Summary of Statistical Analysis of Machine Maintenance Data

Statistical Analysis of Machine Maintenance Data Explained

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Introduction

Reliability and maintenance analysis uses failure and repair records to understand how machines perform over time, to estimate availability, and to detect ageing (degradation). This guide teaches how to analyze failure-history data (pairs of Time To Repair (TTR) and Time To Failure (TTF)) for three machines, compute key statistics, visualize trends, and decide whether machines have entered an ageing stage.

Definition: Reliability is the probability a machine performs its function without failure for a given period. Maintainability measures how quickly a failed machine can be restored to operation.

1. Data structure and preparatory steps

Each machine has a sheet with 300 data pairs (TTR, TTF). From these you should build auxiliary columns and summary tables.

Auxiliary columns to create

  1. TBF (Time Between Failures): $$\text{TBF} = \text{TTF} + \text{TTR}$$
  2. Accumulated TTF (operating time scale): running sum of TTF values.
  3. Accumulated TBF (global time scale): running sum of TBF values.
  4. Failure rate per 100 hours (example): compute the number of failures in each 100-hour window of accumulated TBF, or estimate instantaneous rate as reciprocal of mean TTF: $$\lambda \approx \frac{1}{\overline{\text{TTF}}}$$ and then scale: $$\lambda_{100} = 100,\lambda$$

Quick checklist before analysis

  • Ensure TTF and TTR units are consistent (hours).
  • Fill missing or empty cells if required by imputation rules (documented separately) or flag them for exclusion.
  • Sort records in chronological order if not already.

2. Global analysis (overall behaviour)

Compute these statistics using all data for each variable (TTF, TTR, TBF, Availability): mean, standard deviation, minimum, maximum, and percentages where applicable.

Core formulas (use LaTeX when computing):

  • Mean: $$\overline{x} = \frac{1}{n}\sum_{i=1}^{n} x_i$$
  • Sample standard deviation: $$s = \sqrt{\frac{1}{n-1}\sum_{i=1}^{n} (x_i - \overline{x})^2}$$
  • Availability (for each failure cycle): $$\text{Availability} = \frac{\text{TTF}}{\text{TBF}}\quad(\text{express as percentage }100\times)$$
  • Overall availability (time-weighted): compute total operating time and divide by total global time: $$\text{Availability}_{\text{overall}} = \frac{\sum \text{TTF}}{\sum \text{TBF}}$$

How to present results

  • Use a small table per machine with rows: Mean, SD, Min, Max for TTF, TTR, TBF, and Availability.
  • Add a short text interpretation: e.g. "Machine A has mean TTF = $x$ h (SD $y$ h), mean TTR = $u$ h (SD $v$ h), overall availability = $z%$."
💡 Věděli jste?Fun fact: Did you know that simple availability does not capture downtime distribution; two machines can have the same availability but very different operational profiles if one has frequent short failures and the other rare long failures?

3. Ageing analysis (detecting degradation)

Goal: determine whether failure behavior changes over time indicating ageing, and estimate when ageing begins.

Strategy overview

  1. Use sequential sampling: compute statistics over moving or sequential blocks (e.g., every 50, every 20, every 15 observations). These are already suggested in the workbook.
  2. Plot trends vs. accumulated time: plot mean TTF, mean TTR, TBF, and Availability for each block against accumulated TTF or accumulated TBF.
  3. Look for systematic trends: decreasing TTF, increasing TTR or TBF, decreasing availability, or rising failure rate indicate ageing.

Practical steps

  • Create the three sequential-sample tables: blocks of 50, 20, 15 (non-overlapping sequential samples), computing mean, SD, min, max, availability for each block.
  • Plot each statistic vs. block index or vs. accumulated hours (use accumulated TTF for operating-life-based ageing, accumulated TBF for global-time ageing).
  • Complement with a moving-window analysis (e.g., moving average over 30 failures) to smooth noise.

