30/06/2011

Author : Nicholas Hastings & Melinda Hodkiewics

Nicholas A. Hastings, Albany Interactive Pty Ltd and Melinda R. Hodkiewicz, University of Western Australia

**ABSTRACT**

It is shown how daily production data for industrial process plant can be used as an aid in making improvements in plant performance. A spreadsheet based analysis is presented in which a frequency distribution plot is created and performance indicators for the plant are calculated. The indicators include values for the percentage of days with normal, low and zero output, values for the maximum, average overall and average normal-day production and a measure of the variability of production. These indicators help management to focus on suitable approaches to the improvement of performance in operations, maintenance and reliability. The results also form a basis for comparing different plants in terms of production performance.

**Keywords:** Production Management, Process Plant, Performance Indicators

**INTRODUCTION**

We present a method of analysis of daily production data in process plants to assist plant management personnel, including process managers, maintenance managers and reliability engineers, to improve plant performance. In particular the techniques presented assist with the following:

• Estimation of the incidence of normal production days and of low and zero production days;

• Estimation of the variability of production;

• The selection of the type of improvement needed, such as a focus on reducing low production days or on reducing variability on normal production days.

• Estimation of overall average daily production, maximum daily production and average normal-day production;

• Stabilisation of production levels;

• Focussing the requirements for reliability and process improvements and measuring success;

• Comparison of performance between production facilities.

Production plots of process data have previously been used by Barringer [1]. His method is based on the use of the Weibull distribution [2], [3], which requires specialised software and an interpretation of Weibull parameters in a production management context. Here we present a distribution-free method of analysis based on the use of standard spreadsheet functions.

**PRODUCTION DATA**

Process plants are often expected to produce a steady daily output of product, measured in appropriate units, such as tonnes. In practice, there is variability in the level of production, and days of low or zero production occur for various reasons. These include plant failures, run-up or wind-down of production, operational variations and lack of demand. Production data for process plants is normally available in the form of a daily record of units of product produced. Figure 1 shows, in columns A and B, an extract of such data for a plant referred to as Unit 1. Columns A and B show only the first 15 days of a data series which actually extends over a period of 18 months (538 days) and the analysis given here is based on the full 18 months data. The remaining columns of Figure 1 contain derived figures which will be discussed as the article progresses.

Figure 1

Spreadsheet analysis of production data (The full data in columns A and B and G and H extend to 538 rows, one for each day in the 18 month analysis.)

**FREQUENCY DISTRIBUTION PLOT**

Our analysis is based on the use of a frequency distribution plot. In a frequency distribution plot the numbers of days on which production is at specified levels is plotted against the production level. The graph is produced using the Excel ‘FREQUENCY’ function. This counts how many days occur in each of a number of production-level intervals. To develop the frequency distribution plot we use the following procedure.

• Find the maximum daily production from Column B using the Excel MAX function. The result is 111,893 tonnes shown at cell F7.

• Divide this by 10 and use this quantity (11,189.3 tonnes) as an increment to set interval boundaries in the “bins array” at C4 to C13. Alternatively, a round figure such as 10,000 tonnes might be used as the increment here, but using 10% of the maximum production gives comparable scaling between different applications.

• Set an interval boundary of 1at C3. This is so that we get a count of the number of zero-production days.

• Set an interval boundary 1% greater than the maximum production at C14. This is used in the frequency distribution graph to show the upper limit of production values.

• Enter an Excel FREQUENCY function in cells D3 to D14 specifying B2:B539 as the data array and C3:C13 as the bins array. This gives the counts of days in each production interval as shown in D3:D14. For example, Cell D11 shows that there were 113 days with production between 78,325 tonnes and 89,514 tonnes.

• Use Excel graphics to create a graph from the frequency data at C3:14 and D3:14.

Figure 2 shows the resulting frequency distribution plot.

Figure 2.

Frequency Distribution of Daily Production Unit 1

**PRODUCTION LEVEL ZONES**

In the Figure 2 production frequency distribution plot we identify three zones as follows:

**Normal Production Days**. These days correspond to the bell shaped part of the curve at the right hand end of the graph in Figure 2.

**Zero Production Days**. These are shown by the intercept of the curve with the vertical axis. This is the number shown at Cell D3, 37 days in this case.

