6.19. Samples of n = 4 items are taken from a process atregular intervals. A normally distributed quality char-acteristic is measured and ī and s values are calcu-lated for each sample. After 50 subgroups have beenanalyzed, we have5050Σ1,00 and Σ 5 72i=1(a) Compute the control limit for the i and s controlcharts.(b) Assume that all points on both charts plot withinthe control limits. What are the natural tolerancelimits of the process? (c) If the specification limits are 19 ± 4.0, what areyour conclusions regarding the ability of theprocess to produce items conforming to specifi-cations?(d) Assuming that if an item exceeds the upper spec-ification limit it can be reworked, and if it isbelow the lower specification limit it must bescrapped, what percentage scrap and rework isthe process now producing?(e) If the process were centered at u = 19.0, whatwould be the effect on percentage scrap andrework?

Answered: Image /qna-images/answer/23be8f73-7028-43a9-812b-560d26631ee6.jpg

Answered: 9. Samples of regular intervals. A…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The target fill weight for a box of cereal is 350 g. Each day a sample of 300 boxes is taken, and the number that are underweight is counted. The number of underweight boxes for each of the last 25 days is as follows: 23121919201921272623262225 303022252729353943413929 a) Compute the upper and lower 3σ limits for a p chart. b) Is the process in control? If not, when is it first detected to be out of control?
The critical value for t for n = 10 for a one tail test at α = 5% LOS is
1.9.5. Let a random variable $X$ of the continuous type have a pdf $f(x)$ whose graph is symmetric with respect to $x=c .$ If the mean value of $X$ exists, show that $E(X)=c$Hint: Show that $E(X-c)$ equals zero by writing $E(X-c)$ as the sum of two integrals: one from $-\infty$ to $c$ and the other from $c$ to $\infty .$ In the first, let $y=c-x$ and, in the second, $z=x-c .$ Finally, use the symmetry condition $f(c-y)=f(c+y)$ in the first.
Consider a birth and death process, X = {X(t)} : t ≥ 0 with the 4 states, S = {0, 1, 2, 3} and instant rates per hour are specified implicitly as follows: 1 /λk = 10 minutes for (0 ≤ k ≤ 2) and 1/ µk = 30 minutes for (1 ≤ k ≤ 3) Assume that λk = 0 for k ≥ 3 and µk = 0 for k > 3. a) Derive the limiting distribution, lim t→ ∞ P [X(t) = k] for all k b) Evaluate expectations in minutes for departure times, E [S1 |X(0) = 0] and E [S3 |X(0) = 3]
To set up a p chart to monitor a process that produces computer chips, samples of 300 chips are taken daily, and the number of defective chips in each sample is counted. The numbers of defective chips for each of the last 20 days are as follows: 1213111015 9 1 10 9 15 8 1311 9 1612192018 9 a) Compute the upper and lower 3σ limits for a p chart. b) At which sample is the process first detected to be out of control? c) Suppose that the special cause that resulted in the out-of-control condition is determined. Should this cause be remedied? Explain.
1.19 Suppose x1, . . . , xn is a sample from the process xt = µ + wt − .8wt−1,where wt ∼ wn(0, σ2w).(a) Show that mean function is E(xt) = µ.(b) Use (1.33) to calculate the standard error of ¯x for estimating µ.(c) Compare (b) to the case where xt is white noise and show that (b) issmaller. Explain the result.1.20 (a) Simulate a series of n = 500 Gaussian white noise observations as inExample 1.8 and compute the sample ACF, ρb(h), to lag 20. Compare thesample ACF you obtain to the actual ACF, ρ(h). [Recall Example 1.19.](b) Repeat part (a) using only n = 50. How does changing n affect the results?1.21 (a) Simulate a series of n = 500 moving average observations as in Example 1.9 and compute the sample ACF, ρb(h), to lag 20. Compare thesample ACF you obtain to the actual ACF, ρ(h). [Recall Example 1.20.](b) Repeat part (a) using only n = 50. How does changing n affect the results need solution for 1.21
Suppose that Z comes from standart normal disribution Given P(-k < Z < k ) =0.78 find k=?
1. Suppose that Yt follows the Moving Average process of order 1 (MA(1)) model Yt=ϵt−θϵt−1, where ϵt is i.i.d. with E(ϵt)=0 and Var(ϵt)=σϵ2 . a) Compute the mean and variance of Yt b) Compute the first two autocovariances of Yt c) Compute the first two autocorrelations of Yt
Suppose that Yt follows the Moving Average process of order 1 (MA(1)) model Yt=ϵt−θϵt−1, where ϵt is i.i.d. with E(ϵt)=0 and Var(ϵt)=σϵ2 . a) Compute the mean and variance of Yt b) Compute the first two autocovariances of Yt c) Compute the first two autocorrelations of
Refer to the accompanying data display that results from a sample of airport data speeds in Mbps. Complete parts (a) through (c) below. TInterval (13.046,22.15) x overbar equals 17.598 Sx equals 16.01712719 n equals 50 a. What is the number of degrees of freedom that should be used for finding the critical value t Subscript alpha divided by 2?
Consider a study using a between-groups design with between-groups df = 3 and within-groups df = 4. Given an F ratio of 6.8, the researcher should: a. reject the null hypothesis if alpha is .05 but fail to reject if alpha of .01 b. reject the null hypothesis if alpha is .01 but fail to reject if alpha of .05 c. reject the null for both alpha = .01 or alpha = .05 d. fail to reject the null hypothesis whether alpha is .01 or .05
Let X1,X2,... be a sequence of identically distributed random variables with E|X1|<∞ and let Yn = n−1max1≤i≤n|Xi|. Show that limnE(Yn) = 0

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