Quantitative assessment of RAM driven risk matrix of offset printing machine

2.1. Machine details

The proposed assessment was conducted on a sheetfed offset printing machine (make: Heidelberg, Germany; model No.: CD102). It was manufactured in 2002 and installed in 2005 at United Arab Emirates (UAE) based printing company. It is four-color printing machine having black, cyan, magenta, yellow printing couple with one special colour printing couple. This machine also consists of seven units namely feeding unit, inking unit (in each couple), dampening unit (in each couple), printing unit (in each couple), coating/varnish unit, drying unit, delivery unit as illustrated in Fig. 2. Special printing couple and varnishing unit are generally used for specialty printing. It is to be mentioned that prepress section and post press section are not included in Fig. 2 but play an important role for print production. The machine components as mentioned are marked in Fig. 2 for further processing.

Its plate size is 79×103 cm, maximum paper size is 72×102 cm and maximum print format is 71×102 cm. Different types of coated, uncoated, recycled, texture, matte, glossy, wood-free paper are used on the basis of job. Paper grammage is used in the printing machine in between 80-450 gsm as per job requirement. Offset inks and normal consumables are used for printing. Inside the printing press, the temperature is maintained between 20-26 °C and average relative air humidity was 75-85 %. Most of the printing jobs were scheduled mainly in day shift, however it has both 2-shift roaster and 3-shift roaster depending on job load. Though its maximum speed is up to 15000 impressions per hour, hence it operates at an average printing speed of 4560 impressions per hour as per job requirement from client and availability of paper type and paper grammage. Out of many printing machines, CD102 printing machine is chosen due to its age and failure scenario however it is assumed that the operational condition of the machine is the same.

Fig. 2Four colour sheetfed offset printing machine with special colour couple

2.2. Data representation

The basic operational data of failure number, breakdown time, runtime, good pieces and wastages has been obtained for 309 days out of 365 days which are represented in 3D bubble plot as shown in Fig. 3. The plot shows the numerical values of runtime, breakdown time and number of failures in a 3-Dimensional space best on their X-Y-Z coordinates. Each bubble represents the category of all input variables namely runtime, breakdown time, number of failures, number of good pieces and number of waste pieces. The size of each bubble indicates the number of good pieces obtained from the machine while the colour (from green to red) of each bubble represents the number of waste pieces obtained from the machine. Effect of runtime and breakdown time and good pieces and waste pieces on failure number is also observed here. It is seen that failure number is well dependent on the breakdown time and number of wastages.

2.3. Breakdown details and causes

The basic data are failure number, runtime, breakdown time, number of wastage and good pieces of the printing machine which are observed and then collected from the daily management information system (MIS) during the period of 1st January 2021 to 31st December 2021. From the collected data, various breakdown times and number of failures are identified and the total number of 16 breakdown causes are analysed yearly by failure mode and effect analysis (FMEA) approach which is shown in Table 2. Here the responsible machine components or units are identified for respective breakdown causes. Fig. 4 shows the corresponding pareto analysis of failure number in where dominant failures for different breakdown types will be prioritized for improvement based on the FMEA results. This analysis will again lead to risk estimation both qualitatively and quantitatively later in this study.

Fig. 33D Bubble plot of runtime, downtime, failure number, good pieces and waste pieces on daily basis

Fig. 4Pareto analysis of failure number of individual breakdown type

2.4. Risk assessment

Risk assessment of any machine identifies the present status of the machine and helps production team to plan for the reduction of the probable risk of hazards, continuous production and improve production efficiency along with its economical profitability. It is a technique that identifies, characterizes, quantifies and evaluates the loss from an event. The risk assessment needs failure mode and effect analysis (FMEA) and pareto analysis for each failure. After estimation of probability of these breakdown occurrences, the effects are monitored in terms of time, cost, performance loss, human, environment, business interruption etc. Then the combination of these failures and its effects are used to understand and compare the risk scenario to minimize each kind of risk present in the machine.

Risk assessment of any machine might either be quantitative or qualitative depending on the resource availability in the existing setup. Quantitative risk estimation is the product of probability of failure (PoF) and consequence of a failure (CoF) events. The proposed risk-based maintenance (RBM) based on RAM aims to reduce the overall risk scenario of the operating printing facility. RBM/RAM implementation will reduce the occurrence of unexpected failure by implementing three modules namely risk determination, risk index evaluation and maintenance planning.

