Improved Control Charts Using Different Sampling Techniques

Abstract

Roberts (1959) proposed the memory-based control chart named as exponentially weighted moving average (EWMA) for capturing the minor alterations in ongoing process more effectively as contrasted it with memory less control chart. The EWMA statistic accumulates the information from recent observation as well as considers the past information, thus it executes meliorate than its competitor statistic that considers solely recent information. Thisstatistic isincredibly helpful in distinguishing tiny to moderate fluctuations. The Roberts statistic is extensively used for pinpointing the deviations in running process either to examine the quantitative or qualitative physical phenomena. Here, we introduce a generalized form of standard EWMA statistic. The Roberts statistic becomes the special case of our proposed statistic named as extended exponentially weighted moving average (EEWMA) statistic. This presented statistic depends on contemporary as well past information acquired from the study variable along with the weights and previous information of the suggested statistic. The mean and variance of EEWMA statistic were derived mathematically to build up control limits for surveillance of the process mean. Average run length (ARL) tables are constructed using various values of weights and shifted constant in process mean. Results are equated with competitor charts in cooperation of ARL, which demonstrates the capability of identifying the fluctuation in process mean more rapidly. Application of EEWMA control chart (CC) has also been exemplified with same case study data. It is important to note that EEWMA CC beats other competitor control CC for identifying the small variations. Keeping in mind the importance of earlier detection of small shifts in process mean, we extend our idea and suggest control charts based on Repetitive Sampling Scheme (RSS) and Multiple Dependent State (MDS) sampling using proposed EEWMA statistic for inspecting the small/moderate variation in running process mean very efficiently. The findings of these two sampling schemes based control charts using EEWMA statistic displayed the excellent achievement in term of very quick identification in ongoing process mean when we compared it competitor (Naveed et al., 2018). Simulation study and real life examples are also reviewed for practical implementation of proposed idea.x We also note that life data distributions are so important to judge the probability of failure of any item to be destroyed during the production process. A lot of time is consumed to test the probability of failure of any finished product. To solve this problem, the researcher used truncated life test to develop control chart for life data distribution. We designed a CC utilizing truncated life test when the life time pursues the Half Exponential Power Distribution (HEPD) based on single sampling scheme as well as re-sampling scheme. On the basis of ARLs, comparisons are made with the exponential and half normal distribution. It is demonstrated that the presented chart is more powerful in recognizing the slighter shifts in process parameters.