Lifetime Performance Index Of Products Research Articles

Evaluating the lifetime performance index of products based on progressively Type‐II censored Pareto samples: A new Bayesian approach

AbstractProcess capability indices has been widely applied in industry to assess the performance of industrial processes. For the larger‐the‐better lifetimes of products, the lifetime performance index is commonly considered by industrial managers. This paper confines itself to the the Bayesian statistical inferences about under the Pareto distribution with the progressively Type‐II censored samples. The Bayesian inferences are based on a conjugate continuous prior for the scale parameter and a discrete prior for the shape parameter of the distribution under consideration. Two illustrative examples are given to demonstrate the sensitivity of results to the prior hyperparameters and the underlying distribution of the observations. Finally, a Monte Carlo simulation study is done to evaluate the behavior of the lifetime performance index .

Experimental Design for the Lifetime Performance Index of Weibull Products Based on the Progressive Type I Interval Censored Sample

In this study, the experimental design is developed based on the testing procedure for the lifetime performance index of products following Weibull lifetime distribution under progressive type I interval censoring. This research topic is related to asymmetrical probability distributions and applications across disciplines. The asymptotic distribution of the maximum likelihood estimator of the lifetime performance index is utilized to develop the testing procedure. In order to reach the given power level, the minimum sample size is determined and tabulated. In order to minimize the total cost that occurred under progressive type I interval censoring, the sampling design is investigated to determine the minimum number of inspection intervals and equal interval lengths when the termination time of experiment is fixed or not fixed. For illustrative aims, one practical example is given for the implementation of our proposed sampling design to collect the progressive type I interval censored sample so that the users can use this sample to test if the lifetime performance index exceeds the desired target level.

Bayesian Testing Procedure on the Lifetime Performance Index of Products Following Chen Lifetime Distribution Based on the Progressive Type-II Censored Sample

With the high demands on the quality of high-tech products for consumers, assuring the lifetime performance is a very important task for competitive manufacturing industries. The lifetime performance index CL is frequently used to monitor the larger-the-better lifetime performance of products. This research is related to the topic of asymmetrical probability distributions and applications across disciplines. Chen lifetime distribution with a bathtub shape or increasing failure rate function has many applications in the lifetime data analysis. We derived the uniformly minimum variance unbiased estimator (UMVUE) for CL, and we used this estimator to develop a hypothesis testing procedure of CL under a lower specification limit based on the progressive type-II censored sample. The Bayesian estimator for CL is also derived, and it is used to develop another hypothesis testing procedure. A simulation study is conducted to compare the average confidence levels for two procedures. Finally, one practical example is given to illustrate the implementation of our proposed non-Bayesian and Bayesian testing procedure.

Statistical inference for the lifetime performance index of products with Pareto distribution on basis of general progressive type II censored sample

In this paper, we study the statistical inference for the lifetime performance index of the Pareto distribution based on the general progressive type II censored data. Through data transformation, we derive the maximum likelihood estimator (MLE) of lifetime performance index and confidence interval. Further, the Bayesian estimator and the associated credible interval based on informative and non informative prior functions are also considered under the squared error loss function. Based on the non Bayesian and Bayesian estimators of lifetime performance indicators, the hypothesis testing process is constructed to evaluate the life performance of products. After the Monte Carlo simulation, we find that the Bayesian estimator is far better than MLE, and the Bayesian estimator based on informative prior has the best performance. The estimated mean squared errors for both MLE and Bayesian estimator are small, indicating that our considered method is effective to assess the lifetime performance of the products. Finally, a numerical example is analyzed for illustrative purposes.

Evaluating the lifetime performance index of products based on generalized order statistics from two-parameter exponential model

Assessing the lifetime performance of products is one of the most important topics in the manufacturing industries. In this paper, we assume that the lifetimes of products are independent and have a common two-parameter exponential distribution. The lifetime performance index ( $$C_L$$ ) provides a means for evaluating the performance of a process under a known lower lifetime limit L. We consider a sample of generalized order statistics (GOS), introduced by Kamps (A concept of generalized order statistics. Teubner, Stuttgart, 1995), which contains several models of ordered random variables, e.g. ordinary order statistics, progressively censored order statistics and record values. Then, we obtain the maximum likelihood estimator and the uniformly minimum variance unbiased estimator (UMVUE) of $$C_L$$ on the basis of a GOS sample. These estimators are compared in terms of mean squared error and Pitman measure of closeness criteria. The UMVUE of $$C_L$$ is utilized to develop a novel hypothesis testing procedure in the condition of known L. Finally, in order to illustrate the results, two real data sets due to Lawless (Statistical model and methods for lifetime data, 2nd edn. Wiley, New York, 2003) and Proschan (Technometrics 15:375–383, 1963), and a simulated sample are analyzed.

