# Question

The following x and s charts based on n = 4 have shown statistical control:

(a) Estimate the process parameters µ and σ.

(b) If the specifications are at 705 ± 15, and the process output is normally distributed, estimate the fraction nonconforming.

(c) For the chart, find the probability of a type I error, assuming σ is constant. x

(d) Suppose the process mean shifts to 693 and the standard deviation simultaneously shifts to 12. Find the probability of detecting this shift on the x chart on the first subsequent sample.

(e) For the shift of part (d), find the average run length.

(a) Estimate the process parameters µ and σ.

(b) If the specifications are at 705 ± 15, and the process output is normally distributed, estimate the fraction nonconforming.

(c) For the chart, find the probability of a type I error, assuming σ is constant. x

(d) Suppose the process mean shifts to 693 and the standard deviation simultaneously shifts to 12. Find the probability of detecting this shift on the x chart on the first subsequent sample.

(e) For the shift of part (d), find the average run length.

## Answer to relevant Questions

(a) Thirty observations on the oxide thickness of individual silicon wafers are shown in table 6E.23. Use these data to set up a control chart on oxide thickness and a moving range chart. Does the process exhibit statistical ...The data shown in Table 6E.2 are x and R values for 24 samples of size n = 5 taken from a process producing bearings. The measurements are made on the inside diameter of the bearing, with only the last three decimals ...Use all 60 observations on oxide thickness. (a) Set up an individuals control chart with σ estimated by the average moving range method. (b) Set up an individuals control chart with σ estimated by the median moving range ...A financial services company monitors loan applications. Every day 50 applications are assessed for the accuracy of the information on the form. Results for 20 days are where Di is the number of loans on the ith day that re ...A process is controlled with a fraction nonconforming control chart with three-sigma limits, n = 100, UCL = 0.161, center line = 0.080, and LCL = 0. (a) Find the equivalent control chart for the number nonconforming. (b) Use ...Post your question

0