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Reliability and Sensitivity Analysis of a Wastewater Treatment Plant Operating with Two Blowers as a Single System

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Reliability Engineering for Industrial Processes

Part of the book series: Springer Series in Reliability Engineering ((RELIABILITY))

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Abstract

Utilizing wastewater for irrigation is a pressing necessity in regions grappling with water scarcity. However, before wastewater can be used, it must undergo treatment due to its contamination. Wastewater treatment plants are pivotal in purifying wastewater and rendering it suitable for irrigation. Within these treatment plants, blowers play a crucial role, serving as vital assets. The failure of blowers can result in substantial repair costs. Consequently, it is imperative to conduct a thorough reliability and sensitivity analysis to assess the performance of blowers in wastewater treatment plants. This paper focuses on the reliability and sensitivity analysis of a wastewater treatment facility equipped with two blowers. To support this research, actual failure data from the plant have been collected. When a blower fails, it undergoes an inspection to determine the nature of the failure, which can fall into three categories: instrumental, mechanical, or electrical. The reliability model is constructed by incorporating real-world situations derived from the collected data. This modeling process employs Markov and regenerative processes to estimate key plant performance metrics, including availability, the expected frequency of inspections and repairs, the anticipated busy time for the repairman, and the profit generated. Furthermore, the analysis determines the profit threshold. To understand the influence of various parameters on reliability outcomes, a sensitivity analysis has been undertaken.

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Abbreviations

\({{\text{B}}}_{1}\) :

Blower-1 is operative

\({{\text{B}}}_{2}\) :

Blower-2 is operative

\({{\text{B}}}_{1{\text{i}}}\) :

Blower-1 has failed and is under inspection

\({{\text{B}}}_{2{\text{i}}}\) :

Blower-2 has failed and is under inspection

\({{\text{B}}}_{1{\text{ri}}}\) :

Blower-1 is under repair due to instrumental failure

\({{\text{B}}}_{2{\text{ri}}}\) :

Blower-2 is under repair due to instrumental failure

\({{\text{B}}}_{1{\text{rm}}}\) :

Blower-1 is under repair due to mechanical failure

\({{\text{B}}}_{2{\text{rm}}}\) :

Blower-2 is under repair due to mechanical failure

\({{\text{B}}}_{1{\text{re}}}\) :

Blower-1 is under repair due to electrical failure

\({{\text{B}}}_{2{\text{re}}}\) :

Blower-2 is under repair due to electrical failure

\({\uplambda }_{1}\) :

Constant failure rate for blower-1

\({\uplambda }_{2}\) :

Constant failure rate for blower-2

PDF:

Probability density function

\({{\text{g}}}_{1}\left({\text{t}}\right)\)/\({{\text{g}}}_{2}\left({\text{t}}\right)\)/\({{\text{g}}}_{3}\left({\text{t}}\right)\) :

PDF of repair times for instrumental/mechanical/electrical failure respectively in blower-1

\({{\text{g}}}_{4}\left({\text{t}}\right)\)/\({{\text{g}}}_{5}\left({\text{t}}\right)\)/\({{\text{g}}}_{6}\left({\text{t}}\right)\) :

PDF of repair times for instrumental/mechanical/electrical failure respectively in blower-2

\({\text{h}}\left({\text{t}}\right)\) :

PDF of inspection times for blower-1 and blower-2

\(\mathrm{\alpha }\) :

Constant inspection rate

\({\upgamma }_{1}\) :

Constant repair rate for instrumental failure in blower-1

\({\upgamma }_{2}\) :

Constant repair rate for mechanical failure in blower-1

\({\upgamma }_{3}\) :

Constant repair rate for electrical failure in blower-1

\({\upgamma }_{4}\) :

Constant repair rate for instrumental failure in blower-2

\({\upgamma }_{5}\) :

Constant repair rate for mechanical failure in blower-2

\({\upgamma }_{6}\) :

Constant repair rate for electrical failure in blower-2

\({{\text{p}}}_{1}\) :

Probability of occurrence of instrumental failure in blower-1

\({{\text{p}}}_{2}\) :

Probability of occurrence of mechanical failure in blower-1

\({{\text{p}}}_{3}\) :

Probability of occurrence of electrical failure in blower-1

\({{\text{p}}}_{4}\) :

Probability of occurrence of instrumental failure in blower-2

\({{\text{p}}}_{5}\) :

Probability of occurrence of mechanical failure in blower-2

\({{\text{p}}}_{6}\) :

Probability of occurrence of electrical failure in blower-2

\({{\text{A}}}_{0}\) :

Availability of the plant

\({{\text{B}}}_{0}\) :

Anticipated busy time for inspection by the repairman

\({{\text{BI}}}_{0}\) :

Anticipated busy time of the repairman (instrumental failure)

\({{\text{BM}}}_{0}\) :

Anticipated busy time of the repairman (mechanical failure)

\({{\text{BE}}}_{0}\) :

Anticipated busy time of the repairman (electrical failure)

\({{\text{N}}}_{0}\) :

Expected number of inspections

\({{\text{NI}}}_{0}\) :

Expected number of repairs (instrumental failure)

\({{\text{NM}}}_{0}\) :

Expected number of repairs (mechanical failure)

\({{\text{NE}}}_{0}\) :

Expected number of repairs (electrical failure)

\({\text{P}}\) :

Profit generated by the plant

\({{\text{C}}}_{0}\) :

Revenue per unit up-time generated by the plant

\({{\text{C}}}_{1}\) :

Cost of the repairman (inspection)

\({{\text{C}}}_{2}\) :

Cost of the repairman (instrumental failure)

\({{\text{C}}}_{3}\) :

Cost of the repairman (mechanical failure)

\({{\text{C}}}_{4}\) :

Cost of the repairman (electrical failure)

\({{\text{C}}}_{5}\) :

Inspection cost per unit time

\({{\text{C}}}_{6}\) :

Repair cost per unit time (instrumental failure)

\({{\text{C}}}_{7}\) :

Repair cost per unit time (mechanical failure)

\({{\text{C}}}_{8}\) :

Repair cost per unit time (electrical failure)

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Authors and Affiliations

  1. Department of Applied Mathematics and Science, National University of Science and Technology, Muscat, Oman

    S. Z. Taj & S. M. Rizwan

  2. Department of Applied Science, Government Polytechnic Jhajjar, Jhajjar, India

    Kajal Sachdeva

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  1. S. Z. Taj
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  2. S. M. Rizwan
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  3. Kajal Sachdeva
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Correspondence to S. Z. Taj .

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Editors and Affiliations

  1. Amity Center for Interdisciplinary Research, Amity University, Noida, Uttar Pradesh, India

    P. K. Kapur

  2. Department of Industrial Engineering, Rutgers University, Piscataway, NJ, USA

    Hoang Pham

  3. Amity International Business School, Amity University, Noida, Uttar Pradesh, India

    Gurinder Singh

  4. Amity International Business School, Amity University, Noida, Uttar Pradesh, India

    Vivek Kumar

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Taj, S.Z., Rizwan, S.M., Sachdeva, K. (2024). Reliability and Sensitivity Analysis of a Wastewater Treatment Plant Operating with Two Blowers as a Single System. In: Kapur, P.K., Pham, H., Singh, G., Kumar, V. (eds) Reliability Engineering for Industrial Processes. Springer Series in Reliability Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-55048-5_2

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  • DOI: https://doi.org/10.1007/978-3-031-55048-5_2

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