**Low Production Days**. These lie between zero and the left-hand end of the Normal Production Days range.

**CUT-BACK POINT**

The transition point between Normal and Low production is referred to as the cut-back point. Production levels below the cut-back point are ‘low’ and levels above that value are ‘normal’. As a practical guideline, we estimate the cut-back point as 90% of the average daily production. This is done as follows:

• Calculate the average daily production across all days by totalling the production from Column A and dividing by the number of days. This is 74,182 tonnes, shown at Cell F5.

• The cut-back point is calculated as 90% of this value and is 66,764 tonnes, as shown at Cell F11.

A visual check against Figure 2 shows this to be a reasonable value, as it lies in the area of the left-hand tail of the bell-shaped distribution of normal production days. The cut-back point value is somewhat subjective, so it can be altered if necessary by changing the value in Cell F11.

**KEY PERFORMANCE INDICATORS**

Having estimated the cut-back point, we can calculate several useful key performance indicators. Firstly, we generate Columns G and H, both of which extend for the full 538 days. Column G shows the production on days above the cut-back point and Column H is a counter for these days. The numbers of Normal and Low days can then be calculated, and these can be expressed as percentages as shown in Figure 3.

Figure 3 Key Performance Indicators Unit 1

**Normal Days**

The percentage of Normal Production Days (76% in Figure 3) is a key performance indicator for production at the plant. A primary aim for production management is to increase this figure . Ideally, every day should be a Normal Production Day.

**Low Production Days**

The percentage of Low Production Days (17% in Figure 3) is a key performance indicator for the plant. Management should investigate the causes of Low Production Days and try to reduce their number. Techniques such as Pareto Analysis and Root Cause Analysis can be applied, typically by reliability engineers, with the aim of identifying and eliminating equipment defects and failures. Losses may also be reduced by adjustments to the maintenance plan and by the application of condition monitoring techniques. Production losses due to run-up and wind-down times, or other operational causes, can be identified and addressed, typically by process engineers and operations staff. One of the main advantages of the technique presented here is that it provides a basis for indicating the extent of the Low Production Days and for checking progress in reducing the production loss that these days represent.

**Zero Production Days**

Zero production days can result from many causes, including planned maintenance, breakdowns, lack of demand or lack of input materials or resources. In the graph, the incidence of zero production days is visible and can be assessed in relation to expectations. If down days are planned, whether on a regular or an opportunistic basis, and have been found to be advantageous in terms of equipment reliability and production planning, then we may accept the observed result, but if the number of Zero Production Days is above expectations then management needs to investigate the cause and take steps to remedy the situation. It may also be that a review of the performance measures indicates that the number of down days for maintenance should be increased.

In Figure 3 we see that the number of days with zero production was 7% of the total. Whether this is a concern or not depends on operating circumstances. If it is the practice to have a shut-down one day per month plus two weeks per year, the figure of 7% would be mostly accounted for. On the other hand, if 100% operation was expected, then the 7% loss would be significant.

**Average Daily Production**

This is the average calculated across all days, including Normal, Low and Zero production days. Ultimately, it is the key measure of the output of the plant, and improvements should be reflected in an increase in this value (which, in the example, is 74,182 tonnes). This quantity is useful in creating realistic production plans. It also provides a benchmark against which future improvements in overall performance may be measured.

**Average Normal-day Rate (ANR)**

This is the average level of production which has been achieved on Normal Production days. It is not a maximum, but an average working figure of demonstrated performance on days when the plant is working in the Normal Production range, Low and Zero days having been disregarded. In Figure 3 the ANR is 90,056 tonnes.

From an operations viewpoint, the ANR provides a benchmark against which future performance on Normal days can be evaluated. Operators should consider how this value can be raised by improvements in normal operating practices. However, they should not pursue improvements to a level which is counter-productive in terms of causing excessive wear, failures or damage which can lead to greater overall production losses due to an increase in Low or Zero Production days.

**Maximum Production**

This is the highest daily production achieved over the whole period for which data is available. It serves as an indicator of what can be achieved and as a target towards which the ANR can build. Management should examine how this level of output was achieved and review the extent to which it can become standard practice.

**Coefficient of Variation**

This is the ratio of the standard deviation to the mean, and is a measure of the variability of production. The standard deviation of the daily production is calculated for the data in Column A using the Excel function STDEV and the result is shown in Cell F10 as 31,916 tonnes. The Coefficient of Variation is then obtained by dividing the standard deviation by the Average Daily Production, giving the result of 0.43 shown in Cell F8.

