Please help me :-

Refer to Exercise 1 and suppose the ten most recent values of the quality statistic are .0493, 0485, .0490, 0503, .0492, .0486, .0495, 0494, .0493, and .0488. Construct the relevant portion of the corresponding control chart, and comment on its appearance. Reference exercise 1 A control chart for thickness of rolled-steel sheets is based on an upper control limit of . 0520 in. and a lower limit of .0475 in. The first ten values of the quality statistic (in this case X. , the sample mean thickness of n = 5 sample sheets) are .0506, _0493, .0502, . 0501, .0512, .0498, 0485, .0500, 0505, and .0483. Construct the initial part of the quality control chart, and comment on its appearance.Suppose a control chart is constructed so that the probability of a point falling outside the control limits when the process is actually in control is .002. What is the probability that ten successive points (based on independently selected samples) will be within the control limits? What is the probability that 25 successive points will all lie within the control limits? What is the smallest number of successive points plotted for which the probability of observing at least one outside the control limits exceeds .10?A cork intended for use in a wine bottle is considered acceptable if its diameter is between 2.9 cm and 3.1 cm (so the lower specification limit is LSL = 2.9 and the upper specification limit is USL = 3.1 ). a. If cork diameter is a normally distributed variable with mean value 3.04 cm and standard deviation .02 cm, what is the probability that a randomly selected cork will conform to specification? b. If instead the mean value is 3.00 and the standard deviation is .05, is the probability of conforming to specification smaller or larger than it was in (a)?If a process variable is normally distributed, in the long run virtually all observed values should be between u - 30 and u + 30 , giving a process spread of 60. a. With LSL and USL denoting the lower and upper specification limits, one commonly used process capability index is u - 30 . The value Co = 1 indicates a process that is only marginally capable of meeting specifications. Ideally, C. should exceed 1.33 (a "very good" process). Calculate the value of C, for each of the cork production processes described in the previous exercise, and comment. b. The Co index described in (a) does not take into account process location. A capability measure that does involve the process mean is M + 30. Calculate the value of Cox for each of the cork-production processes described in the previous exercise, and comment. [Vote: In practice, m and s have to be estimated from process data; we show how to do this in Section 16.2] c. How do Go and Gok compare, and when are they equal?In the case of known u and o, what control limits are necessary for the probability of a single point being outside the limits for an in-control process to be .005?Consider the control chart based on control limits , + 2.81 or/v. a. What is the ARL when the process is in control? b. What is the ARL when n = 4 and the process mean has shifted to p = Up + 0? c. How do the values of parts (a) and (b) compare to the corresponding values for a 3-sigma chart?The table below gives data on moisture content for specimens of a certain type of fabric. Determine control limits for a chart with center line at height 13.00 based on o = .600, construct the control chart, and comment on its appearance. O = .600.\fRefer to Exercises 8 and 9, and now employ control limits based on using the sample ranges to estimate o. Does the process appear to be in control? Reference Exercises 8 The table below gives data on moisture content for specimens of a certain type of fabric. Determine control limits for a chart with center line at height 13.00 based on o = .600, construct the control chart, and comment on its appearance. O = .600, Reference Exercises 9 Refer to the data given in Exercise 8, and construct a control chart with an estimated center line and limits based on using the sample standard deviations to estimate o. Is there any evidence that the process is out of control?The accompanying table gives sample means and standard deviations, each based on n = 6 observations of the refractive index of fiber-optic cable. Construct a control chart, and comment on its appearance. [Hint: Xx = 2317.07 and Es = 30.34.]and Day Day 95.47 1.30 13 97.02 1.28 97.38 .88 14 95.55 1.14 HAWN- 96.85 1.43 15 96.29 1.37 96.64 1.59 16 96.80 1.40 96.87 1.52 17 96.01 1.58 96.52 1.27 18 95.39 98 96.08 1.16 19 96.58 1.21 96.48 79 20 96.43 .75 96.63 1.48 21 97.06 1.34 10 96.50 80 22 98.34 1.60 11 97.22 1.42 23 96.42 1.22 12 96.55 1.65 24 95.99 1.18 Day I Day 95.47 1.30 13 97.02 1.28 97.38 .88 14 95.55 1.14 96.85 1.43 15 96.29 1.37 96.64 1.59 16 96.80 1.40 96.87 1.52 17 96.01 1.58 96.52 1.27 18 95.39 .98 96.08 1.16 19 96.58 1.21 96.48 .79 20 96.43 75 96.63 1.48 21 97.06 1.34 10 96.50 .80 22 98.34 1.60 11 97.22 1.42 23 96.42 1.22 12 96.55 1.65 24 95.99 1.18Refer to Exorcise 11. An assignable cause was found for the unusually high sample average mirciva index on day 22.Rocompute control limits after deleting the data from this day. What do You conclude? Reference exercise 11 The accompanying table gives sample means and standard deviations, each based on n . G observations of the refractive index of fiber-optic cable. Construct a control chart, and comment on its appearance. [Him So =3170 ONE. = 3034.Jand Day F Day 95.47 1.30 13 