Time Truncated Life Test Research Articles

Moving average control charts for the rayleigh and inverse rayleigh distributions under time truncated life test

AbstractIn this paper, the moving average control chart is developed under time truncated test to monitor the number of failures when the lifetime of an item follows the Rayleigh and inverse Rayleigh distributions. The number of failures is detected when a planned number of items has been placed on a time truncated testing experiment. The average run lengths (ARL) for various parameter settings are used to evaluate the performance of the proposed control chart. Also, the control chart parameters such as test time multiplier () and chart coefficient (k) are obtained by contemplating the in‐control ARL for various sample sizes. The study revealed that the proposed control chart outperform the existing time truncated attribute control chart in the quick detection of shifts in process parameters. The application of the proposed chart methodology is also demonstrated using simulated data.

Efficient designs of modeling attribute control charts for a Weibull distribution under truncated life tests

In this paper, the designs of the attribute control chart for the Weibull distribution under the time truncated life tests are investigated. Thus, some models are presented for the determination of optimal parameters. All models have the same cost function to be minimized. However, in the economic-statistical model and multi-objective model, the producer’s risk and the consumer’s risk must be satisfied as constraints. These risks are also considered as simultaneous objective functions in the multi-objective model. Therefore, different algorithms are proposed to specify design parameters. For the multi-objective model, the concept of data envelopment analysis (DEA) is utilized in the proposed algorithm. DEA is a powerful non-parametric approach to evaluate the relative efficiency of a group of decision-making units (DMUs) with multiple inputs and outputs. Through simulation studies and comparisons, the results of the proposed models are investigated. Besides, a real example for the inspection of chip products is provided to illustrate and compare the performance of various models.

Single-stage and two-stage total failure-based group-sampling plans for the Weibull distribution under neutrosophic statistics

If the sample or population has vague, inaccurate, unidentified, deficient, indecisive, or fuzzy data, then the available sampling plans could not be suitable to use for decision-making. In this article, an improved group-sampling plan based on time truncated life tests for Weibull distribution under neutrosophic statistics (NS) has been developed. We developed improved single and double group-sampling plans based on the NS. The proposed design neutrosophic plan parameters are obtained by satisfying both producer’s and consumer’s risks simultaneously under neutrosophic optimization solution. Tables are constructed for the selected shape parameter of Weibull distribution and various combinations of neutrosophic group size. The efficiency of the proposed group-sampling plan under the neutrosophic statistical interval method is also compared with the crisp method grouped sampling plan under classical statistics.

Economic design of repetitive group sampling plan based on truncated life test under exponentiated half logistic distribution

In this paper, we propose repetitive group sampling plan based on time truncated life test under exponentiated half logistic distribution by considering percentile lifetime of the product as its quality characteristic when shape parameter value of exponentiated half logistic distribution is known. In this research, the design parameters are determined for various percentile ratios using the method of two points on the operating characteristic curve. Tables are constructed for various values of shape parameters to choose optimal parameters. The sampling procedure of proposed repetitive group sampling plan is illustrated with real time data and the consequence of misspecification of shape parameter on lot acceptance probability is also investigated. The proposed plan is also compared with single and double sampling plans in terms of discriminating power and average sample number under two other lifetime distributions. Moreover, an economic design of the proposed repetitive group sampling plan is discussed and optimal plan is selected to fulfill both producer’s and consumer’s risks with minimum cost.

Monitoring number of non-conforming items based on multiple dependent state repetitive sampling under truncated life tests

In this study, an attribute np control chart based on multiple dependent state repetitive sampling is proposed for monitoring the lifetime of the products since the lifetime of the products is considered as an important quality characteristic of many production processes. It is assumed that the lifetime of the product follows any one of the three lifetime distributions namely Weibull distribution, gamma distribution, and Pareto distribution of second kind with known shape parameter. The proposed chart is based on two pairs of control limits that utilize past subgroup information some times in addition to the current samples’ information under time truncated life test. The performance of the proposed chart is assessed by using out-of-control average run length. In order to get specific average run length, the optimal values of the parameters are determined by using a search procedure. A real time example is provided to assess the performance of the proposed chart. Moreover, performance of the proposed chart is compared with the control chart designed under single sampling procedure by using out-of-control average run length.

Single and Double Acceptance Sampling Plans Based on the Time Truncated Life Tests for the Compound Weibull-Exponential Distribution

Acceptance sampling plans are one of the important statistical tools in production sector. While the producers want the protection of the quality of the products and minimum variability between them, the consumers expect the products to satisfy the quality characteristics. It is worth to mention that the acceptance sampling plans protect both the interest of the producers and the consumers. For some products, the life time might be an important quality characteristic. In this case, the satisfaction of the quality control of the products can be controlled using a suitable life time test based on the acceptance sampling plans for the life time of the products. In the industry, the acceptance sampling plans based on the life time test of the product life are called as reliability. The fact that it is almost impossible to inspect all the products due to the limitations of both cost and time, the acceptance sampling plans are used based on a truncated life time test with a censoring scheme. In this study, optimal plan parameters are obtained for single and double acceptance sampling plans when the life time of a product follows compound Weibull-Exponential distribution.

