00181 ðd17515ad1b09ad29b923c2e3121477

182

McWilliams

considered before implementing any economic control chart plan based on the usual unconstrained approach.

Appendix A: Symbols Used in the Model

Input Yariables

X = exponential parameter (Mean = 1/X)

A = number of standard deviations slip when out of control PO, pi = proportion of nonconforming items produced when in and out of control

E = time to sample and chart one item To = expected search time when false alarm Ti = expected time to discover the assignable cause T2 = expected time to repair the process 5i = 1 if production continues during searches; 0 otherwise Â§2 = 1 if production continues during repair; 0 otherwise Co = Ä…uality cost/hour while producing in control Cl = Ä…uality cost/hour while producing out of control (> Co)

Y = cost per false alarm W = cost to locate and repair the assignable cause a = fixed cost per sample b = cost per unit sampled Tmax ⁼ specified maximum value of Pq 95

r, 0 = parameters for Erlang distribution of S3 (r/0 = Ti + T2)

Outnut and Calculated Yariables C = expected cost per hour n, n* = sample size and its optimal value h, h* = time between samples (hours) and its optimal value L, L* = control limit (in standard deviation units) and its optimal value

R, R*

x

s

ARL1

rejection value for sampling by attributes and its optimal value expected time of occurrence of the assignable cause, within a sampling interval

(1 - (1 + Xh)e-^Xh]/mi - e“^Xh)]

expected number of samples taken while the process is in control e“^^h/(l - e“^xh)

average run length while in control