97.02 1.28 97.38 14 05 55 1.14 96.85 1.43 96.29 1.37 96.64 1.59 96.80 96.87 1.52 17 9601 1.SH 96.52 1.27 95.39 1.16 19 96 SH 1.21 96.AH .79 96.43 .75 96.61 1.48 21 97.06 1.34 10 96.50 12 98.34 1.60 11 97.22 1.42 96.42 1.21 12 96.55 1.65 24 95.90 Day 95.47 1.30 13 97.02 1.28 97.38 14 95.55 1.14 96.85 1,43 15 96.29 1.37 96.64 1.59 In 96.80 96.87 1.52 17 96,01 1.58 96.52 1.27 95.39 96.08 1.16 19 96.5H 1.21 96 48 179 20 96,43 .75 96.63 1/48 21 97.06 1.34 10 96.50 . HO 22 98.34 1.60 11 97.22 1.42 23 90.42 1.22 12 96.55 1.65 24 95.99 1.18Consider a 3-sigma control chart with a center line at po and based on n = 5. Assuming normality, calculate the probability that a single point will fall outside the control limits when the actual process mean isApply the supplemental rules suggested in the text to the data of Exercise 8. Are there any out- of-control signals? Reference exercise 8 The table below gives data on moisture content for specimens of a certain type of fabric. Determine control limits for a chart with center line at height 13.00 based on o = .600, construct the control chart, and comment on its appearance. OF = .600.Calculate control limits for the data of Exercise 8 using the robust procedure presented in this section. Reference exercise 8 The table below gives data on moisture content for specimens of a certain type of fabric. Determine control limits for a chart with center line at height 13.00 based on o = .600, construct the control chart, and comment on its appearance. D = .600.A manufacturer of dustless chalk instituted a quality control program to monitor chalk density. The sample standard deviations of densities for 24 different subgroups, each consisting n = 8 of chalk specimens, were as follows: 204 .315 .096 .184 230 .212 .322 .287 145 .211 .053 .145 .272 .351 .159 .214 .388 .187 .150 .229 .276 .118 .091 -056 Calculate limits for an S chart, construct the chart, and check for out-of-control points. If there is an out-of-control point, delete it and repeat the processSubgroups of power supply units are selected once each hour from an assembly line, and the high-voltage output of each unit is determined. a. Suppose the sum of the resulting sample ranges for 30 subgroups, each consisting of four units, is 85.2. Calculate control limits for an R chart b. Repeat part (a) if each subgroup consists of eight units and the sum is 106.2.The following data on the deviation from target in the parallel orientation is taken from Table 1 of the article cited in Example 16.5. Sometimes a transformation of the data is appropriate, either because of nonnormality or because subgroup variation changes systematically with the subgroup mean. The authors of the cited article suggested a square root transformation for this data (the family of Box-Cox transformations is y = x, so A = .5 here; Minitab will identify the best value of A). Transform the data as suggested, calculate control limits for y = 14, so A = .5 , R, and S charts, and check for the presence of any out-of-control signals. X, R, and S charts,Calculate control limits for an $ chart from the refractive index data of Exercise 11. Does the process appear to be in control with respect to variability? Why or why not? Reference exercise 11 The accompanying table gives sample means and standard deviations, each based on n = 6 observations of the refractive index of fiber-optic cable. Construct a control chart, and comment on its appearance. [Mine, Ex, = 2317.07 and Ss; = 30.34.]and Day Day 95.47 1.30 13 97.02 1.28 97.38 88 14 95.55 1.14 96.85 1.43 15 96.29 1.37 NOUAWNE 96.64 1.59 16 96.80 1.40 96.87 1.52 17 96.01 1.58 96.52 1.27 18 95.39 .98 96.08 1.16 19 96.58 1.21 96.48 .79 20 96.43 .75 96.63 1.48 21 97.06 1.34 10 96.50 .80 22 98.34 1.60 11 97.22 1.42 23 96.42 1.22 12 96.55 1.65 24 95.99 1.18 Day Day 95.47 1.30 13 97.02 1.28 97.38 .88 14 95.55 1.14 96.85 1.43 15 96.29 1.37 96.64 1.59 16 96.80 1.40 96.87 1.52 17 96.01 1.58 96.52 1.27 18 95.39 98 96.08 1.16 19 96.58 1.21 96.48 .79 20 96.43 .75 96.63 1.48 21 97.06 1.34 10 96.50 .80 22 98.34 1.60 11 97.22 1.42 23 96.42 1.22 12 96.55 1.65 24 95.99 1.18When S" is the sample variance of a normal random sample, $ has a chi-squared distribution with n - 1 di, so (# - 1)572 This suggests that an alternative chart for controlling process variation involves plotting the sample variances and using the control limits XML = 998 from which Xmeg Xmal =.998 A - I 1 - 1 Construct the corresponding chart for the data of Exercise 11. [Hint: The lower- and upper-tailed chi-squared critical values for 5 of are .210 and 20.515, respectively.] Reference exercise 11 The accompanying table gives sample means and standard deviations, each based on n = 6 observations of the refractive index of fiber-optic cable. Construct a control chart, and comment on its appearance. [Hint: Ex, = 2317.07 and Es, = 30.34.]and Day Day 95.47 1.30 13 97.02 1.28 97.38 88 14 WN 95.55 1.14 96.85 1.43 15 96.29 1.37 96.64 1.59 16 96.80 1.40 96.87 1.52 17 96.01 1.58 96.52 1.27 18 95.39 98 96.08 1.16 19 96.58 1.21 96.48 .79 20 96.43 .75 96.63 1.48 21 97.06 1.34 10 96.50 .80 22 98.34 1.60 11 97.22 1.42 23 96.42 1.22 12 96.55 1.65 24 95.99 1.18 Day Day 95.47 1.30 13 97.02 1.28 97.38 88 14 95.55 1.14 96.85 1.43 15 96.29 1.37 GUAWN- 96.64 1.59 16 96.80 1.40 96.87 1.52 17 96.01 1.58 96.52 1.27 18 95.39 .98 96.08 1.16 19 96.58 1.21 96.48 .79 20 96.43 75 96.63 1.48 21 97.06 1.34 10 96.50 .80 22 98.34 1.60 11 97.22 1.42 23 96.42 1.22 12 96.55 1.65 24 95.99 1.18