A control chart for the generalized exponential distribution under time truncated life test

The usual assumption in the application of control chart is that the process follows a normal distribution. However, in practice, the underlying process distribution is either unknown or non-normal and the use of control chart assuming normality often leads to false alarm in the process. In this article, an attribute control chart under a truncated life test is proposed when the lifetime of a product follows a generalized exponential distribution assuming that the shape parameter is known and a shift in scale parameter has occurred. The control chart coefficient and the truncation constant are determined and the performance of the attribute control chart constructed on time truncated life test is evaluated in terms of the average run length (ARL). Tables of out-of-control ARL are also provided when the scale parameter are shifted. The application of the proposed chart is demonstrated using a simulated dataset for industrial use.

The Application of Lognormal Distribution on the New Two-Sided Group Chain Sampling Plan

This paper gives emphasis on the technical aspect of acceptance criteria in acceptance sampling plans, more specifically the family of two-sided group chain sampling plans. The new two-sided complete group chain sampling plan (NTSCoGCh) operates with five acceptance criteria, while the two-sided group chain sampling plan (TS-GCh) operates with three acceptance criteria. Generally, the number of acceptance criteria has a direct influence on the probability of lot acceptance; the more criteria being accepted leads to higher probability of lot acceptance. This paper suggests a new, balanced plan for the family of two-sided group chain sampling plans. The plan, named the new two-sided group chain sampling plan (NTSGCh), operates with four acceptance criteria. The Lognormal distribution is used to represent the production sequence of manufactured products in this study. A time truncated life test simulation is carried out to obtain the minimum number of groups required and the probability of lot acceptance. The findings show that the NTSGCh outperformed its predecessors. In conclusion, the NTSGCh is a viable alternative for implementation in the industry.

Moving Average control charts for Burr X and Inverse Gaussian distributions

The Burr X and Inverse Gaussian (IG) distributions are considered in this paper to design an attribute control chart for time truncated life test with Moving Average (MA) scheme w. The presentation of the MA control chart is estimated in terms of average run length (ARL) by using the Monte Carlo simulation. The ARL is decided for different values of sample sizes, MA statistics size, parameters’ values, and specified average run length. The performance of this new MA attribute control chart is compared with the usual time truncated control chart for Burr X and IG distributions. The performance of a new control chart is better than the existing control chart.

Design of multiple-deferred state sampling plans for exponentiated half logistic distribution

This paper aims to develop a multiple deferred state sampling plan for a time-truncated life test if the lifetime of the item follows exponentiated half logistic distribution. The optimal parameters of the proposed plan, such as the number of successive lots required for making the decision whether to accept or reject the current lot, sample size, the rejection and acceptance numbers are obtained using two points approach. The implementation of the proposed plan is illustrated with examples. Tables are constructed for various combinations of consumer’s and producer’s risks. Comparison is also made with existing sampling plans under exponentiated half logistic distribution.

An Attribute np Control Chart for Monitoring Mean Life Using Multiple Deferred State Sampling Based on Truncated Life Tests

In this paper, we design an attribute [Formula: see text] control chart for monitoring the mean life of the product where the lifetime follows the Pareto distribution of the second kind. The lifetime of the product is determined by time truncated life test and the multiple deferred state sampling is used to declare the status of the manufacturing process. Control limit coefficients and multiple deferred state sampling parameters such as sample size and number of successive subgroups required to declare the state of the process are determined such that the in-control average run length is as near as possible to the target average run length. Out-of-control average run lengths are calculated for the determined parameters using various shift constants. The performance of the chart is compared with other existing chart in terms of average run length.

Economic design of an attribute control chart for monitoring mean life based on multiple deferred state sampling

AbstractIn this paper, we design an attribute np control chart using multiple deferred state (MDS) sampling under Weibull distribution based on time truncated life test. This chart is constructed for monitoring the variation of mean life of the product in a manufacturing process. The optimal parameters of MDS sampling and the control limit coefficients are determined so that the in‐control average run length (ARL) is as close as to the target ARL. The optimal parameters of MDS sampling are sample size and number of successive subgroups required for declaring the current state of process. Out‐of‐control ARL is considered as a measure of the performance of proposed chart and reported with determined optimal parameters for various shift constants. The out‐of‐control ARL of the proposed chart obtained under various distributions is compared with each other. The performance of proposed control chart is compared with the performance of the existing control chart designed under single sampling. In addition, the economic design of proposed chart using variable sampling interval scheme is discussed, and sensitivity analysis on expected costs is also investigated.

