# A SkSP-R Plan under the Assumption of Gompertz Distribution
## 5 Real Life Examples
The estimated parameters \(\alpha\) and \(\theta\) values are 1.3509349 and 0.2496109, respectively, based on Data I. Suppose that a researcher likes to set the mean life \(\mu_{0}\) as 0.4 unit and termination ratio \(t_{0}/\mu_{0}=0.5\); then, based on these values, termination time \(t_{0}\) is 0.2. For the considered setup, \(\alpha=1.3509349\), \(t_{0}/\mu_{0}=0.5\), \(\beta=0.25\), and \(\alpha_{p}=0.05\); the plan parameters of suggested SkSP-R plan are \((n=28,c=5,i=2,f=0.5,k=1,m=2)\); and the process is described follows:  
1. Start normal inspection and put \(n=28\) items on test for prefixed time \(t_{0}=0.2\). Detect and count the number of sample items that failed before the experiment duration, say, \(d=3\), and \(d\leq 5\). Hence, accept the lot. 2. When \(i=2\), consecutive lots are not rejected under normal inspection based on time truncated life test; end the normal inspection and follow SI. 3. Throughout SI, test only a fraction \(f=0.5\) of lots chosen at random. SI is continued up to a point where a sampled lot is rejected. 4. After \(k=1\), where a lot is rejected, consecutively sampled lots are accepted; hence, utilize the resampling method for the immediate next lot as in Step 5. 5. In the resampling technique, perform the inspection based on a reference plan. If the lot is not rejected, then keep SI. If the lot is not accepted, resampling is formed for \(m=2\) times and the lot is rejected if it is not accepted on \((m-1)=2-1\)st resubmission. 6. If a lot is not accepted on resampling scheme, then immediately proceed to the normal inspection provided in Step 1. 7. Remove or correct all the nonconforming items found with asserting units in the rejected lots. The ASN value is 22.65489. When the quality ratio is \(\mu/\mu_{0}=3\), the probability of acceptance of the lot is 0.9882626. Data II: The data set was obtained by [33]. It consists of 63 observations the strengths of 1.5 cm glass fibers, measured by the National Physical Laboratory, England. The data include the following: 0.77, 0.81, 0.84, 0.93, 1.04, 0.55, 0.74, 1.11, 1.13, 1.24, 1.25, 1.27, 1.28, 1.29, 1.30, 1.36, 1.39, 1.42, 1.48, 1.52, 1.53, 1.54, 1.55, 1.48, 1.49, 1.49, 1.50, 1.76, 1.76, 1.77, 1.81, 1.82, 1.84, 1.50, 1.51, 1.73, 1.84, 1.89, 2.00, 1.58, 1.59, 1.60, 1.61, 1.61, 1.61, 1.68, 1.68, 1.69, 1.70, 1.70, 1.61, 1.62, 1.62, 1.63, 1.64, 1.66, 1.66, 1.66, 1.67, 2.01, and 2.24. Figure 4 illustrates the histogram density, empirical CDF and P-P plot of the GmzD for the second data set. Figure 3: Histogram density, empirical CDF and P-P plot of the GmzD for the first data set. The estimated values of parameters \(\alpha\) and \(\theta\) are 0.2741801 and 0.0024180, respectively, for the Data II. Suppose that the researcher wants to set the mean life \(\mu_{0}\) to be 1.2 unit and termination ratio \(t_{0}/\mu_{0}\) as 0.5; then, by using this information, termination time \(t_{0}\) is 0.6. For the considered setup, \(\alpha=0.2741801,t_{0}/\mu_{0}=0.5\), \(\beta=0.25,\alpha_{p}=0.05\), and the plan parameters of proposed SkSP-R plan are \((n=54,c=1,i=2,f=0.5,k=1,m=2)\); moreover, the process is as follows:  
1. Start normal inspection and put \(n=54\) items on the test for prefixed time \(t_{0}=0.6\). Detect and count the number of sample items which failed before the experiment duration, say, \(d=1\), and \(d\leq 1\). Thus, we accept the lot. 2. When \(i=2\), consecutive lots are accepted under normal inspection based on time truncated life test, and the normal inspection is discontinued. A switch to the skipping inspection is made. 3. During the skipping inspection, inspect only a fraction \(f=0.5\) of lots selected at random. The skipping inspection is continued until a sampled lot is rejected. 4. If the lot is rejected after \(k=1\), consecutively sampled lots are accepted; then, proceed to the resampling procedure for the immediate next lot as in Step 5 provided below. 5. During resampling procedure, perform the inspection using the reference plan. If the lot is accepted, then continue the skipping inspection.