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Identification and Determination of the Desired QET in Support ProcessesTable of Contents:
These processes divided into relevant subprocesses based on the suggested QET are presented in Figure 3.15. Numerical Application of QET in the Determined Scope for Support Processes• HSE Management (Failure Mode and Effects Analysis—FMEA) Health, Safety, and Environmental (HSE) management is one of the most important issues to be seriously considered by any organization in the 21st century. The best tool for carrying it out is through FMEA. But, before forming the main table, the FIGURE 3.15 Desired QET in support processes. triple issues must be considered as a prerequisite for the main table. Such a prerequisite table is presented in Table 3.15.: The main table for FMEA is included in Table 3.16. • Maintenance Management (Reliability Analysis) The numerical application of the model in the reliability analysis section is related to the failure time of the Computer Numerical Control (CNC) machine linked up with the selected manufacturing factory of DIO. All failure times of the latter machine were gathered for 30 months. The data related to the failure time of the CNC machine for 30 months and the conclusions of Statistical Distribution Functions (SDF), together with relevant calculations for each are assembled in several sheets of an Excel program. Before doing this, the applicable and useful SDF are introduced: TABLE 3.15 Triple issues in FMEA
Main Table for FMEA in HSE management TABLE 3.16
RPN < 150 > The subprocess is under control. 150 < RPN < 250 » The subprocess must be contorlled. RPN > 250 —> The subprocess requires an action plan. RD: Relevant descriptions, RA: Recommendation action(s), D: Date. The popular statistical distribution functions usually deployed in the maintenance departments for calculating reliability are as follows: 3.5.1.1 Exponential Distribution Function One of the best statistical distribution functions deployed for describing the life cycle of insulating oils, fluids (dielectrics), certain material, products, and the failure time of factories equipment is provided in Nelson, 2004. The probability density of this statistical distribution function is as follows:
Where t is the failure time and X is the failure rate. Regarding the definition of the reliability function, the following obtains:
So, we have: 3.5.1.2 Ultra Exponential Distribution Function This statistical distribution function is considered where equipment or systems with very short or very long breakdown times are utilized. Certain computers with breakdown times, very long at times, are suitable for applications in this type of distribution function (Nelson, 2004). The probability density of this statistical distribution function is as follows:
In this formula, t is the failure time and X is the failure rate, and к is the constant value 0 3.5.1.3 Gamma Distribution Function This function, one of the traditional statistical distribution functions, is usually deployed for a large number of equipment or gears along with an accelerated test where the location parameter is a linear function of (possibly transformed) stress (Nelson, 2004). The probability density of this statistical distribution function is as follows:
a parameter is a unitless pure number. It is also designated as the “slope” parameter. (.1 parameter is called the characteristic life. This parameter has the same units as t, e.g., hours, months, cycles, etc. The shape parameter (a) and the scale parameter (p) are positive. 3.5.1.4 Weibull Distribution Function The Weibull distribution is often used for the product life since it models either increasing or simply decreasing failure rates. It is also used as a distribution for such product properties as strength (electrical or mechanical), resistance, etc., in accelerated tests. It is used to describe the life cycle of roller bearings, electronic components, ceramics, capacitors, and dielectrics in accelerated tests. According to the extreme value theory, it may describe a “weakest link” product. Such a product consists of many parts from the same life distribution, and the product fails with the first part of failure (Nelson, 2004). The probability density of this statistical distribution function is as follows: a parameter determines the shape of the distribution and p parameter determines the spread. And considering Equation (3.38) related to the definition of the reliability function, we have: 3.5.1.5 Normal Distribution Function In a normal (or Gaussian) distribution function, the hazard function increases without limit. Thus, it may be used for describing products w'ith wearout failure. It has been used to describe the life span of incandescent lamp (light bulb) filaments and electrical insulations. It is also used as the distribution function for such product properties as strength (electrical or mechanical), elongation, and impact resistance in accelerated tests (Nelson, 2004). The probability density of this statistical distribution function is as follows: In the above formula, p is the population mean and may have any value, о is the population standard deviation and must be positive, and p and о are in the same measurement units. 3.5.1.6 LogNormal Distribution Function The lognormal distribution is widely used for live data, including metal fatigue, solidstate components (semiconductors, diodes, etc.), and electrical insulations. The lognormal and normal distributions are related to each other, and this fact is used to analyze lognormal data with the same methods used on normal data (Nelson, 2004). The probability density of this statistical distribution function is as follows: where p is the mean of the log of life—not of life, p is called the log mean and may have any value from oo to +oo, о is the standard deviation of the log of life—not of life, a is called the log standard deviation and must be positive, and p and о are not “times” like t, rather, they are unitless pure numbers. Moreover, the relevant formulas which can be used are as follows (Nelson, 2004) (Porter, 2004):
After finding the proper statistical distribution function (in this application, the exponential distribution function), we can refer to the related formula for calculating the reliability of the mentioned equipment or machine (in this application, a CNC machine). Therefore, we have the formula R(t,X) = [—e ^{A}' ]? = e~^{x}‘ Then we will have: R(t, X) = Figure 3.16 presents the information in this regard (Karbasian and Rostamkhani, 2019). FIGURE 3.16 Failure times data for a CNC machine. Additional explanations and mathematical calculations results for choosing the best Statistical Distribution Function (SDF) have been attached to Appendix. Exercises

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