The first module of RBM/RAM methodology consists of the combination of sequential failure event which is to be quantified and calculated probability. To do that, time-motion study are conducted to identify the failures with proper systematic fault-finding techniques like FTA, reliability block diagram (RBD) and FMEA. Then an in-depth analysis are made with those identified failures for further reliability assessment. However, reliability assessment is one of most popular and important parameters to analyse potential failure scenarios of a machine. By definition, it is the ability of an item to perform a required function under given conditions for a given interval of time before it is undergone a breakdown. Mathematically, reliability function is derived from Eq. (1) where, $R\left(t\right)$ is the reliability at time $t$, $F\left(t\right)$ is cumulative failure distribution (CDF) function or correlation coefficient and $f\left(x\right)$ is failure probability density function (PDF). This probabilistic failure model can be estimated by Pearson correlation technique as shown in Eq. (2):

where, $x$ – breakdown time (in minute), $f\left(x\right)$ – Cumulative % of failure (calculated from number of failures per day and sum of number of failures for one year), $N$ – sum of total operating time for one year (in minute) and $F\left(t\right)$ – correlation coefficient.

From the concept of probability, it is known that the correlation coefficient must be in between +1.0 to –1.0 [5]. If the correlation coefficient estimates positive value, then the failure rate is increasing, otherwise the rate is decreasing. The analysis of bathtub curve [20] explains the different significant stages of failure i.e. showing infant mortality, useful life and wear-out stage of machine by the help of estimated failure rate ($\lambda$) as shown in Eq. (3) where MTBF is mean time between failure:

During risk analysis availability is also important factor as it explores the availability of a machine during breakdown and repairment. Hence, availability and reliability are two different and necessary criteria in practicing maintenance methodologies. Reliability deals with the system in use which completes its task before failure occurs within a specified period of time. By definition availability is the probability of a system that has been failed and experienced by a repair action during its available time. It can also be defined as the probability of system which is readily available to perform the required function in the given work environment for a specified period of time and under stipulated working conditions. In general the availability $A_s$ of a system is a complex function of reliability $R\left(t\right)$, maintainability $M\left(t\right)$ and supply effectiveness $S_E$ which can also be expressed by Eq. (4):

Mathematically availability can be sub-categorized into inherent availability ($A_{in}$) and operational availability ($A_{op}$) which is defined by Eq. (5) and Eq. (6) for better understanding:

Here, mean time to repair or MTTR is the ratio of repair time to failure number and mean downtime or MDT is the ratio of breakdown time to failure number where breakdown time is the summation of inspection time and repair or replacement time of each and every failure causes etc.

After reliability or failure assessment, consequence assessment are conducted whose main objective is to prioritize equipment and their components on the basis of their contribution to a system failure. So, consequence or severity of failure are estimated on the basis of different accounted loss caused from human wages loss cost, system performance loss, financial loss due to maintenance, environment loss, human health loss, any other losses etc.

Human wages loss cost (HWLC) is the loss which includes the cost of workers idleness due to machine breakdown. Breakdown time-period (DT) is the combination of both inspection time and repair time. System performance loss during production due to component failure which can be assessed [10, 20] either by expert’s opinion or by calculating the production loss cost (PLC). Maintenance loss cost (MLC) accounts for damage to the property or asset which is the summation of different cost of inspection, specialized equipment or personnel hired, maintenance, spare parts repair or replacement etc. Human health loss cost (HHLC) is the cost of health-related expenses of all the affected staffs during production due to illness or accident or hospitalization or disability etc. Environment loss cost (ELC) is the cost of damage per area zone within the building, plant, residence, agricultural land etc. to restore from the damaged state to natural ecofriendly state. However, in this study environmental loss is neglected and human health loss didn’t occur during production. All the losses and consequences of failure (CoF) are summarized in Eqs. (7) to (10):

In the second module of RBM/RAM acceptable risk criteria (ARC) is set according to the ALARP (as low as reasonably possible) to determine the risk index (RI) as shown in Eq. (11). If the RI value is more than 1 then it is said to be highly risky:

Risk of the machine in terms of both breakdown causes and machine components can be assessed quantitatively with the help of risk matrix by representing possible system risk levels or risk score values. The components of the risk matrix are likelihood, severity and risk impact. The likelihood of risk or probability of failure occurrence from an event or historical data has been considered as five ranges like remote, unlikely, possible, probable and highly probable which is quantified by giving scores from 1 to 5 as illustrated in Table 3. The failure impact is the severity or consequence of failures which have been considered as five ranges i.e. negligible, minor, significant, major, catastrophic which is again quantified by giving scores from 1 to 5 which is also illustrated in Table 3. The risk level criteria have been set as per industrial norms and regulations which is illustrated in Table 4. Table 5 shows also the criteria for setting scores for different level of inspection time.

