weibulltools (version 2.0.0)

mcs_delay: Adjustment of Operating Times by Delays using a Monte Carlo Approach

Description

In general, the amount of available information about units in the field is very different. During the warranty period, there are only a few cases with complete data (mainly failed units) but lots of cases with incomplete data (usually censored units). As a result, the operating time of units with incomplete information is often inaccurate and must be adjusted by delays.

This function reduces the operating times of incomplete observations by simulated delays (in days). A unit is considered as incomplete if the later of the two dates is unknown, i.e. date_2 = NA. See 'Details' for some practical examples.

Random delay numbers are drawn from the distribution determined by complete cases (described in 'Details' of dist_delay).

Usage

mcs_delay(
  date_1,
  date_2,
  time,
  status = NULL,
  id = paste0("ID", seq_len(length(time))),
  distribution = c("lognormal", "exponential")
)

Value

A list containing the following elements:

• data : A tibble with classes wt_mcs_data and wt_reliability_data if status is provided. Since the class wt_reliability_data enables the direct usage of data inside estimate_cdf.wt_reliability_data, the required lifetime characteristic is automatically set to the operating time time.

  If status = NULL class is wt_mcs_data, which is not supported by estimate_cdf due to missing status.

  The tibble contains the following columns:

  • date_1 : Earlier dates. If argument date_1 is a list of length i, i > 1 (described in Arguments) multiple columns with names date_1.1, date_1.2, ..., date_1.i and the corresponding values of the earlier dates are used.

  • date_2 : Later dates. In the case of a list with length greater than 1, the routine described above is used.

  • time : Adjusted operating times for incomplete observations and input operating times for the complete observations.

  • status (optional) :

    • If argument status = NULL column status does not exist.

    • If argument status is provided the column contains the entered binary data (0 or 1).

  • id : Identification of every unit.

• sim_data : A tibble with column sim_delay that holds the simulated delay-specific numbers for incomplete cases and 0 for complete cases. If more than one delay was considered multiple columns sim_delay.1, sim_delay.2, ..., sim_delay.i with corresponding delay-specific random numbers are presented.

• model_estimation : A list containing a named list ("delay_distribution") with output of dist_delay. For multiple delays the list contains as many lists as there are delays, i.e. ("delay_distribution.1", "delay_distribution.2", ..., "delay_distribution.i").

Arguments

date_1

A vector of class character or Date, in the format "yyyy-mm-dd", indicating the earlier of the two dates. Use NA for missing elements.

If more than one delay should be considered it must be a list where the first element contains the earlier dates of the first delay and the second element contains the earlier dates of the second delay, and so forth.(See 'Examples').

date_2

A vector of class character or Date, in the format "yyyy-mm-dd", indicating the later of the two dates. Use NA for missing elements.

If more than one delay should be considered it must be a list where the first element contains the later dates of the first delay and the second element contains the later dates of the second delay, and so forth. (See 'Examples').

time

A numeric vector of operating times. Use NA for missing elements.

status

Optional argument. If used it has to be a vector of binary data (0 or 1) indicating whether unit i is a right censored observation (= 0) or a failure (= 1). The effect of status on the return is described in 'Value'.

id

A vector for the identification of every unit.

distribution

Supposed distribution of the delay random variable. If more than one delay is to be considered and different distributions are assumed for each delay, the argument distribution must have the same length as list date_1 (and date_2). For example, in the case of two delays with different distributions, one has to specify the argument as distribution = c("lognormal", "exponential"). Then the lognormal distribution is applied to the first delay and the exponential distribution to the second (See 'Examples').

Details

In field data analysis time-dependent characteristics (e.g. time in service) are often imprecisely recorded. These inaccuracies are caused by unconsidered delays.

For a better understanding of the MCS application in the context of field data, two cases are described below.

• Delay in registration: It is common that a supplier, which provides parts to the manufacturing industry does not know when the unit, in which its parts are installed, were put in service (due to unknown date_2, i.e. registration or sales date). Without taking the described delay into account, the time in service of the failed units would be the difference between the repair date and date_1 (i.e. the production date) and for intact units the difference between the present date and date_1. But the real operating times are (much) shorter, since the stress on the components have not started until the whole systems were put in service. Hence, units with incomplete data (missing date_2) must be reduced by the delays.