How to estimate start of ageing

  • Find the earliest block where the statistic (e.g., mean TTF) de
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Reliability Maintenance Analysis

Klíčová slova: Reliability and Maintenance Analysis

Klíčové pojmy: Create TBF as TTF + TTR, Compute mean, SD, min, max for TTF, TTR, TBF, Overall availability = sum(TTF)/sum(TBF), Block sampling (50,20,15) to detect trends, Plot mean statistics vs accumulated hours to spot ageing, Estimate failure rate as $\lambda\approx 1/\overline{\text{TTF}}$ and scale to 100 h, Use moving averages and statistical tests (trend significance), Flag sustained deviation (e.g., >20%) as ageing indicator, Prefer time-weighted availability for comparisons, Verify and handle outliers before concluding ageing

## Introduction Reliability and maintenance analysis uses failure and repair records to understand how machines perform over time, to estimate availability, and to detect ageing (degradation). This guide teaches how to analyze failure-history data (pairs of Time To Repair (TTR) and Time To Failure (TTF)) for three machines, compute key statistics, visualize trends, and decide whether machines have entered an ageing stage. > **Definition:** Reliability is the probability a machine performs its function without failure for a given period. Maintainability measures how quickly a failed machine can be restored to operation. ## 1. Data structure and preparatory steps Each machine has a sheet with 300 data pairs (TTR, TTF). From these you should build auxiliary columns and summary tables. ### Auxiliary columns to create 1. TBF (Time Between Failures): $$\text{TBF} = \text{TTF} + \text{TTR}$$ 2. Accumulated TTF (operating time scale): running sum of TTF values. 3. Accumulated TBF (global time scale): running sum of TBF values. 4. Failure rate per 100 hours (example): compute the number of failures in each 100-hour window of accumulated TBF, or estimate instantaneous rate as reciprocal of mean TTF: $$\lambda \approx \frac{1}{\overline{\text{TTF}}}$$ and then scale: $$\lambda_{100} = 100\,\lambda$$ ### Quick checklist before analysis - Ensure TTF and TTR units are consistent (hours). - Fill missing or empty cells if required by imputation rules (documented separately) or flag them for exclusion. - Sort records in chronological order if not already. ## 2. Global analysis (overall behaviour) Compute these statistics using all data for each variable (TTF, TTR, TBF, Availability): mean, standard deviation, minimum, maximum, and percentages where applicable. ### Core formulas (use LaTeX when computing): - Mean: $$\overline{x} = \frac{1}{n}\sum_{i=1}^{n} x_i$$ - Sample standard deviation: $$s = \sqrt{\frac{1}{n-1}\sum_{i=1}^{n} (x_i - \overline{x})^2}$$ - Availability (for each failure cycle): $$\text{Availability} = \frac{\text{TTF}}{\text{TBF}}\quad(\text{express as percentage }100\times)$$ - Overall availability (time-weighted): compute total operating time and divide by total global time: $$\text{Availability}_{\text{overall}} = \frac{\sum \text{TTF}}{\sum \text{TBF}}$$ ### How to present results - Use a small table per machine with rows: Mean, SD, Min, Max for TTF, TTR, TBF, and Availability. - Add a short text interpretation: e.g. "Machine A has mean TTF = $x$ h (SD $y$ h), mean TTR = $u$ h (SD $v$ h), overall availability = $z\%$." Fun fact: Did you know that simple availability does not capture downtime distribution; two machines can have the same availability but very different operational profiles if one has frequent short failures and the other rare long failures? ## 3. Ageing analysis (detecting degradation) Goal: determine whether failure behavior changes over time indicating ageing, and estimate when ageing begins. ### Strategy overview 1. Use sequential sampling: compute statistics over moving or sequential blocks (e.g., every 50, every 20, every 15 observations). These are already suggested in the workbook. 2. Plot trends vs. accumulated time: plot mean TTF, mean TTR, TBF, and Availability for each block against accumulated TTF or accumulated TBF. 3. Look for systematic trends: decreasing TTF, increasing TTR or TBF, decreasing availability, or rising failure rate indicate ageing. ### Practical steps - Create the three sequential-sample tables: blocks of 50, 20, 15 (non-overlapping sequential samples), computing mean, SD, min, max, availability for each block. - Plot each statistic vs. block index or vs. accumulated hours (use accumulated TTF for operating-life-based ageing, accumulated TBF for global-time ageing). - Complement with a moving-window analysis (e.g., moving average over 30 failures) to smooth noise. ### How to estimate start of ageing - Find the earliest block where the statistic (e.g., mean TTF) de