A Variable Control Chart under the Truncated Life Test for a Weibull Distribution

In this manuscript, a variable control chart under the time truncated life test for the Weibull distribution is presented. The procedure of the proposed control chart is given and its run length properties are derived for the shifted process. The control limit is determined by considering the target in-control average run length (ARL). The tables for ARLs are presented for industrial use according to various shift parameters and shape parameters in the Weibull distribution. A simulation study is given for demonstrating the performance of the proposed control chart.

Determination of optimal quick switching system with varying sample size for assuring mean life under Weibull distribution

Conventional sampling plans are applied to dispose an individual lot or isolated lot that requires a large sample size. Consequently, the inspection time and cost needed to make a decision under conventional plans are high. In order to reduce the sample size and to inspect the series of lots with minimum cost and time, special purpose plans are utilized. In this article, we propose one of the special purpose plans, namely, a quick switching sampling system that is also known as a two-plan sampling system. Through this sampling system, the Weibull-distributed mean life of the product is ensured based on time-truncated life tests. The proposed system is designed with the intention of minimizing the average sample number using two points on the operating characteristic curve approach. The optimal parameters of the proposed system are determined for different combinations of producer’s risk and consumer’s risk. Implementation of the proposed system is also explained and the performance of the proposed system is compared with other existing plans. In addition, the effects of misspecification of shape parameters on optimal parameters and the probability of acceptance are discussed.

A Control Chart for Time Truncated Life Tests Using Exponentiated Half Logistic Distribution

A Control Chart for Time Truncated Life Tests Using Exponentiated Half Logistic Distribution

Economic design of quick switching sampling system for assuring Weibull distributed mean life

ABSTRACTIn this paper, we propose the quick switching sampling system for assuring mean life of a product under time truncated life test where the lifetime of the product follows the Weibull distribution and the mean life is considered as the quality of the product. The optimal parameters of the proposed system are determined using two points on the operating characteristic curve approach for various combinations of consumer's risk and ratio of true mean life time and specified life time. Tables are constructed to determine the optimal parameters for specified acceptable quality level and limiting quality level along with the corresponding probabilities of acceptance. The proposed system is compared with other existing sampling plans under Weibull lifetime model. In addition, an economical design of the proposed system is also discussed.

Optimal designing of multiple deferred state sampling plan for assuring percentile life under Weibull distribution

In this paper, we have proposed a multiple deferred state sampling plan for a time-truncated life test when the lifetime follows the Weibull distribution. The proposed sampling plan assures the percentile life of the products. The optimal plan parameters of the proposed plan such as the sample size, acceptance numbers, and number of successive lots required for making decision (n, c 1, c 2, m) are determined based on two points on the operating characteristic curve approach. The optimal parameters of the proposed plan are determined using an optimization problem for various combinations of producer’s risk, consumer’s risk, and percentile ratios. An illustrative example is also provided for describing the implementation of the proposed plan. Finally, we have investigated economic aspect of designing of the proposed plan under Weibull distribution.

EWMA np Control Chart for the Weibull Distribution

Abstract In this paper, we will present the design of an attribute exponentially weighted moving average (EWMA) control chart based on the number of failures under a time-truncated life test. It is assumed that the lifetime of the product follows the Weibull distribution. The performance of the proposed chart is discussed in terms of the average run length. The efficiency of the proposed chart is given over the existing attribute control chart. The proposed chart performs better than the existing chart in detecting shifts in the manufacturing process, as compared to the existing control chart. A simulation example is given to illustrate the proposed chart.

Time-truncated attribute sampling plans using EWMA for Weibull and Burr type X distributions

ABSTRACTAcceptance sampling, widely used in various production industries, is a very vital tool of quality control. In this paper, a new attribute acceptance-sampling plan is developed based on the exponentially weighted moving average statistic under a time-truncated life test when the product lifetime follows the Weibull distribution or the Burr type X distribution. The performance measures such as the probability of acceptance and the average sample number are derived. Tables are constructed for the selection of optimal parameters of the proposed sampling plan so as to minimize the average sample number satisfying the producer's and the consumer's risks. Illustrative example is also given for the application of the proposed plan. It is also shown that the proposed plan requires a smaller sample size compared to the single sampling plan.

Optimal Designing of a Multiple Deferred State Sampling Plan for Weibull Distributed Life Time Assuring Mean Life

SYNOPTIC ABSTRACTThis article proposes the multiple deferred (dependent) state sampling plan for a time-truncated life test when the lifetime of product follows the Weibull distribution. The quality of the product is considered in terms of mean lifetime. The optimal plan parameters of the proposed plan, such as the sample size, the acceptance and rejection numbers, and the number of successive (preceding) lots needed for making the decision whether to accept or reject the current lot, are determined using the approach of two points on the operating characteristic curve. Tables are constructed for different combinations of producer's and consumer's risks. The implementation of the proposed plan is also explained with a descriptive example. Comparison is also made with the existing sampling plans. In addition, an economic design of the proposed plan is also discussed and the optimal plans are determined, such that both producer's and consumer's risks are satisfied with minimum total cost of inspection.