7. PCDrives has a statistically in-control manufacturing process that is normally distributed. Samplemeans and ranges for 15 samples of size 5 can be found in the Problems Data workbook. Determineprocess capability indexes by estimating the standard deviation using formula (8.34). If thespecifications are 70 ± 25, what percentage will be out of specification? PCDrives             Sample x-bar    R   1 77.4 18.3   2 60.2 20.1   3 63.5 22.6   4 64.0 27.5   5 58.4 15.3   6 74.4 17.9   7 70.8 26.8   8 74.6 30.6   9 77.3 19.2   10 65.7 14.6   11 63.4 24.5   12 76.6 21.7   13 71.7 25.5   14 70.9 29.7   15 59.6 14.5

A shirt manufacturer buys cloth by the 100-yard roll from a supplier. For setting up a control chart to manage the irregularities (e.g., loose threads and tears), the following data were collected from a sample provided by the supplier. SAMPLE 1 2 3 4 5 6 7 8 9 10 IRREGULARITIES 3 5 2 6 5 4 6 3 4 5 Determine the c¯�¯ , Sc�� , UCL and LCL for a c-chart with z = 2. Note: Round your answers to 2 decimal places.   Suppose the next five rolls from the supplier had three, two, five, three, and seven irregularities. Is the supplier process under control? multiple choice Yes No

A shirt manufacturer buys cloth by the roll from a supplier. For setting up a control chart to manage the irregularities (e.g., loose threads and tears), the following data were collected from a sample provided by the supplier.   Sample Irregularities 1 2 2 1 3 4 4 2 5 0 6 4 7 3 8 0 9 2 10 1 Total 19   Calculate the LCL and UCL for a c-chart with z=2 LCL= 0, UCL = 4.66 LCL= 0, UCL = 3.28 LCL= -0.86, UCL = 3.28 LCL= -0.86, UCL = 3.51 LCL= -0.86, UCL = 4.66

Control charts for X-bar and S are maintained for the fill volume of protein shake drink. The specifications are 330 + 10 mL. After 40 samples of size n=7 are analyzed, we find that: 40 40 = 13,200 Si = 296 i=1 i=D1 Find the best estimate of the process standard deviation. 7.498 7.400 7.570 2.737 7.713 8.032

2) The specification for a Lindemann’s stainless steel chimney liner requires a thickness of 7.1 mm ± 0.1 mm. The firm’s quality analyst determines that the liner process operates at a mean thickness of 7.13 mm with the standard deviation of the process being 0.02 mm.   a) Calculate the upper and the lower limits for the stainless steel chimney liner. b) Calculate the Cpand Cpkfor this process.   Hint: Cp = (Upper Specification Limit – Lower Specification Limit)/6sigma Cpk = minimum of [(Upper Specification Limit – Xbar)/3sigma], [(Xbar – Lower Specification Limit)/3sigma]

A shirt manufacturer buys clothes by the 100-yard roll from a supplier. For setting a control chart to manage the irregularities (e.g., loose threads and tears), the following data were collected from a sample provided by the supplier.   Sample 1 2 3 4 5 6 7 8 9 10 Irregularities 3 5 2 6 5 4 6 3 4 5   Which type of control chart should be used? Construct a control chart with two-sigma control limits. Suppose the next five rolls from the supplier had three, two, five, three, and seven irregularities. Is the supplier process under control? Explain and show work

A microbrewery tracks its output in gallons over a five hour period for each of seven days. Their data is in the table below, and they went ahead and calculated the averages and ranges for the individual samples and the overall averages Their data and the factors tables can be found below. Calculate the upper (LCL) and lower (UCL) control limits for X bar, and R charts for their process. Day (X values) X̅   R 1 46 49 45 47 48 47.0   4 2 43 52 46 52 44 47.4   9 3 45 55 46 51 43 48.0   12 4 39 44 42 43 40 41.6   5 5 45 50 48 50 42 47.0   8 6 44 48 45 45 40 44.4   8 7 41 44 52 50 47 46.8   11           X̿ = 46.03 R̅ 8.14     Xbar chart - LCL = 40.48, UCL=46.25, R chart LCL=0, UCL=14.01 Xbar chart - LCL = 44.21, UCL=48.41, R chart LCL=0.49, UCL=17.18 Xbar chart - LCL = 42.61, UCL=49.45, R chart LCL=0.65, UCL=15.63 Xbar chart - LCL = 44.21, UCL=51.62, R chart LCL=0, UCL=17.18 Xbar chart - LCL = 41.31, UCL=50.75, R chart LCL=0, UCL=17.18

Hermitage DNA Labs, LLC collected temperature readings in an analysis process. The data can be found in the Problems Data Compute the mean and range of each sample and calculate control limits for x-bar and R charts using the appropriate From the charts constructed, does the process appear to be in statistical control?

Refer to Table 56.1-Factors for Computing Control Chart Limits.(3.sigma) for this problem. Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: a) What is the value of x? mm (round your response to two decimal places). b) What is the value of R? R=mm (round your response to two decimal places). c) What are the UCL, and LCL; using 3-sigma? Day 1 2 3 4 5 Upper Control Limit (UCL;)mm (round your response to two decimal places) Lower Control Limit (LCL;)mm (round your response to two decimal places). d) What are the UCL and LCL using 3-sigma? Upper Control Limit (UCLR)-mm (round your response to two decimal places). Lower Control Limit (LCL)-mm (round your response to two decimal places) Mean x (mm) 154.9 151.2 155.6 155.5 154.6 Range R (mm) 4.4 4.8 4.3 5.0 4.7 Next

Suppose that a quality characteristic is normally distributed with specifications at 100 ± 20. The process standard deviation is 6.(a) Suppose that the process mean is 100. What are the natural tolerance limits? Calculate Cp and Cpk and interpret these ratios. What fraction of parts do you expect to be defective?(b) Suppose that the process mean is 106. What are the natural tolerance limits? What is thefraction defective? Calculate Cp and Cpk and interpret these ratios.