Control Charts Based on the Exponential Distribution: Adapting Runs Rules for thetChart

A Control Chart for Gamma Distributed Variables Using Repetitive Sampling Scheme

“…We see from the Table 4 that the proposed control provides the smaller values of for various values as compared to existing control chart. For example, when = 370 and = 1.1, the proposed control provides =216, while it is 244 from the chart by proposed by Santiago and Smith (2013). So, the proposed control chart performs better than control charts proposed by Santiago and Smith (2013) in terms of detecting early shift in the manufacturing process.…”

“…For example, when = 370 and = 1.1, the proposed control provides =216, while it is 244 from the chart by proposed by Santiago and Smith (2013). So, the proposed control chart performs better than control charts proposed by Santiago and Smith (2013) in terms of detecting early shift in the manufacturing process. The efficiency of proposed chart is also compared with existing control chart for the gamma distribution.…”

“…In this section, the performance of the proposed control chart is compared with t-chart by Santiago and Smith (2013) for the exponential distribution because gamma distribution reduces to the exponential distribution when = 1. In Table 4 we compare the performance of two control chart for the same values of shifts and other specified parameters in terms of ARLs values.…”

“…The proposed chart reduces to the chart by Santiago and Smith (2013) when and . It is assumed here that the control limits have the following forms and that they are constructed from the data when the process is in control.…”

“…Recently, Santiago and Smith (2013) proposed the control chart called a t-chart when the time between events follows the exponential distribution. They used the variable transformation proposed by Nelson (1994) to transform the exponential distributed data to an approximate normal data.…”