Description Usage Arguments Details Value References See Also Examples

Calculate the optimum parameters, n(sample size), h(sampling interval), w(weight to the present sample) and k(number of s.d. from control limits to center line) for economic Design of the EWMA control chart .

1 2 3 4 5 6 7 8 9 10 11 | ```
ecoEwma(h, w, k, n, delta = 2, lambda = 0.05, P0 = NULL,
P1 = NULL, C0 = NULL, C1 = NULL, Cr = 25, Cf = 10,
T0 = 0.0167, Tc = 1, Tf = 0, Tr = 0, a = 1, b = 0.1,
d1 = 1, d2 = 1, nlevels = 30, sided = "two",
par = NULL, contour.plot = FALSE, call.print = TRUE,
...)
echEwma(h, w, k, n, delta = 2, lambda = 0.05, P0 = NULL,
P1 = NULL, C0 = NULL, C1 = NULL, Cr = 25, Cf = 10,
T0 = 0.0167, Tc = 1, Tf = 0, Tr = 0, a = 1, b = 0.1,
d1 = 1, d2 = 1, sided = "two")
``` |

`h` |
sampling interval. It can be a numeric vector or left undefined. See 'Details' |

`w` |
the weight value between 0 and 1 given to the latest sample. It must be specified. |

`k` |
control limit coefficient. It can be a numeric vector or left undefined. See 'Details' |

`n` |
sample size. It can be an integer vector or left undefined. See 'Details' |

`delta` |
shift in process mean in standard deviation units when assignable cause occurs (delta = |mu1 - mu0|/sigma), where sigma is the standard deviation of observations; mu0 is the in-control process mean; mu1 is the out-of-control process mean. Default value is 2. |

`lambda` |
we assume the in-control time follows a exponential distribution with mean 1/lambda. Default value is 0.05. |

`P0` |
profit per hour earned by the process operating in control. See 'Details'. |

`P1` |
profit per hour earned by the process operating out of control |

`C0` |
cost per hour due to nonconformities produced while the process is in control. |

`C1` |
cost per hour due to nonconformities produced while the process is out of control.(C1 > C0) |

`Cr` |
cost for searching and repairing the assignable cause, including any downtime. |

`Cf` |
cost per false alarm, including the cost of searching for the cause and the cost of downtime if production ceases during search. |

`T0` |
time to sample and chart one item. |

`Tc` |
expected time to discover the assignable cause. |

`Tf` |
expected search time when false alarm occurs. |

`Tr` |
expected time to repair the process. |

`a` |
fixed cost per sample. |

`b` |
cost per unit sampled. |

`d1` |
flag for whether production continues during searches (1-yes, 0-no). Default value is 1. |

`d2` |
flag for whether production continues during repairs (1-yes, 0-no). Default value is 1. |

`nlevels` |
number of contour levels desired. Default
value is 30. It works only when |

`sided` |
distinguish between one- and two-sided EWMA
control chart by choosing "one" and "two", respectively.
See details in |

`par` |
initial values for the parameters to be optimized over. It can be a vector of length 2 or 3. See 'Details' |

`contour.plot` |
a logical value indicating whether a contour plot should be drawn. Default is FALSE. |

`call.print` |
a logical value indicating whether the "call" should be printed on the contour plot. Default is TRUE |

`...` |
other arguments to be passed to contour function. |

Parameter `w`

should always be given, because the
range of `w`

is so restricted that optimization
algorithms usually don't converge.

When parameter `par`

is specified, optimization
algorithms would be used as default. `par`

can be
specified as: `par = c(h, k)`

where `h`

and
`k`

are the initial values of smapling interval and
control limit when `n`

is specified; or ```
par =
c(h, k, n)
```

. Good inital values may lead to good optimum
results.

