ANALYSIS METHODOLOGY

Understanding the Setup

• Machine's Type as Subjects: Each individual machine in our study is treated as a subject. ('Type')

• Failure as Event of Interest: The 'event' being studied is the occurrence of a failure. ('Time_wear_min')

• Censoring: Machines that don't experience failure during the observation period are right-censored. ('Target'==0)

• Machine Type: This is our primary grouping variable.

• Failure Type: 

  • Included as a covariate: To see if failure types have different relationships with survival within each machine type.

  • Competing Risks: If different failure types can occur independently, they might be modeled as competing risks.

Interpreting Our Results In Context

• Multivariate log-rank Test: The significant result suggests that different machine types exhibit differences in their overall survival patterns, with respect to how quickly failures tend to occur.

• Pairwise Standard log-rank Tests These help us pinpoint which specific pairs of machine types differ significantly in their failure distributions.

INDICATIONS

• Machine types 'H', 'M', and 'L' were analyzed.

• Machine type 'H' experiences failures significantly sooner than types 'M' and 'L'.

• Possible Context:

  • Machine type 'L' is inherently less reliable.

  • Machine type 'H' operates under heavier, more failure-prone conditions.

We are specifically interested in the bidirectional relationship between machine types and failure types. Let's discuss how survival analysis tools could be used to investigate this and how to interpret our results.

Survival Analysis Techniques

Multivariate log-rank Test: Our initial test is a good start. This highlights whether there's an overall association between machine type and failure patterns.

Pairwise Standard Log-rank Tests: These are helpful for isolating specific machine type comparisons.

Kaplan-Meier Curves: Plotting these stratified by:

• Machine Type (with separate curves for each type in one plot)

• Failure Type (with separate curves for each failure type in one plot)

Cox Proportional Hazards Model: 

• Modeling Machine Type Effect: Include machine type as a categorical covariate and examine the corresponding hazard ratios to understand how specific machine types affect the risk of different failure types.

• Modeling Failure Type Effect: Include failure types as predictors to see how they influence the overall risk of failure, potentially controlling for machine type.

Important Considerations

Competing Risks: If multiple failure types can occur independently on the same machine, competing risks models might be more appropriate.

Interaction Effects: We explored whether interaction terms between machine type and failure type are meaningful in our Cox proportional hazard models. This reveals us if certain failure types are more strongly associated with specific machine types.

Interpreting our Results Under This Goal

Focus on whether:

Specific machine types are associated with increased or decreased risk of certain failure types.

Specific failure types have differing survival patterns (time to failure) depending on the machine type in which they occur.

Analysis Strategies

1. Visual Exploration with Kaplan-Meier Curves:

   • Stratify by Machine Type: Create plots where each curve represents a machine type ('H', 'M', 'L') and shows the survival distribution for each failure type separately within that machine type. This helps visualize if failure-specific patterns differ depending on the machine.

   • Stratify by Failure Type: Create plots where each curve represents a failure type (e.g., "Heat Dissipation Failure"), and see how the survival distributions differ across machine types for that specific failure.

2. Cox Proportional Hazards Modeling

   • Machine Type Impact:

     • Model each failure type as the event of interest.

     • Include machine type as a categorical predictor (H, M, L).

     • Examine hazard ratios and coefficients to quantify how much a specific machine type increases or decreases the risk of a given failure type, relative to a baseline machine type.

   • Failure Type Impact:

     • Model 'time to any failure' as the event.

     • Include failure types as predictors. This will indicate whether certain failure types are associated with shorter or longer overall survival, potentially controlling for machine type.

   • Interactions: Investigate interaction terms (machine type * failure type) to see if the effect of a failure type on survival depends on the machine type.

Focus of Interpretation

• Machine-Specific Risk: Which machine types are most prone to specific failure types? Are the riskiest failures the same across all machine types? Do any machine types show general resilience to several failure types?

• Failure-Driven Differences: Do any failure types have particularly high hazard ratios, indicating they strongly influence failure times? Do the survival patterns for a given failure type look drastically different across machine types?

Observations (Hyp Hypothetical, based on our data)

• "Machine type 'H' shows a significantly increased risk of Heat Dissipation Failure compared to 'M' and 'L'."

• "Overstrain Failure occurs earlier on average in machine type 'L' compared to the other types."

• "While Power Failure has a low overall hazard ratio, its effect on survival is more pronounced in machines of type 'M' (interaction).