• Delay in report: Authorized repairers often do not immediately notify the manufacturer or OEM of repairs that were made during the warranty period, but instead pass the information about these repairs in collected forms e.g. weekly, monthly or quarterly. The resulting time difference between the reporting (date_2) of the repair in the guarantee database and the actual repair date (date_1), which is often assumed to be the failure date, is called the reporting delay. For a given date where the analysis is made there could be units which had a failure but are not registered and therefore treated as censored units. In order to take this case into account and according to the principle of equal opportunities, the lifetime of units with no report date (date_2 = NA) is reduced by simulated reporting delays.

References

Verband der Automobilindustrie e.V. (VDA); Qualitätsmanagement in der Automobilindustrie. Zuverlässigkeitssicherung bei Automobilherstellern und Lieferanten. Zuverlässigkeits-Methoden und -Hilfsmittel.; 4th Edition, 2016, <ISSN:0943-9412>

See Also

estimate_cdf

Examples

# Data for examples:
date_of_production   <- c("2014-07-28", "2014-02-17", "2014-07-14",
                          "2014-06-26", "2014-03-10", "2014-05-14",
                          "2014-05-06", "2014-03-07", "2014-03-09",
                          "2014-04-13", "2014-05-20", "2014-07-07",
                          "2014-01-27", "2014-01-30", "2014-03-17",
                          "2014-02-09", "2014-04-14", "2014-04-20",
                          "2014-03-13", "2014-02-23", "2014-04-03",
                          "2014-01-08", "2014-01-08")

date_of_registration <- c(NA, "2014-03-29", "2014-12-06", "2014-09-09",
                          NA, NA, "2014-06-16", NA, "2014-05-23",
                          "2014-05-09", "2014-05-31", NA, "2014-04-13",
                          NA, NA, "2014-03-12", NA, "2014-06-02",
                          NA, "2014-03-21", "2014-06-19", NA, NA)

date_of_repair <-       c(NA, "2014-09-15", "2015-07-04", "2015-04-10", NA,
                          NA, "2015-04-24", NA, "2015-04-25", "2015-04-24",
                          "2015-06-12", NA, "2015-05-04", NA, NA,
                          "2015-05-22", NA, "2015-09-17", NA, "2015-08-15",
                          "2015-11-26", NA, NA)

date_of_report <-       c(NA, "2014-10-09", "2015-08-28", "2015-04-15", NA,
                          NA, "2015-05-16", NA, "2015-05-28", "2015-05-15",
                          "2015-07-11", NA, "2015-08-14", NA, NA,
                          "2015-06-05", NA, "2015-10-17", NA, "2015-08-21",
                          "2015-12-02", NA, NA)

time_in_service <- rep(1000, length(date_of_production))
status <- c(0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0)

# Example 1 - MCS for delay in registration:
mcs_regist <- mcs_delay(
  date_1 = date_of_production,
  date_2 = date_of_registration,
  time = time_in_service,
  status = status,
  distribution = "lognormal"
)

# Example 2 - MCS for delay in report:
mcs_report <- mcs_delay(
  date_1 = date_of_repair,
  date_2 = date_of_report,
  time = time_in_service,
  status = status,
  distribution = "exponential"
)

# Example 3 - Reproducibility of random numbers:
set.seed(1234)
mcs_report_reproduce <- mcs_delay(
  date_1 = date_of_repair,
  date_2 = date_of_report,
  time = time_in_service,
  status = status,
  distribution = "exponential"
)

# Example 4 - MCS for delays in registration and report with same distribution:
mcs_delays <- mcs_delay(
  date_1 = list(date_of_production, date_of_repair),
  date_2 = list(date_of_registration, date_of_report),
  time = time_in_service,
  status = status,
  distribution = "lognormal"
)

# Example 5 - MCS for delays in registration and report with different distributions:
## Assuming lognormal registration and exponential reporting delays.
mcs_delays_2 <- mcs_delay(
  date_1 = list(date_of_production, date_of_repair),
  date_2 = list(date_of_registration, date_of_report),
  time = time_in_service,
  status = status,
  distribution = c("lognormal", "exponential")
)