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Reliability analysis of a rodding anode plant in aluminum industry with multiple units failure and single repairman

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Abstract

The paper presents reliability analysis of a rodding anode plant in aluminum industry with multiple unit failure and single repairman. Manufacturing process of raw aluminum blocks in this plant passes through eight stations. Failure of any of the stations brings the plant to a complete halt, except the butt & thimble removal press stations because of the parallel standby arrangement, and does not affect the system operation completely unless both the units fail. Six years of real maintenance data on component failures, repairs and associated costs are used in this analysis. Measures of system effectiveness is gauged through reliability indices such as mean time to plant failure, availability of the plant, busy period of repairman and expected number of repairs. Effect of repair rate, failure rate and repair cost on system performance w.r.t. revenue is shown graphically. Theory of Semi-Markov and regenerative stochastic processes is used in the analysis.

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Abbreviations

\(O_{i}\) :

State \(i\) is operative

\(D_{i}\) :

State \(i\) is down

\(\lambda_{i}\) :

Estimated of failure rate of \(i{\text{th}}\) unit

\(\alpha_{i}\) :

Estimated of repair rate of ith unit

\(F_{irj }\) :

jth unit of ith station is under repair

\(F_{iWrj }\) :

jth unit of ith station is waiting for repair

\(F_{iRj }\) :

jth unit of ith station is continuing for repair from the previous state

\(p_{ij} , p^{\left( k \right)}_{ij}\) :

Probability of transition from a regenerative state \(i\) to a regenerative state \(j\) without visiting any other state in \(\left( {0,t} \right]\), probability of transition from a regenerative state \({\text{i}}\) to a regenerative state \({\text{j}}\) via state \(k\) state (0,t]

\(*\)/LT :

Symbol of Laplace transform

\(**\)/LST :

Symbol of Laplace–Steiltje’s transform

\(m_{ij} , m^{\left( k \right)}_{ij}\) :

The unconditional mean time taken to transit to any regenerative state from the epoch of entery into regenerative state \(j\) without visiting any failed states, visiting failed state \(k\) once

\(\mu_{i}\) :

Sojourn time in the regenerative state \(i\)

\(\copyright\) :

Laplace convolution

:

Steiltje’sconvolution

\(\phi_{0} \left( t \right)\) :

Cumulative distribution function \(c.d.f\) of the first passage time from a regenerative state \(i\) to a failed state

\(A_{i} \left( t \right)\) :

The probability of the unit entering into upstate at instant \(t\), giving that the unit entered in regenerative state \(i\) at \(t = 0\)

\(B_{i} \left( t \right)\) :

Probability that the repairman is busy in inspection of instant t, given that the system entered regenerative state \({\text{i}}\) at \(t = 0\)

\(V_{i} \left( t \right)\) :

Expected number of visits of the repairman, given that the system entered regenerative state \(i\) at \(t = 0\)

\(M_{i} \left( t \right)\) :

The probability that the system initially up in regenerative state \(i\), is up at a time \(t\) without visiting to any regenerative state

\(W_{i} \left( t \right)\) :

Probability that that the repairman is busy in regenerative state \(i\) at time \(t\) without passing any other regenerative state

\(p.d.f, c.d.f\) :

Probability density function, Cumulative distribution function

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Caledonian College of Engineering, Seeb, Oman

    Yaqoob Al Rahbi & S. M. Rizwan

  2. Department of Mechanical Engineering, Glasgow Caledonian University, Glasgow, Scotland, UK

    B. M. Alkali & Andrew Cowell

  3. Department of Mathematics, MD University, Rohtak, Haryana, India

    G. Taneja

Authors
  1. Yaqoob Al Rahbi
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  2. S. M. Rizwan
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  3. B. M. Alkali
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  4. Andrew Cowell
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  5. G. Taneja
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Correspondence to Yaqoob Al Rahbi.

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Al Rahbi, Y., Rizwan, S.M., Alkali, B.M. et al. Reliability analysis of a rodding anode plant in aluminum industry with multiple units failure and single repairman. Int J Syst Assur Eng Manag 10, 97–109 (2019). https://doi.org/10.1007/s13198-019-00771-3

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  • DOI: https://doi.org/10.1007/s13198-019-00771-3

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