How to Estimate the Stochastic Performance of your Production System in 5 Minutes

“Technical” reliability engineering is “quantitative”.  This implies that the benefits of improvement measures (e.g.: design changes or alternative maintenance strategies) can be quantified in terms of system performance parameters.  Refer, for example, Figure 1.

Notes to Figure 1:

• Number of simulations: 100
• Simulation time: 5 years
• Unit (¤): an unspecified currency

It is evident from Figure 1 that the proposed alternative design (B) is superior in terms of the selected production system performance parameters.  The decision to implement the design change may be made based on the estimated benefits (refer Figure 1) alongside the required Capital Expenditure (CapEx).

The example above demonstrates that quantitative estimates of system performance are helpful for making good decisions, thereby ensuring that company resources are wisely invested.  The essential starting point, however, is a baseline estimate of the current (stochastic) production system performance.

Methods for estimating stochastic system performance

There are various methods of estimating the stochastic performance of the production system.  For example:

• Top-down estimates based on historical production system performance.
• Bottom-up estimates based on phenomenological asset models (refer Figure 1).

Whilst both methods (and combinations thereof) will find application, initial estimates are usually made based on available historical data.

This article demonstrates two simple approaches that may be used to estimate and visualize the stochastic system performance based on the fictious historical production data shown at Table 1.

Table 1: Fictitious historical production data.

Year	Production volume (kt)	Production loss (kt)
2016	95.43	4.57
2017	94.30	5.70
2018	95.40	4.60
2019	91.81	8.19
2020	98.02	1.98

Note to Table 1: the Maximum Theoretical Capacity (assuming zero losses), or MTC, is 100 kt per annum.

Method 1: Empirical Cumulative Density Function (CDF) of production volumes

The empirical CDF shown at Figure 2 was plotted based on the historical production data at Table 1 using R.  R is a freely available language and environment for statistical computing and graphics which provides a wide variety of statistical and graphical techniques.  RAMS Mentat GmbH has developed a user-friendly interface for conducting Life Data Analysis (LDA) using R.

The empirical CDF at Figure 2 may be interpreted (alongside the data at Table 1), for example, as follows:

• It is estimated that annual production will be less than 95.43 kt with a probability of 75 %.
• It is estimated that annual production will be less than 94.3 kt with a probability of 25 %.

In this case, the five data points have resulted in a very “blocky” CDF.  There are, of course, alternative methods for making more precise estimates of system performance.  Nonetheless, the CDF provides, for example, a good basis for determining the probability that next year’s production target can be met!

Since no statistical parameters are estimated using this method, the empirical CDF cannot be used directly for modeling.  However, it provides a valuable opportunity to compare model estimates with the historical reality, i.e.: a very valuable high-level model plausibility check.

Method 2: Weibull analysis of production losses

The Weibull probability plot of production losses shown at Figure 3 was plotted based on the historical production loss data at Table 1 using R via the RAMS Mentat GmbH “Life Data Analysis” (LDA) tool.

The probability plot at Figure 3 may be interpreted, for example, as follows:

• It is estimated that annual production losses will be less than 5 kt with a probability of 50 %.
• It is estimated that annual production losses will be less than 2 kt with a probability of 6 %.

The Weibull probability plot enables the characteristic parameters of the Weibull distribution to be estimated (Beta = 2.736, Eta = 5.64).  These parameters may be directly utilized to create a high-level model of the production system.

It is noted that the five data points have resulted in relatively broad confidence intervals.  More detailed data analysis (e.g.: based on data describing individual loss events) and modeling will enable the confidence intervals to be significantly tightened.

Summary

The first – and arguably most important – step in technical reliability engineering is to establish a quantified estimate of the current system performance.

This article has demonstrated that initial estimates of stochastic system performance are possible within minutes.  Further, it has been shown that the baseline system performance estimate provides:

• A means of estimating the probability with which agreed production targets can be fulfilled.
• A basis for estimating the business case associated with proposed improvement measures.

RAMS Mentat GmbH has developed an innovate technical and systems engineering approach – and supporting tools – that enables the reliability and safety performance of an entire production system to be optimized with consideration of capital investment, operational and maintenance cost constraints.