Risk priority number (RPN) measurement is important for subjective assessment of risk and for prioritizing breakdown occurrence for corrective actions where inspection (or detectability) factor is considered. It can be said that if inspection time can be lowered then downtime can be reduced and if inspection is zero then downtime consists of repair time only. As per availability analysis, breakdown time is the combination of time of inspection (or detection) and repair. An attempt has been made to quantify the detection score level by assessing the inspection time (or detection time). Risk priority number (RPN) is the product of PoF or likelihood or occurrence (O), CoF or severity (S) and inspection or detection (D) level as shown in Eq. (12). Finally, in RPN matrix format, detection or inspection score and risk score (product of PoF and CoF) is set on $x$-axis and $y$-axis respectively for matrix visualization:

In the third module of RBM/RAM methodology, reduction of risk level is executed by reducing PoF with the help of proper maintenance planning and managerial implication. Maintenance planning includes maintainability parameters and proper implementation of maintenance decisions made by management. For proper maintenance action implementation, estimation of optimal maintenance duration along with re-estimation of the updated PoF, CoF and RI are generated to account for the probable profit gain or improvement of other parameter. Maintainability can be derived both qualitatively and quantitatively, which is the characteristics of maintenance planning, material design and installation.

Maintainability indicator rating (MIR) can be derived by Delphi technique [7, 21] for easy and quick analysis of maintenance. It is a qualitative approach on the basis of scaling of maintenance complexity level criteria as tabulated in Table 6 with a expert panel made up of managers, engineers, technicians and operators who are operating and maintaining the required assets or equipment. It may also require repetitive sets of structured questionnaires session for probable best fitted maintenance criteria outcome.

It is known that maintainability of an equipment is the restoration property from breakdown to its original position within a specific time period after completion of the recommended maintenance action. Similar to reliability investigation, theory of probability distributions plays a significant role in maintainability analysis as well. Maintainability percentage of the machinery was predicted according to the repair time, begins with time $t=$ 0 and will be finished at time $t$ [20, 22]. The mathematical form of maintainability function is mentioned in Eq. (13), where $t$ indicates the time to repair, $g\left(t\right)$ denotes the repair time of probability density function (PDF) and $M\left(t\right)$ indicates the function of maintainability:

However, for quantitative approach, the percentage of maintainability is estimated by using Pearson correlation technique and shown in Eq. (14), where, $x$ – repair or replacement time of said breakdown (in minute), $g\left(x\right)$ – cumulative % of repairment of existing failure (which is calculated from number of repair per day and sum of number of repairs for one year), $N$ – sum of total operating time for one year (in minute) and $M\left(t\right)$ – correlation coefficient:

Here prediction of optimal maintenance duration is accomplished for affected machine or subsystem by determining maintenance interval time (MaIT). It is estimated for the justification of the improved maintenance planning, reliability or efficiency of machine in a production system. The mathematical expression of MaIT is shown in Eq. (15) [6, 10]:

where ${PoF}_U$ is the updated failure probability after maintenance planning and ${PoF}_E$ is the existing failure probability and $t$ is the annual runtime (in days) for maintenance interval.

