Question

Problem 2 Using the provided data, and assuming the target mean is μ0-10 and 5-0.8 answer the following: a) UsingA0. and L-3, please construct an EWMA chart, also please indicate at which sample the out-of-control condition is detected. b) What are the steady state values of control limits for the EWMA chart in part (a)? Please show your calculation.

Answer 1

a)

x<-c(500, 500,255,106,88.8, 35.9, 31.3,17.5,15.9, 10.3,6.53,6.09, 4.36,3.63,2.87,1.93) > > library (qcc) > q<-ewma (x, lambda-0.1, nsigmas-3 , mu- 10, std.dev-o.e) summary (q) Call: ewma (data x, std.dev -0.8, lambda 0.1, nsigmas3, mu 10) ewma chart for x Summary of group statistics: Min. 1st u Median Mean 3rd Qu.Max. 1.9300 5.6575 16.7000 99.1319 93.1000 500.0000 Group sample size: 1 Number of groups: 16 Center of group statistics: 99.13187 Standard deviation: 0.8 Smoothing parameter: 0.1 Control limits: LCL [1,] [2,] 98.89187 99.37187 98.80899 99.45476 [16,1 98.59081 99.67294

b)

Steady State Upper Control Limit (2-2) Lower Control Limit (2-2) Given: CALCULATION: UCL 10+3(0.8[vo.1/2-0.1) = 10+2.4(0.2294) 10+0.5506 UCL-10.5506 LCL 10-3(0.8)1[v0.1/(2-0.1)] -10-24(0.2294) = 104.5506 LCL 9.4494