When parameters `h`

, `k`

, `n`

are all
undefined, `ecoEwma`

function will try to find the
global optimum point to minimize the ECH (Expected Cost
per Hour) using optimization algorithms (`optim`

function), but in this case `n`

would not be
integer. It is usually helpful for the experimenter to
find the region where the optimum point may exist
quickly. When `h`

and `k`

are undefined but
`n`

is given as an integer vector, `ecoEwma`

function will try to find the optimum point for each
`n`

value using optimization algorithms. When
`h`

, `k`

and `n`

are all given,
`ecoEwma`

function will use a "grid method" way to
calculate the optimum point, that is ECH for all the
combinations of the parameters will be calculated. The
"grid method" way is much slower than using optimization
algorithms, but it would be a good choice when
optimization algorithms fail to work well.

For cost parameters either P0, P1 or C0, C1 is
needed. If P0 and P1 are given, they will be used first,
else C0 and C1 will be used. For economic design of the
EWMA chart, when `d1`

and `d2`

are both 1, only
if the difference between P0 and P1 keeps the same, the
results are identical. If the difference between C0 and
C1 keeps the same, the optimum parameters are almost the
same but the ECH(Expected Cost per Hour) values will
change.

`echEwma`

is used to calculate the ECH (Expected
Cost per Hour) for one given design point.

The `ecoEwma`

function returns an object of class
"edcc", which is a list of elements `optimum`

,
`cost.frame`

, `FAR`

and `ATS`

.
`optimum`

is a vector with the optimum parameters
and the corresponding ECH value; `cost.frame`

is a
dataframe with the optimum parameters and the
corresponding ECH values for all given `n`

(if
`n`

is not specified, `cost.frame`

won't be
returned); `FAR`

indicates the false alarm rate
during the in-control time, which is calculated as
lambda*(average number of false alarm); `ATS`

indicates the average time to signal after the occurrence
of an assignable cause, calculated as h*ARL2 - tau, where
tau is the expected time of occurrence of the assignable
cause given it occurs between the i-th and (i+1)st
samples. The `echEwma`

function returns the
calculated ECH value only.

Weicheng Zhu, Changsoon Park (2013), edcc: An R Package
for the Economic Design of the Control Chart.
*Journal of Statistical Software*, 52(9), 1-24.
http://www.jstatsoft.org/v52/i09/

Lorenzen and Vance (1986). The economic design of control
charts: a unified approach, *Technometrics*, 28.
3-10.

`ecoXbar`

, `ecoCusum`

,
`xewma.arl`

, `update.edcc`

,
`optim`

,`contour`

1 2 3 4 5 6 7 8 9 | ```
#Douglas (2009). Statistical quality control: a modern introduction, sixth edition, p470.
## Set w from 0.1 to 1 by 0.1 to catch the trend.
ecoEwma(w=seq(0.1,1,by=0.1),P0=110,P1=10,Cf=50)
#yy = ecoEwma(h = seq(.7,1,by=.01), w = seq(0.8,1,by=.01),k = seq(2.9,3.3, by = 0.01), n = 4:5, P0 = 110, P1 = 10, Cf = 50, contour.plot = TRUE)
##$optimum
##Optimum h Optimum k Optimum n Optimum w ECH
## 0.81000 2.99000 5.00000 0.95000 10.36482
#contour(yy)
``` |

```
Loading required package: spc
$optimum
Optimum h Optimum k Optimum n Optimum w ECH
0.8282283 3.0311392 5.3426142 1.0000000 10.3603658
$cost.frame
Optimum h Optimum k Optimum n Optimum w ECH
1.0425911 2.017433 9.573487 0.1 11.62842
0.9416400 2.509054 8.106431 0.2 11.11996
0.8936145 2.728392 7.085852 0.3 10.83632
0.8657535 2.850289 6.418526 0.4 10.66056
0.8483392 2.925022 5.970261 0.5 10.54421
0.8372298 2.972906 5.667958 0.6 10.46501
0.8303430 3.003967 5.470132 0.7 10.41171
0.8267789 3.022460 5.357692 0.8 10.37827
0.8260608 3.031458 5.315691 0.9 10.36159
0.8282283 3.031139 5.342614 1.0 10.36037
$FAR
[1] 0.002881128
$ATS
[1] 0.465852
```

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