample size and acceptance number are considered decision variables. A numerical example is presented, and a set of sensitivity analysis are provided to highlight the effectiveness of the proposed model. The results reveal that when the inspection cost is high, the classical EPQ model achieves a lower expected total cost for the production system compared with the EPQ model with the inspection. In contrast, when the NC cost is high, the EPQ model with the inspection policy outperforms the classical EPQ model, which can significantly decrease the expected total cost.

An index of capability for bivariate zero-inflated processes

Rapid technological advancement and implementation of automation and computerization in today's manufacturing set up resulted in many high quality processes, where defects are rarely observed. There are many high quality manufacturing processes where two or more types of defects may be generated from different types of equipment/process problems. The zeroinflated defects data containing two types of defects are commonly modeled by bivariate zero-inflated (BZI) Poisson distribution. Pal and Gauri (2022a) proposed a methodology for measuring capability of a BZI Poisson process. However, they ignored the count of zero defect (ZD) products produced in a BZI process. Because of that, Pal and Gauri (2022a) proposed approach fails to discriminate the BZI processes which produces different proportions of ZD units but having almost the same proportion of nonconforming items with respect to the USL of combined number of defects or USLs of individual defect types. In this paper, a new measure of process capability for BZI processes is proposed that can truly discriminate different BZI processes taking into account the USL of combined number of defects (or USLs of individual defect types) as well as the proportion of ZD units produced in these processes. The proposed methodology is illustrated using two case studies. The results of the case studies show that the proposed index well represents the true capability of BZI processes.

The situation analysis of hot dry rock geothermal energy development in China-based on structural equation modeling

In order to combat climate change, China proposed a dual carbon target in 2020. (China's 2030 and 2060 Goals). If the goals can be achieved as scheduled, it will help the world achieve the carbon neutrality goal earlier and improve the increasingly serious global climate. Reducing the utilization of fossil fuels and increasing the share of clean energy in primary energy are major ways to achieve China's 2030 and 2060 Goals. As a geothermal resource with large reserves, high energy storage, clean and pollution-free, dry hot rocks can effectively contribute to the goals. To promote the utilization of dry hot rock, this paper quantitatively studies the factors affecting the development and utilization of dry hot rock, and first summarizes five major influencing factors, namely, resources, environment, market, exploration and development technology, and effective use of technology. Then questionnaire survey based on these five factors was designed and distributed by email to geothermal energy experts in universities (China University of Geosciences, etc.) and research institutions (Chinese Academy of Sciences, etc.). Finally, the questionnaires are subjected to a reliability credibility test and validity analysis to remove the non-conforming items, and the structural equation model was constructed to analyze the data. The results show that environment, market and exploration and development technology have significant effects on dry hot rocks, while resources and effective use of technology have insignificant effects on dry hot rocks. Finally, some suggestions to promote the development of dry hot rocks in China are proposed.

Evaluation and optimal designing of a new system of skip-lot reinspection schemes

A new sampling plan by integrating the resampling concept in a skip-lot sampling plan of type SkSP-3 with a single sampling plan as the reference plan is proposed and designated as SkSP-3-R plan. The performance metrics are derived by using the Markov chain formulation. A designing methodology using two points on the operating characteristic curve approach is proposed to determine the plan parameters of the SkSP-3-R plan involving minimum the average sample number. The execution of the proposed SkSP-3-R plan is discussed with an illustrative example. The comparative study shows that the proposed plan has better performance where the inspection is involved in terms of nonconforming items rather than nonconformities. In addition, it demonstrates that the proposed SkSP-3-R plan is more efficient than SkSP-2 plan, SkSP-3 plan, SkSP-2-R plan, and SSP. Based on average run length, the SkSP-3-R plan's characteristic of response-to-change in quality is also investigated.

The 𝑛𝑝-Chart with 3-𝜎 Limits and the ARL-Unbiased 𝑛𝑝-Chart Revisited

Abstract In the statistical process control literature, counts of nonconforming items are frequently assumed to be independent and have a binomial distribution with parameters ( n , p ) (n,p) , where 𝑛 and 𝑝 represent the fixed sample size and the fraction nonconforming. In this paper, the traditional n ⁢ p np -chart with 3-𝜎 control limits is reexamined. We show that, even if its lower control limit is positive and we are dealing with a small target value p 0 p_{0} of the fraction nonconforming ( p ) (p) , this chart average run length (ARL) function achieves a maximum to the left of p 0 p_{0} . Moreover, the in-control ARL of this popular chart is also shown to vary considerably with the fixed sample size 𝑛. We also look closely at the ARL function of the ARL-unbiased n ⁢ p np -chart proposed by Morais [An ARL-unbiased n ⁢ p np -chart, Econ. Qual. Control 31 (2016), 1, 11–21], which attains a pre-specified maximum value in the in-control situation. This chart triggers a signal at sample 𝑡 with probability one if the observed number of nonconforming items, x t x_{t} , is beyond the lower and upper control limits (𝐿 and 𝑈), probability γ L \gamma_{L} (resp. γ U \gamma_{U} ) if x t x_{t} coincides with 𝐿 (resp. 𝑈). A graphical display for the ARL-unbiased n ⁢ p np -chart is proposed, taking advantage of the qcc package for the statistical software R. Furthermore, as far as we have investigated, its control limits can be obtained using three different search algorithms; their computation times are thoroughly compared.