3.1. Failure and system vulnerability analysis

The production system line investigation in Table 2 shows that the main systems that affect the product quality are caused by different failure causes of different units of sheetfed printing machine of Heidelberg CD102. To identify all these possible causes of failure leading to undesired system stoppage fault tree analysis (FTA) is conducted [23]. It is a probabilistic top-down approach and used in safety and reliability engineering to show how a system can fail and to determine the best ways to reduce risk. To perform FTA, failures are identified and defined then it is constructed with graphical logic representation of fault events as shown in Fig. 5(a). Here the basic events namely the reasons or items are placed at the bottom, then they are connected with respective logic gates to form intermediate events and finally top undesired event of ‘breakdown of machine’. It is important to note that OR gates are used only when any one input event happens/occurs from all the input events then the output event will occur whereas AND gate are used when all inputs have occurred then output event occurs. For example, failure cause of ‘p/pc’ is formed with ‘OR’ logic gate by the basic events of plate change (p) and plate crack (pc). Similarly, ‘paper’ is constructed with paper loading (PL), paper cutting, inventory delay, non-uniform stock of paper, improper relative humidity (RH) etc. There are few individual and undeveloped events like ‘ca’, ‘qc/ma’, ‘s’, ‘mpl’, ‘bc’ etc. which are directly connected to top event for machine failure. The corresponding failure probabilities for each breakdown causes are also analysed later.

The vulnerability of the said production system under investigation is analysed by applying reliability block diagram (RBD) analysis tool [7]. RBD is an important tool in maintenance operation that can be applied in prospective and retrospective events (redesign, modification or continuous improvement) of a machine. It displays the logical connections and interaction among the different components that make up the system using asset blocks. Then these blocks can be analysed using mathematical methods to determine the level of system vulnerability. The input of the RBD is obtained from the FTA in Fig. 5(b), since RBD is the natural outcome of FTA. In designing the equivalent RBD of the FTA as shown in Fig. 5(b), the OR-gate was represented in a series, whereas the AND-gate is a parallel arrangement in the RBD.

However, FTA is the complementary tool of FMEA in risk analysis but the only difference is that it does not give account on the prioritization of failure event modes whereas FMEA can capture potential failures and their impact and risk which can be used for prioritizing and scaling for the estimation of risk priority number for failure mode effect and criticality (FMEA/FMECA) assessment as shown earlier in Table 2. Thus, after completing the system failure investigation and its vulnerability to producing poor quality products or system breakdown, FMEA analysis is carried out to drill down to component level. This is vital to understand the failure mode of each basic event from the FTA and thus gives clarity to the risk priority of individual event and later directs to the estimation of RI and RPN in terms of both breakdown time and breakdown loss cost.

Fig. 5Analysis of CD102 on the basis of breakdown causes or type in their respective printing machine unit a) FTA and b) RBD

a)

b)

3.2. Probability of failure (PoF)

Failure probability is estimated from the collected press data as it is the function of runtime, breakdown time and failure number. Table 7 represents the monthly reliability; probability of failure and failure rate estimated from Eqs. (1), (2) and (3). Applying Pearson’s correlation method, the PoF and reliability value of the printing machine is 0.6228 and 0.3772 for 309 production day in a year. Also, failure rate is used for the representation of bath-tub curve obtained from the daily production data of one year as shown in Fig. 6. Fig. 7 shows the graphical representation of monthly failure probability and its reliability analysis. The bathtub curve presented here indicates that the machine under study is entering into the ‘wear-out’ stage from its ‘useful life cycle’ stage.

Fig. 6Bath-tub curve for 309 operational days out of 365 days

Fig. 7Monthly failure probability and reliability analysis

After reliability and failure analysis, different availability parameters are checked to understand the inspection and repair status and scenario of printing machine which are tabulated in Table 8 and illustrated in Fig. 8 on monthly basis. It is important to note that the inspection rate (IpR) is the ratio of failure number to inspection time. Also repair rate (RpR) is the ratio of failure number and repair time. IpR and RpR is the integral part of availability analysis and also linked to maintenance analysis. It is seen that lower the failure rate in terms of IpR and RpR, higher the availability of a machine which implies improved productivity. But as the machine is slowly entering into wear-out stage from useful life period, the failure rate is increasing with respective inspection and repairment operation and as a result availability is decreasing gradually.

