A Control Chart for Gamma Distributed Variables Using Repetitive Sampling Scheme

Abstract

In this manuscript, a control chart is designed when the quality characteristic of interest follows a gamma distribution using repetitive sampling. The Wilson-Hilferty approximation is used to transform the gamma distributed characteristic to a normal random variable. Two pairs of control limits are established and their control constants are determined by considering the specified in-control average run length (ARL). The out-of-control ARL is derived when the process is shifted in terms of the scale parameter of the Gamma distribution. The ARLs are presented for various values of the shape parameter according to process shift parameters. A simulated example is given to illustrate the proposed control chart.

Design of a t‐chart using generalized multiple dependent state sampling

“…Under a fixed ARL 0 , the chart having the smaller ARL 1 s is considered to be superior in detecting process shifts. Many authors discussed ARL as a performance metric for the detection of process shift for a specific magnitude. To measure the overall effectiveness of the proposed control chart, extra quadratic loss (EQL) is used.…”

“…Average run length (ARL) is used to evaluate the performance of any control chart scheme . The ARL measure for the chart performance is studied by many authors including . The MDS sampling scheme has been utilized in the SPC by many authors including Ahmad et al, Aslam et al, Azam et al, Khan et al, and Knoth …”

Process Monitoring for Gamma Distributed Product under Neutrosophic Statistics Using Resampling Scheme

“…Another reason in which the normal distribution is inappropriate is the size of the collected data, particularly the single size data. However, these situations are handled by using the gamma distribution as an excellent substitute for the normal distribution in the study carried out by Khan et al [26] and Saghir et al [11]. In general, the gamma distribution is very common in modeling the waiting time of the events or modeling the failure time of the systems or the processes of Aksoy [27] and Saghir et al [10].…”

“…Recently, Aslam et al [52] designed the control chart for the gamma distribution using the indeterminate environment. More information regarding the control charts can be found in the study carried out by Intaramo and Pongpullponsak [53], Charongrattanasakul and Pongpullponsak [54], Panthong and Pongpullponsak [55], Aslam et al [29], Aslam et al [56], Fernández [57], Khan et al [26], Aslam et al [58], and Mashuri and Ahsan [59].…”

Design of a Control Chart for Gamma Distributed Variables Under the Indeterminate Environment

“…Reference [11] studied the control chart for this distribution using a narrow confidence interval method. References [12] and [13] designed a chart for the gamma distribution under resampling approaches.…”