A delay-time model to integrate the sequence of resumable jobs, inspection policy, and quality for a single-component system

This study proposes a model that integrates the schedule of a sequence of resumable jobs and inspection policy in a critical single-component system, following a deterioration process modeled with a delay-time concept. Thus, the system can be in a good, defective or failed state. When the system is in a defective state, it decreases in product quality, which leads to an increase in the proportion of non-conforming items and rework activities. If the system fails, a minimal repair is required to restore the system to an operational condition but in a defective state. Consequently, we established a limit of m consecutive minimal repairs to prevent the system from producing a substantial proportion of non-conforming items. So, we propose a mathematical framework and a simulation model to minimize the expected total costs. Also, we develop a Genetic Algorithm to tackle medium-size instances and analyze some special cases of the model. Therefore, we solved a numerical case and performed a sensitive analysis. We compare the Genetic Algorithm with a heuristic algorithm, and our model with its straight simplification. In this last comparison, in the worst case tested, the ”ignorance cost” could reach 335%. • The production quality shall be affected by the degraded state of the system. • Degradation is investigated on the basis of generating nonconforming products. • A systematic approach to searching for good solutions is proposed by integrating an simulator with a heuristic method. • A relationship between the generation rate of non-conforming items wit the degradation of the system is proposed. • The Model integrates the schedule of a sequence of jobs and inspection policy for the processing of n jobs. • Potential damage to the company’s reputation can result from naive models.

Optimized np Attribute Control Chart Using Triple Sampling

This paper studies an attribute control chart for monitoring the number of nonconforming items using a triple sampling (TS-np) which has not yet been applied to attribute control charts. The chart design and procedure for the decision about the state of the process are given. Mathematical expressions for the average run length (ARL) for in-control and out-of-control processes and the average sample number (ASN) are given. A bi-objective genetic algorithm that seeks to minimize the ASN and the probability of type 2 error is implemented in order to optimize the design of the TS-np control chart. A comparison between TS-np, single sampling np (SS-np), double sampling np (DS-np), and multiple dependent state repetitive sampling (MDSRS) control charts is carried out in terms of the out-of-control average run length (ARL1). Tables of ARL1 values for TS-np are presented in comparison with MDSRS and DS-np for various scenarios. The operation of the proposed control chart is shown through simulated data. Finally, it is concluded that the proposed TS-np chart has a better performance in terms of ARL1 detecting small and moderate shifts in the process nonconforming rate in-control (p0) compared with MDSRS and DS-np.

A production-inventory model under quality-maintenance policy with rework process in the presence of random failures and multiple assignable causes

ABSTRACT This research presents simultaneous design of production planning, maintenance strategy and control chart in which two issues are considered: (1) multiple assignable cause and (2) equipment failure. The first one means that various factors may shift the process to an out-of-control state; while the second one means that the equipment is not always available and may be suddenly failed. Also, to reduce the production costs, a rework process is performed on the nonconforming items right after the regular cycle. Furthermore, three types of maintenance activities are applied based on system conditions. The corrective maintenance is conducted when the equipment failure occurs. The preventive maintenance is accomplished when the process continues until the end of the cycle, and the predictive maintenance is performed whereas the chart issues a true alarm. To check the effectiveness of the model, three comparative studies are examined. The first one compares the suggested model with a similar model without the rework process; the second one demonstrates the importance of employing the statistical process monitoring; and the last one compares the model with a similar model without considering the equipment failure. The results show the superiority of the integrated model compared to the others in the cost-saving.

Economic optimization of acceptance interval in conformity assessment: 1. Process with no systematic effect

In inspections for conformity assessment, an acceptance interval smaller than the tolerance interval is often determined in order to reduce the risk of consumers obtaining non-conforming items in the market. The presence of non-conforming items in the market impairs the evaluation of items by customers and may have an impact on revenue by decreasing prices. However, setting too small an acceptance interval reduces the revenue from the process by decreasing the number of the items available in the market. We thus propose a method to determine the optimum acceptance interval in conformity assessment by means of maximization of the revenue from processes. For this purpose, we give a mathematical model for the price of an item and its cost in the production process. Through theoretical analysis and simulations, it is shown that a parameter in the price model is the key in the optimization. In this paper we report a method for processes where no systematic effect component of measurement uncertainty exists, and in part 2 of this series we will report an extended method in which systematic effects are taken into consideration.

