عنوان مقاله [English]
Process capability indices (PCIs) as quantitative measures of process performance in satisfying the customers expectations have been widely used in industry. as comparative ratios between voice of the customer and voice of the process. The independency of observations over time is one of the assumptions of the most PCIs developed. However, the development of sampling technology has led to increasing the number of sampling as well as decreasing the time interval between sampling. This leads to occurrence of autocorrelation between successive observations and violation of the independency between observations.There are different point estimators and confidence intervals for the process capability indices of autocorrelated data in the literature. In this paper for the first time, confidence intervals of Cpm and Cpmk are estimated using Circular Block Bootstrap resampling technique when the data are autocorrelated and modeled by an AR(1) process.looseness=1 Estimating the PCIs sampling distribution through simulation studies showed that increasing autocorrelation coefficients leads to decreasing in sampling standard deviation and bias in the PCIs estimators. However, larger sample sizes have resulted in more accurate estimations and lower bias, skewness and kurtosis of estimators.looseness=1In addition, performance of the proposed interval estimators are compared through numerical examples. Simulations results of two different methods of confidence interval indicate that 95% standard bootstrap (SB) method often outperforms the Biased-Corrected and accelerated (BCa) Percentile Bootstrap method without considering the magnitude of autocorrelation coefficient. Moreover, the effects of various autocorrelation coefficients, sample sizes, mean values and standard deviations on the proposed confidence intervals have been appraised.looseness=1 Finally, by comparing the results of the proposed method and existing methods in the literature, some advantages of the bootstrap have been mentioned. Generally, considerable volume of available data is brought about average coverage percentage (ACP) close to a nominal confidence level and lower average interval length (AIL) with more accuracy. In addition, the proposed methods have often lower AILs, and give acceptable ACPs particularly in weak autocorrelation coefficients.