A control chart for the generalized exponential distribution under time truncated life test
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ORIGINAL RESEARCH
A control chart for the generalized exponential distribution under time truncated life test Olatunde Adebayo Adeoti1 · Precious Ogundipe1 Received: 7 April 2020 / Accepted: 27 August 2020 © Society for Reliability and Safety (SRESA) 2020
Abstract 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. Keyword Attribute control chart · Truncated life test · Generalized exponential distribution · Average run length
1 Introduction A control chart is a graphical representation of the collected information, which contains three horizontal lines, also known as control limits. The central line (CL) is the average value for the process, while the upper and lower control limits (UCL and LCL) are obtained in such a way that almost all of the data points fall within these limits, which indicate that the process is in a state of control (Rao 2018). If any of the data points falls outside the limits, it is an indication that the process is out of control. The control limits on the control chart are so placed as to disclose the presence or absence of the assignable causes of quality variation and if out of control, the sample point(s) must be detected and quickly eliminated for the process to remain in a state of statistical control. The control chart was first introduced by Walter Shewhart in the 1920s for efficient monitoring of the process in the Bell laboratories. Control charts are considered essential tools for monitoring the manufacturing process and * Olatunde Adebayo Adeoti [email protected]; [email protected] Precious Ogundipe [email protected] 1
Department of Statistics, Federal University of Technology, Akure 340001, Ondo state, Nigeria
attain high quality of the manufactured products. These tools help to facilitate the monitoring and maintenance of processes such that the product meets the given specifications set by the organization (Rao 2019). Control charts are widely used in both manufacturing and non-manufacturing process environments (see de Vries and Conlin 2003; Woodall 2006; Hwang et al. 2008). The control charts are divided into attribute control charts and variable control charts. An attribute
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