A closer look at the equivalence of Bernoulli and geometric CUSUM control charts

AbstractSome researchers have incorrectly concluded that the geometric CUSUM is superior to the Bernoulli CUSUM as a procedure for monitoring a repetitive process, even though the two procedures have been proved to be equivalent for detecting an upward shift in the proportion of nonconforming items. We use an exact Markov‐chain‐based methodology to re‐examine the relationship between geometric CUSUM and Bernoulli CUSUM control charts. Exact methods allow us to differentiate between similar but different‐valued quantities that have contributed to some misunderstandings in the literature. We show that for a random‐shift model, evaluations of steady‐state average number of inspected items until a signal (ANIs) are identical for both geometric CUSUMs and Bernoulli CUSUMs, provided the correct choices of return levels are made. We also show that a steady‐state geometric CUSUM based on a fixed‐shift model only uses the geometric CUSUM states, while a steady‐state geometric CUSUM based on a random‐shift model will reach the states of a Bernoulli CUSUM after a long series of zeros. We note that our conclusions are contrary to the published results of other researchers, and we examine these differences in detail.Layman's Abstract: Since, their introduction by Walter Shewhart in 1931, control charts such as the Shewhart p‐chart have had widespread application for monitoring the output quality from manufacturing processes, such as the proportion (p) in the stream of manufactured items that are nonconforming. But the Shewhart p‐chart is not very effective for monitoring processes when the proportion p is less than about 4 percent. Other charts, such as the geometric CUSUM (proposed in 1991) and the Bernoulli CUSUM (proposed in 1999) have been shown to be superior at identifying changes in p when p is small. Some researchers have relied on simulation‐based investigations to compare these two CUSUMs, and have incorrectly concluded that the geometric CUSUM is superior to the Bernoulli CUSUM, even though the two procedures have been proved to be equivalent for detecting an upward shift in the proportion p. Using exact, Markov‐chain‐based methodology, we re‐examine the relationship between the geometric CUSUM and the Bernoulli CUSUM control charts and demonstrate that these two charts are equivalent when evaluated correctly. Exact methods allow us to precisely compare these two monitoring schemes and correct some erroneous conclusions that have appeared in the literature.

Process quality recheck for Gamma quality characteristic from supplier products: a case study on radio-frequency power

Quality fraud seriously damages the right-to-known of customers. Therefore, it is necessary for customers to recheck the process quality level declared by suppliers, which is often measured by process capability indices (PCIs). However, there exist two practical problems when rechecking PCIs based on a quality characteristic (QC). First, QC data often do not follow normal distributions. Second, to enhance the market competitiveness, the supplier usually conducts a full inspection and eliminates the non-conforming items before selling them, which causes the QC data to be truncated. To overcome these problems, motivated by the radio-frequency (RF) power output data, this paper proposes a two-phase process capability recheck method, including data-filling and generalised p-value (GE-P) test. The novel data-filling method integrates the quantile-filling (QA) and bias-correction closed-form (BC) estimator for Gamma distributions, and simulation results show it performs better than the traditional methods on unbiasedness and consistency. Based on the filling pseudo-complete data, GE-P is adopted to complete the recheck by testing whether the process capability reaches the supplier declared level. Numerical analysis indicates it performs well on two types of errors. Finally, a real case study on the motivating example is presented to verify the effectiveness of the proposed method.

Designing of variables repetitive group sampling plan for consumer protection

Due to the development of modern technology, it is possible to reduce the variation of products quality during the production. However, it is necessary to propose a designing methodology of sampling plans to guarantee the consumers protection in terms of maximum limit of outgoing non-conforming items while protecting the producers a good quality level. Hence, in this paper, we propose the designing methodology of variables repetitive group sampling plan indexed by acceptable quality level and average outgoing quality limit. We develop an optimization model for determining the optimal parameters with minimum average sample number at the acceptable quality level by simultaneously considering two inequalities. The optimal plan parameters are determined for both cases of known and unknown standard deviation. Results show that the proposed plan reduces the required sample size than the existing single sampling plan to provide protection to the consumers in terms of average outgoing quality.

An economic manufacturing quantity model with rework process for deteriorating products under maintenance-quality policy

ABSTRACT This paper presents an integrated model of three interrelated topics including the statistical process monitoring, maintenance scheduling, and production cycle length for imperfect manufacturing systems. The novelty of this paper is to take five features into consideration, including: (1) The produced items deteriorate over time, hence, the inventory is depleted in two ways i.e. responding to demand and gradually deteriorating products; (2) The non-conforming products can be reworked to increase the cost-saving by eliminating the waste items; (3) A non-uniform sampling scheme is employed such that the hazard rate does not exceed its threshold value; (4) The economic-statistical design of a control chart is used to accelerate the detection of process faults as well as reduce the risk of false alarms; and (5) The time value of money is taken into account to obtain more precise financial flow estimations. Finally, four comparative studies along with a sensitivity analysis on the most important parameters are conducted. The results confirm that considering the product deterioration and time value of money improves the model adaptability in real-world applications. Besides, employing the variable sampling scheme and the rework operations reduces the production rate of non-conforming items. The results also show that the total cost in economic-statistical model is slightly higher than that of the economic one. However, the economic-statistical model performs severely better than the economic one in terms of both in-control and out-of-control average run length metrics.