New Reliability Tool for the Millennium: Weibull Analysis of Production Data

The authors will demonstrate how a major Chemical Process company has successfully utilized this new technique to answer questions such as: 1. Do I have a reliability problem or a production problem? 2. What is the demonstrated capacity of my plant? 3. What are efficiency/utilization losses costing me? 4. What is the reliability of my process plant? The Weibull technique described has helped the company define a strategic course of action based on quantification of process reliability. This tool when added to its reliability improvement arsenal will help any company optimize availability of its products to its customers and maximize profits to its stakeholders. Introduction To Weibull Plots Most reliability issues have too much information and too little knowledge. Process plants have vast quantities of data concerning equipment and operating conditions. The problem is trying to make the data speak about reliability in terms that are understandable to the ordinary person. One simple method is to use the daily production output from the process and let the production data “speak”. Every production process has daily output data usually organized and studied in time sequence. Few organizations view the data as output from a “black box” to study the results in statistical format to see patterns in the data. Weibull analysis is one way to organize plant data as described by Abernethy (1998). Weibull plots, the tool of choice for most reliability issues, will be used in this paper in a nontraditional manner. The Weibull plots will define reliability of processes and calculate losses from failure of the process to perform. The production losses in units of output are a precursor for money. When problems are explained in money and time, everyone understands them. The cost of process failures often exceeds the cost of individual equipment failures by many multiples. We anguish over failure of pumps and heat exchangers—these are the low cost pawns, and what we should worry about are expensive process failures—this is the high priced king. The Weibull Analysis of Production Data 3 problem is to decide if you have a reliability problem with equipment or a problem with the production process. Weibull plots help explain and categorize problems in a visual format understandable by engineers, process owners, and management. Why Use A Weibull Plot? Definitions for Weibull process details are given below. Weibull probability plots organize many different types of data into straight line X-Y plots. Engineers need data plots, with straight lines, for comprehension at a practical level. For engineers and processes owners the relationship is simple—no cartoon, no comprehension. Weibull distributions are chosen pragmatically. When data produces a straight line on a Weibull probability plot, the data is considered to be from a Weibull distribution. Weibull distributions are complicated as they are non-linear and usually non-symmetrical distributions. Traditional Weibull plots utilize age-to-failure data obtained from component failures to make straight-line plots. For components, the slope of the Weibull line tells the failure mode for the component. This is an important feature for letting the data “talk” about what portion of the bathtub curve is best represented, i.e., infant mortality, chance failures, or old age wear out. Traditional Weibull analysis carefully separates different failure modes to get clean data with suspensions (i.e., the data is censored) so only single modes of failure are represented in each straight line Weibull plot. When mixed failure modes are plotted on a Weibull plot, cusps often appear that give clues to changes and provide evidence for mixed failure modes. Process reliability techniques will take advantage of the cusps to provide information about process reliability. Figure 1 shows Weibull probability graph paper. The X-axis is a log scale, and it will be used to plot the daily production from a production unit. The Y-axis is an irregularly divided scale resulting from taking the log of another log. The Y-axis is plotted in a reliability scale rather than the traditional cumulative scale reflecting unreliability. Notice Weibull plot scales magnify problems in the lower left hand corner so they can easily be observed as shown by the darkened rectangular areas highlighted by the ellipses in Figure 1. Both ellipses are 4%*0.9 units of production. How Does Scalar Production Data Get Into An X-Y Format? Production data from a process is usually acquired as daily output. If weekly or monthly data summaries are used, the smoothing of the data hides reliability of the process. The daily output reflects conditions upstream and downstream from the pay-point under measurement. Daily output is a scalar value. Statisticians have worked out a scheme for handling the conversion of scalar results into a X-Y coordinate system. Data is ranked from low to high to form N pieces of information. The rank of each value is identified with its “i” position for use with Bernard’s median rank equation which gives the reliability Y-position as 1 (i 0.3)/(N + 0.4). The details are explained in Abernethy. Production Output (tons/day) .1