The assessment on the lifetime performance index of products with Gompertz distribution based on the progressive type I interval censored sample

It is a very important topic in the manufacturing industry to evaluate whether the quality of products adhered to the desire level. The larger-the-better process capability index (PCI) C L is frequently used to measure the performance of lifetimes of products. Gompertz distribution has many applications in the lifetime data analysis. The maximum likelihood estimator for C L is utilized to develop a hypothesis testing procedure with respect to a lower specification limit based on the progressive type I interval censored sample. Finally, two practical examples are given to demonstrate the application of our proposed testing procedure to assess whether the lifetime performance reached the desire level.

Pareto analysis for the lifetime performance index of products on the basis of progressively first-failure-censored batches under balanced symmetric and asymmetric loss functions

ABSTRACTOne of the most important topics in manufacturing industries is the evaluation of performance lifetimes of products. Based on a given lifetime performance index, this paper deals with evaluating the performance of a process subject to a given lower specification limit. We confine ourselves to the progressively first-failure-censored data coming from a common Pareto distribution. With both the Bayesian and the non-Bayesian approaches being investigated here, we pay more attention to Bayesian estimators under balanced type loss functions. The results are presented under the balanced versions of two well-known loss functions, namely the squared error loss and the Varian's linear-exponential (LINEX) loss. Moreover, based on the Bayesian and the non-Bayesian approaches, the problem of testing hypotheses on the lifetime performance index is studied. Also, a simulation study is performed to assess the obtained results. Finally, two illustrative examples are given.

The performance assessment on the lifetime performance index of products following Chen lifetime distribution based on the progressive type I interval censored sample

In the competitive manufacturing markets, quality engineers frequently are dedicated to evaluate whether the quality performance of products met the desire level. The lifetime performance index (LPI) C L is used to monitor the larger-the-better performance of lifetimes of products. Chen lifetime distribution with bathtub shape or increasing failure rate function has many applications in the lifetime data analysis. The maximum likelihood estimator for C L is derived and used to propose a hypothesis testing procedure under a lower specification limit based on the progressive type I interval censored sample. Finally, two practical examples are given to demonstrate the application of our proposed testing procedure to assess whether the lifetime performance reached the desire level.

A hypothesis testing procedure for the evaluation on the lifetime performance index of products with Burr XII distribution under progressive type I interval censoring

ABSTRACTIt is a very important topic these days to assessing the lifetime performance of products in manufacturing or service industries. Lifetime performance indices CL is used to measure the larger-the-better type quality characteristics to evaluate the process performance for the improvement of quality and productivity. The lifetimes of products are assumed to have Burr XII distribution. The maximum likelihood estimator is used to estimate the lifetime performance index based on the progressive type I interval censored sample. The asymptotic distribution of this estimator is also developed. We use this estimator to build the new hypothesis testing algorithmic procedure with respect to a lower specification limit. Finally, two practical examples are given to illustrate the use of this testing algorithmic procedure to determine whether the process is capable.

A computational algorithm for the evaluation on the lifetime performance index of products with Rayleigh distribution under progressive type I interval censoring

Abstract It is a very important topic these days to assessing the lifetime performance of products in manufacturing or service industries. Lifetime performance indices C L is used to measure the larger-the-better type quality characteristics to evaluate the process performance for the improvement of quality and productivity. The lifetimes of products are assumed to have Rayleigh distribution. The maximum likelihood estimator is used to estimate the lifetime performance index based on the progressive type I interval censored sample. The asymptotic distribution of this estimator is also developed. We use this estimator to build the new hypothesis testing algorithmic procedure with respect to a lower specification limit. Finally, two practical examples are given to illustrate the use of this testing algorithmic procedure to determine whether the process is capable.

Computational testing algorithmic procedure of assessment for lifetime performance index of products with Weibull distribution under progressive type I interval censoring

The assessing of the lifetime performance is a very important topic in manufacturing or service industries. Process capability indices had been widely used to evaluate the process performance to the continuous improvement of quality and productivity. The lifetimes of products are assumed to have Weibull distribution with a known shape parameter and the larger-the-better lifetime performance index is considered. The maximum likelihood estimator is used to estimate the lifetime performance index based on the progressive type I interval censored sample. The asymptotic distribution of this estimator is also investigated. We use this estimator to develop the new hypothesis testing algorithmic procedure with respect to a lower specification limit. Finally, two practical examples are given to illustrate the use of this testing algorithmic procedure to determine whether the process is capable.

Computational testing algorithmic procedure of assessment for lifetime performance index of products with one-parameter exponential distribution under progressive type I interval censoring

Process capability indices had been widely used to evaluate the process performance to the continuous improvement of quality and productivity. When the lifetime of products possesses a one-parameter exponential distribution, the larger-the-better lifetime performance index is considered. The maximum likelihood estimator is used to estimate the lifetime performance index based on the progressive type I interval censored sample. The asymptotic distribution of this estimator is also investigated. We use this estimator to develop the new hypothesis testing algorithmic procedure in the condition of known lower specification limit. Finally, two practical examples are given to illustrate the use of this testing algorithmic procedure to determine whether the process is capable.