Fig. 8Availability analysis of CD102

3.3. Consequence of failure (CoF)

The CoF analysis of printing machine under study has been conducted by using the Eqs. (7), (8), (9) and (10). It is also important to note that PLC estimation obtained from the product of percentage wastage $\left(i.e.\frac{\mathrm{w}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{g}\mathrm{e}\times 100}{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{}\mathrm{o}\mathrm{u}\mathrm{t}\mathrm{p}\mathrm{u}\mathrm{t}}\right)$ and raw material cost (which is the summation of the daily plate and exposing cost, paper cost, thinner and chemical cost, other material cost etc.). HWLC is obtained from the product of breakdown time or downtime and human labour cost per minute (i.e. salary of printer, feeder man, helper per month converted to United Arab Emirates Dirham (AED) considering 26 working days per month and 8 hours shift per day). MLC is the summation of inspection, repair or replacement and maintenance cost of different breakdown and here observed major costs are the blanket change, breakdown/scheduled/preventive maintenance, pipeline leakage, varnish section, coating blade replacement/repair, dampening section and other costs etc. However, there is less impact on environment due to these breakdowns and wastage/ink/chemical residual etc. and no injuries or accidents witnessed during the period of study due to different preventive measures taken in advance by the company thus the environmental loss and human health loss has taken as zero severity in this study and not included. The other losses observed during this period are considered as negligible and therefore not considered. Finally, the CoF calculation is done using Eq. (10) and the results are tabulated below in Table 9.

3.4. Actual risk and RI estimation

From the above results, actual risk in United Arab Emirates Dirham (AED) is estimated on both annual basis and monthly basis to understand the current risk status of machine using Eq. (11) as shown in Table 10. This actual risk is then needed to compare with the allotted yearly or monthly budget for maintenance. The yearly acceptable risk criteria (ARC) for an annual or monthly basis is 227280 AED or 18940 AED which has been collected from the accounts department of the printing company. The estimated overall risk index is 1.13 which is greater than 1 by using Eq. (11). This implies the machine needs a maintenance action for reduction of risk in terms of failure and its corresponding cost. As the overall risk index is higher than 1, it indicates that the system needs to reduce the risk index. This motivates the analysis of risk factors for individual breakdown causes for which scoring of actual risk and RPN is useful to generate risk matrix.

Fig. 9. shows the comparative analysis between different kinds of availability parameters (like $A_{op}$ and $A_{in}$) and risk index on monthly basis. Availability percentage was measured by the dataset distribution which includes failure and repair times but excludes inspection times to understand how fast the maintenance, repair or replacement was made after inspection. While the availability ratio or percentage is reducing, the risk on that respective period or month is increasing again which validate the previous failure and reliability analysis.

Moreover, once the risks is identified, their probabilities of failure along with their impacts have been modelled in terms breakdown loss cost or breakdown time. It is then needed to conduct quantitative risk prioritisation for better understanding of priority-based scenario of risk pattern of every failure causes present in the machine components. To accomplish this, Monte Carlo Simulation (MCS) method has been performed by considering only the stochastic uncertainty of activities to learn the total failure duration or cost. Generally, in MCS, expert judgement and numerical methods are combined to generate a probabilistic result through simulation routine. This mathematical approach is noted for its ability to analyse uncertain scenarios from a probabilistic perspective. MCS also allows the analysis of opportunities, uncertainties, and threats. This technique can be invaluable to risk managers and helpful for estimating project durations and costs [17]. Fig. 10 shows the MCS based prioritization of failure type based actual risk in terms of breakdown loss cost. This simulation has been generated with the assistance of Python Jupyter Network and Anaconda Prompt environment. The Numpy and Pandas library with 10,000 simulations are utilised to achieve accurate prioritization. Similarly, simulation based on MCS based prioritization of failure type on actual risk in terms of breakdown time can also be generated for better understanding of risk. This analysis will help for the scaling of actual risk and can be extended to RPN as well.

Fig. 9Comparative analysis between availability vs risk index

Fig. 10Monte Carlo based simulation for the prioritization of failure type based on actual risk or loss in terms of cost

3.5. Risk scoring and RPN scoring

In this section an attempt has been made to develop risk matrices by considering failure number as likelihood and breakdown time and its loss cost both as severity. The criteria of likelihood is fixed by considering highest failure occurrence value of 137 which is divided by 5 (due to 5 levels of likelihood) to estimate the criteria intervals of 27.4, 54.8, 82.2, 109.6 and 137 respectively and fix the scores of likelihood from 1 to 5 accordingly as shown in Table 11 (Part a). On the basis of opinion of management and finance department, severity in terms of both breakdown time and breakdown loss cost are given by different levels of score interval from 1 to 5 as shown in Table 11 (Part b) and Table 11 (Part c). Similar methodology has been adopted to estimate the risk interval and inspection interval as illustrated in Table 11 (Part d) and Table 11 (Part e) respectively.

