Launch the Reliability Growth Platform

Launch the Reliability Growth platform by selecting Analyze > Reliability and Survival > Reliability Growth. The launch window, using data from TurbineEngineDesign1.jmp, is shown in Reliability Growth Launch Window.

Reliability Growth Launch Window

The launch window includes a tab for each of two data formats: Time to Event Format and Dates Format.

•	Time to Event Format assumes that time is recorded as the number of time units; for example, days or hours, since initial start-up of the system. The test start time is assumed to be time zero. On the Time to Event Format tab, the time column or columns are given the Time to Event role.

•	Dates Format assumes that time is recorded in a date/time format, indicating an absolute date or time. On the Dates Format tab, the time column or columns are given the Timestamp role.

Rows with missing data in the columns Time to Event, Timestamp, or Event Count are included in the analysis.

Note: Both data formats require times or time intervals to be in non-decreasing order.

Time to Event

Time to Event is the number of time units that elapse between the start of the test and the occurrence of an event (a failure or test termination). The test start time is assumed to be time zero. Note that the Time to Event role is available only on the Time to Event Format tab.

Two conventions are allowed (see Exact Failure Times versus Interval Censoring for more information):

•	A single column can be entered. In this case, it is assumed that the column gives the exact elapsed times at which events occurred.

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Two columns can be entered, giving interval start and end times. If an interval’s start and end times differ, it is assumed that the corresponding events given in the Event Count column occurred at some unknown time within that interval. We say that the data are interval-censored. If the interval start and end times are identical, it is assumed that the corresponding events occurred at that specific time point, so that the times are exact (not censored).

The platform requires that the time columns be sorted in non-decreasing order. When two columns giving interval start and end times are provided, these intervals must not overlap (except at their endpoints). Intervals with zero event counts that fall strictly within a phase can be omitted, as they do not affect the likelihood function.

Timestamp

Timestamp is an absolute time; for example, a date. As with Time to Event, Timestamp allows times to be entered using either a single column or two columns. Note that the Timestamp role is available only on the Dates Format tab.

For times entered as Timestamp, the first row of the table is considered to give the test start time:

•	When a single column is entered, the timestamp corresponding to the test start, with an event count of 0, should appear in the first row.

•	When two columns, giving time intervals, are entered, the first entry in the first column should be the test start timestamp. (See Phase for more information.)

Other details are analogous to those described for Time to Event Format in the section Time to Event. See also Exact Failure Times versus Interval Censoring for more information.

Event Count

This is the number of events, usually failures addressed by corrective actions (fixes), occurring at the specified time or within the specified time interval. If no column is entered as Event Count, it is assumed that the Event Count for each row is one.

Phase

Reliability growth programs often involve several periods, or phases, of active testing. These testing phases can be specified in the optional Phase column. The Phase variable can be of any data or modeling type. For details about structuring multi-phase data, see Test Phases. For an example, see Piecewise NHPP Weibull Model Fitting with Interval-Censored Data.

This produces a separate analysis for each value that appears in the column.

Data Table Structure

The Time to Event Format and the Dates Format enable you to enter either a single column or two columns as Time to Event or Timestamp, respectively. This section describes how to use these two approaches to specify the testing structure.

Exact Failure Times versus Interval Censoring

In some testing situations, the system being tested is checked periodically for failures. In this case, failures are known to have occurred within time intervals, but the precise time of a failure is not known. We say that the failure times are interval-censored.

The Reliability Growth platform accommodates both exact, non-censored failure-time data, and interval-censored data. When a single column is entered as Time to Event or Timestamp, the times are considered exact times (not censored).

When two columns are entered, the platform views these as defining the start and end points of time intervals. If an interval’s start and end times differ, then the times for failures occurring within that interval are considered to be interval-censored. If the end points are identical, then the times for the corresponding failures are assumed to be exact and equal to that common time value. So, you can represent both exact and interval-censored failure times by using two time columns.

In particular, exact failures times can be represented in one of two ways: As times given by a single time column, or as intervals with identical endpoints, given by two time columns.

Model-fitting in the Reliability Growth platform relies on the likelihood function. The likelihood function takes into account whether interval-censoring is present or not. So, mixing interval-censored with exact failure times is permitted.

Failure and Time Termination

A test plan can call for test termination once a specific number of failures has been achieved or once a certain span of time has elapsed. For example, a test plan might terminate testing after 50 failures occur. Another plan might terminate testing after a six-month period.

If testing terminates based on a specified number of failures, we say that the test is failure terminated. If testing is terminated based on a specified time interval, we say that the test is time terminated. The likelihood functions used in the Reliability Growth platform reflect whether the test phases are failure or time terminated.

Test Phases

Reliability growth testing often involves several phases of testing. For example, the system being developed or the testing program might experience substantial changes at specific time points. The data table conveys the start time for each phase and whether each phase is failure or time terminated, as described below.

Single Test Phase

When there is a single test phase, the platform infers whether the test is failure or time terminated from the time and event count entries in the last row of the data table.

•	If the last row contains an exact failure time with a nonzero event count, the test is considered failure terminated.

•	If the last row contains an exact failure time with a zero event count, the test is considered time terminated.

•	If the last row contains an interval with nonzero width, the test is considered time terminated with termination time equal to the right endpoint of that interval.

Note: To indicate that a test has been time terminated, be sure to include a last row in your data table showing the test termination time. If you are entering a single column as Time to Event or Timestamp, the last row should show a zero event count. If you are entering two columns as Time to Event or Timestamp, the right endpoint of the last interval should be the test-termination time. In this case, if there were no failures during the last interval, you should enter a zero event count.

Multiple Test Phases

When using Time to Event Format, the start time for any phase other than the first should be included in the time column(s). When using Dates Format, the start times for all phases should be included in the time column(s). If no events occurred at a phase start time, the corresponding entry in the Event Count column should be zero. For times given in two columns, it might be necessary to reflect the phase start time using an interval with identical endpoints and an event count of zero.

In a multi-phase testing situation, the platform infers whether each phase, other than the last, is failure or time terminated from the entries in the last row preceding a phase change. Suppose that Phase A ends and that Phase B begins at time tB. In this case, the first row corresponding to Phase B contains an entry for time tB.

•	If the failure time for the last failure in Phase A is exact and if that time differs from tB, then Phase A is considered to be time terminated. The termination time is equal to tB.

•	If the failure time for the last failure in Phase A is exact and is equal to tB, then Phase A is considered to be failure terminated.

•	If the last failure in Phase A is interval-censored, then Phase A is considered to be time terminated with termination time equal to tB.

The platform infers whether the final phase is failure or time terminated from the entry in the last row of the data table.

•	If the last row contains an exact failure time with a nonzero event count, the test is considered failure terminated.

•	If the last row contains an exact failure time with a zero event count, or an interval with nonzero width, the test is considered time terminated. In the case of an interval, the termination time is taken as the right endpoint.