In process plants, reduction of variability is important for two reasons: firstly because low variability assists with the smooth running of plant, and secondly because a process with low variability results in lower stockpiles for a given throughput. This latter observation is based on queuing theory and is an example of the application of the Pollaczek-Khintchine formula [3]. Business costs are reduced by reducing variability in processing time because smaller stockpiles mean less capital tied up in inter-process stocks. Also, reduced variability leads to improvements in planning, due to greater certainty regarding the level of production output. Such improvements can lift the overall performance of a plant.

The value of the coefficient of variation provides an indication of the variability of daily production across all days and provides a benchmark for comparisons of, or changes in, such variability.

**Ideal Situation**

Process plants normally have a nameplate production capacity. Design or process modifications may result in a current rated capacity which is higher than the original nameplate value. The ideal situation is one with no Zero or Low Production Days and where the production on all days is constant and at or above the rated capacity. The coefficient of variation would then be zero.

In a less than ideal, but realistic, situation where maintenance down-days and other factors occur, the parameters developed here allow management to relate actual performance to the ideal, and provide pointers to, and measures of, improvements in plant performance.

The days of zero or low tonnage are targets for investigation for the reliability engineers or others responsible for long-term strategy development. This may include a review of shutdown strategy and the development of maintenance tactics targeted at the elimination of causes of unscheduled down time. The Average Normal-day Rate for the example plant is approximately 90,000 tonnes, but there are many days where actual production exceeds this by a considerable margin. There may be a number of reasons for this, and management will want to understand factors that may produce the values shown here, and what limits the achievement of a more consistent and higher daily tonnage. The investigation of these issues is often the domain of the process engineers and operations groups as they seek to increase the level and reduce the variability in day-to-day production throughput.

**PLANT COMPARISONS**

A valuable feature of the performance indicators is in comparing the performance of different plants, or of the same plant through time. Figures 4 and 5 show the performance indicators for one process plant, Unit 8; Figures 6 and 7 show the indicators for another one, Unit 9. Which plant shows the better performance?

Figure 4. Key performance indicators unit 8

From Figure 4 we see that Unit 8 has 64% Normal days and 29% Low days whereas Figure 6 shows that Unit 9 has 80% and 14% respectively. This indicates a superior performance for Unit 9, and that the incidence of Low days in Unit 8 should be investigated. Also, the coefficient of variation is 0.53 for Unit 8 and 0.37 for Unit 9, so that the degree of production variability is much higher for Unit 8. The degree of variability for Unit 8 should be investigated by operations and process management. The actual production levels in these Units are quite different in terms of tonnes throughput, but our performance indicators form a basis for comparison and an indication of areas for improvement.

**CONCLUSION**

A method has been presented for creating production data plots for process plant and for calculating key performance indicators, using spreadsheet techniques. This provides measures of daily production, including the overall average value, the average normal-day rate, the maximum daily production value and the coefficient of variation, which is a measure of the variability of daily production. The methods lend themselves, both visually and analytically, to the identification of the extent of normal, low and zero production days. The indicators form a basis for directing reliability engineers, process engineers and operations staff to the most critical areas required in order to increase production and to reduce process variability. The indicators can also be applied to forming comparisons of plant performance, which may be used to evaluate differing operating or maintenance strategies, to compare plant performance in different time periods, or to make comparisons across a range of plants. The key performance indicators developed here are a valuable tool for managers of process plants.

**REFERENCES**

1. Barringer H P and Roberts W T Jr., Process Reliability: Do You Have It? – What is it Worth to your Plant to Get It? AIChE National Spring Meeting, New Orleans, LA, USA, 2002. www.barringer1.com

2. RelCode Weibull Analysis Software. Albany Interactive Pty Ltd. www.albanyint.com.au

3. Forbes C, Evans M A, Hastings N A J and Peacock J B, Statistical Distributions, 4th edition, Wiley

The authors may be contacted at: naj.hastings@bigpond.com and Melinda.hodkiewicz@uwa.edu.au

Figure 5

Frequency distribution of daily production for Unit 8

Figure 6

Key Performance Indicators for Unit 9

Figure 7

Frequency distribution of daily production for Unit 9