For risk assessment of the printing machine, it is now necessary to evaluate the risk values and RPN values for each type of breakdown causes by considering the following combination.

Combination I: Failure numbers, breakdown times and inspection times for each breakdown type

Combination II: Failure numbers, breakdown loss cost and inspection times for each breakdown type

Table 12 and Table 13 represent the results of risk values and RPN values of each breakdown type for combination I and combination II respectively. It is to be noted here that during estimation of breakdown loss cost (as shown in Table 13), production loss cost (PLC) is considered as zero because of zero wastage due to non-functioning of the machine at the stage of failure condition.

3.6. Risk matrix

A risk matrix is generally used to assess the level of risk of a machine and assist the management decision making process. It takes into consideration the category of probability or likelihood against the category of consequence severity. In this present investigation the risk assessment matrix of printing machines under study for different types of breakdown causes has been developed by considering both breakdown time and breakdown loss cost. Table 14 represents the risk matrix for different breakdown causes on the basis of breakdown time and breakdown loss cost respectively. Whereas Table 15 represents the RPN matrix for different breakdown causes by considering breakdown time and breakdown loss cost respectively. These risk matrices help the management to prioritize the risk for different causes of breakdown and develop an appropriate mitigation strategy. Here the extremely lower risk values for the particular breakdown causes are positioned in the first cell situated in an extreme downward left side of the matrix. Higher the risk, it tends to the extreme right side of the topmost corner in the matrix. In other words, it can be said that red colored situated in the top right corner of the matrix indicates the high-risk zone whereas green color situated in the left bottom corner indicates the low-risk zone. It is recommended for organizations to schedule periodic assessments of risk matrix as it needs regular monitoring and iteration to meet the challenges of constantly changing scenario of production process. With the help of an up-to-date risk assessment matrix, it is possible to identify emerging threats and properly allocate resources to mitigate their impact.

The mapping of risk is based on the different levels of consequences of failure probability for each type of breakdown. It is not necessary that highest PoF should possess highest consequence level thus it may vary case to case. For example, ‘p/pc’ has highest PoF of 0.4413 with different consequence level of breakdown time of 6785 minutes and inspection time of 3400 minutes and breakdown loss cost of 3805.69 AED thus it gives a result of different risk zones in risk matrix and RPN matrix under study. It is also observed that the breakdown cause ‘p/pc’ under machine component ‘A’ and ‘E’ falls on the high-risk zone for both risk matrix and RPN matrix with respect to breakdown time, whereas these causes under machine component ‘A’ and ‘E’ shifts to the medium risk zone for both matrix zone with respect to breakdown loss cost. This may be due to the effect of less running cost required for this cause i.e. ‘p/pc’. The position of the maintenance time for breakdown or schedule (mb/ms) remains same in the risk and RPN matrices for both breakdown time and breakdown loss cost due to negligible consequences for these causes. Therefore, it can be said that overall, three breakdown causes namely ‘p/pc’, ‘ca’ and ‘mb/ms’ are responsible for high-risk zones during the study period. In other words, it can be stated that all nine number of machine components falls under high-risk zone when breakdown time is considered. While seven number of machine components falls under high-risk zone when breakdown loss cost is considered.

3.7. Maintenance interval (MaIT)

The risk of operation consisting of five aforementioned levels of 5×5 matrix for both actual risk and RPN are shown into the study. For high profitability point of view, the updated PoF is assumed to be 0.01 (on the basis of ALARP methodology) for lowest risk zone located at the extreme bottom left cell in the matrix which also lies under the lowest score criteria of the likelihood interval scale. Now out of 365 days of financial year of 2021, 309 operational days are used as $t$ for the estimation of MaIT as shown in Eq. (15). The maintenance interaval time in days for different breakdown causes/types are shown in Table 16. It is observed that the printing machine under study must undergo an overall maintenance interval of 76 days annually by considering all the breakdown types. It is also seen that the maximum probability of failure for breakdown type ‘p/pc’ requires lowest needed maintenance interval and minimum failure probability for breakdown type ‘cb’ requires highest maintenance interval time. However very few breakdown types seem to have higher MaIT for higher failure probability due to the effect of severity factor of the same. Thus, this will help the printing machine to be more reliable to the press organization for their improved printing production as well as it will prevent the machine from entering to ‘wear-out stage’ from its ‘useful life cycle’.