Statistical Inferences for the Lifetime Performance Index of the Products with the Gompertz Distribution under Censored Samples

Manufacturers often apply process capability indices in the quality control. This study constructs statistical analysis methods of assessing the lifetime performance index of Gompertz products under progressively type II right censored samples. The maximum likelihood estimator of the index is inferred by data transformation and then utilized to develop a hypothesis testing procedure and a confidence interval to assess product performance. We also give one example and some Monte Carlo simulations to assess the behavior of the testing procedure and confidence interval. The results show that our proposed method can effectively evaluate whether the lifetime of products meet the requirement.

Computational procedure of lifetime performance index of products for the Burr XII distribution with upper record values

Process capability analysis has been widely applied in the field of quality control to monitor the performance of industrial processes. In practice, lifetime performance index (or the larger-the-better process capability indices (PCIs)) C L is a popular means to assess the performance and potential of their processes, where L is the lower specification limit. Moreover, record values often arise in industrial stress testing, meteorological analysis, hydrology, seismology, athletic events, and other similar situations. In this study, a two-stage maximum likelihood estimation applied to estimate lifetime performance index C L of non-normal processes. Further, this study will apply data transformation technology to construct a maximum likelihood estimator (MLE) of C L under the Burr XII distribution with the upper record values. The MLE of C L is then utilized to develop a hypothesis testing procedure in the condition of known L. Finally, we give simulation study and two examples to illustrate the use of the testing procedure under given significance level α .

Computational testing algorithmic procedure of assessment for lifetime performance index of products with two-parameter exponential distribution based on the multiply type II censored sample

Process capability indices have been widely used to evaluate the process performance to the continuous improvement of quality and productivity. Since the lifetime of products may possess a two-parameter exponential distribution, 14 estimators are used to estimate the lifetime performance index based on the multiply type II censored sample. These estimators are utilized to develop the new hypothesis testing algorithmic procedure in the condition of known L. Finally, two practical examples are illustrated to employ the testing algorithmic procedure to determine whether the process is capable.

Implementing lifetime performance index of products with two-parameter exponential distribution

The manufacturing industry has prioritised enhancing the quality, lifetime and conforming rate of products. Process capability indices (PCIs) are used to measure process potential and performance. The process capability is evaluated with product survival time and a longer lifetime implies a better process capability and a higher reliability. In order to save experimental time and cost, a censored sample arises in practice. In the case of product possessing a two-parameter exponential distribution, this study constructs a uniformly minimum variance unbiased estimator (UMVUE) of the lifetime performance index based on the type II right-censored sample. Then the UMVUE of the lifetime performance index is utilised to develop the new hypothesis testing procedure in the condition of known lower specification limit. Finally, two practical examples are illustrated to employ the testing procedure to determine whether the product is reliable.

Implementing lifetime performance index of products with two-parameter exponential distribution

The manufacturing industry has prioritised enhancing the quality, lifetime and conforming rate of products. Process capability indices (PCIs) are used to measure process potential and performance. ...

Assessing the lifetime performance index of products with the exponential distribution under progressively type II right censored samples

In practice, lifetime performance index C L is used to measure the potential and performance of a process, where L is the lower specification limit. Progressive censoring scheme is quite useful in many practical situations where budget constraints are in place or there is a demand for rapid testing. In this paper, under the assumption of exponential distribution, this study constructs a maximum likelihood estimator ( MLE) of C L based on the progressively type II right censored sample. The MLE of C L is then utilized to develop the hypothesis testing procedure in the condition of known L . The new testing procedure can be employed by product managers to assess whether the lifetime of products (or items) adheres to the required level in the condition of known L . Finally, we give one example to illustrate the use of the testing algorithmic procedure under given significance level.

Assessing the lifetime performance index of products from progressively type II right censored data using Burr XII model

Process capability analysis has been widely applied in the field of quality control to monitor the performance of industrial processes. In practice, lifetime performance index C L is a popular means to assess the performance and potential of their processes, where L is the lower specification limit. Nevertheless, many processes possess a non-normal lifetime model, the assumption of normality is often erroneous. Progressively censoring scheme is quite useful in many practical situations where budget constraints are in place or there is a demand for rapid testing. The study will apply data transformation technology to constructs a maximum likelihood estimator (MLE) of C L under the Burr XII distribution based on the progressively type II right censored sample. The MLE of C L is then utilized to develop a new hypothesis testing procedure in the condition of known L. Finally, we give two examples to illustrate the use of the testing procedure under given significance level α.

Computational procedure for assessing lifetime performance Index of products for a one-parameter exponential lifetime model with the upper record values

Process capability indices are used to measure the potential and performance of a process. This study constructs a uniformly minimum variance unbiased estimator (UMVUE) of the lifetime performance index based on the upper record values for a one-parameter exponential lifetime model. The UMVUE of the lifetime performance index is subsequently utilized to develop a hypothesis testing procedure for the condition of a known lower specification limit. Finally, three examples and a Monte Carlo simulation are presented to assess the behaviour of this test statistic for testing the null hypothesis under given significance levels. Product managers can use the proposed testing procedure to determine whether or not a process adheres to a required level of performance.